# Stats

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```					                                                                                            Common Core-Delaware Standards – Grades 9–12 – Statistics and Probability Overview

Domain                                                                                  Matched Common Core Standard                                                            Delaware Standards
Summarize, represent, and interpret data on a single count or measurement variable.
DE.8.4.3 Represent: Construct displays of data to represent individual sets of
data (e.g., histograms, box plots) or to explore the relationship between related
Grades 9-12: Interpreting Categorical and Quantitative Data

sets of data (scatter plots, line graphs); describe the correspondence between
Represent data with plots on the real number line (dot plots, histograms, and
data sets and their graphical displays
box plots). CC.9-12.S.ID.1
DE.9.4.2 Represent: Select and interpret the most appropriate display for a
given purpose and set(s) of data (e.g., histograms, parallel box plots, stem-and-
leaf plots, scatter plots)
DE.8.4.6 Analyze: Find and use appropriate measures of center (mean, media,
mode) and spread (range, interquartile range) to interpret data
DE.9.4.2 Represent: Select and interpret the most appropriate display for a
Use statistics appropriate to the shape of the data distribution to compare    given purpose and set(s) of data (e.g., histograms, parallel box plots, stem-and-
center (median, mean) and spread (interquartile range, standard deviation) of  leaf plots, scatter plots)
two or more different data sets. CC.9-12.S.ID.2                                DE.10.4.2 Analyze: Recognize how linear transformations of one variable data
DE.11.4.4 Analyze: Compute and use standard deviation to analyze data
variability
DE.9.4.5 Analyze: Describe the effect of outliers in both one-variable and two-
Interpret differences in shape, center, and spread in the context of the data
variable contexts
sets, accounting for possible effects of extreme data points (outliers). CC.9-
DE.10.4.2 Analyze: Recognize how linear transformations of one variable data
12.S.ID.3
DE.9.4.4 Analyze: Analyze the validity of statistical conclusions on both one-
and two-variable data
Use the mean and standard deviation of a data set to fit it to a normal
DE.11.4.4 Analyze: Compute and use standard deviation to analyze data
distribution and to estimate population percentages. Recognize that there are
variability
data sets for which such a procedure is not appropriate. Use calculators,
DE.11.4.5 Analyze: Apply benchmark percents described by the "empirical rule"
spreadsheets, and tables to estimate areas under the normal curve. CC.9-
(68%-95%-99.7% rule) in a normal distribution
12.S.ID.4
DE.11.4.6 Analyze: Recognize approximate norm distributions
DE.12.4.6 Probability: Use the normal distribution to calculate probabilities

Page 1 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Statistics and Probability Overview

Domain                                                                                                       Matched Common Core Standard                                                                   Delaware Standards
Summarize, represent, and interpret data on a single count or measurement variable.
two categorical and quantitative variables.
Summarize categorical data for two categories in two-way frequency tables.            No Delaware Match
Interpret relative frequencies in the context of the data (including joint, marginal,
Grades 9-12: Interpreting Categorical and Quantitative Data

and conditional relative frequencies). Recognize possible associations and
trends in the data. CC.9-12.S.ID.5
DE.8.4.3 Represent: Construct displays of data to represent individual sets of
data (e.g., histograms, box plots) or to explore the relationship between related
Grades 9-12: Interpreting Categorical and Quantitative Data (continued)

sets of data (scatter plots, line graphs); describe the correspondence between
data sets and their graphical displays
DE.8.4.4 Analyze: Defend or dispute conclusions drawn from the interpretation
of data by comparing sets of data or exploring possible relationships based
Represent data on two quantitative variables on a scatter plot, and describe
upon scatter plots of related data and approximate lines of fit
how the variables are related. CC.9-12.S.ID.6
DE.9.4.3 Represent: Find an appropriate mathematical model of a linear or
exponential function and use the model to make predictions recognizing the
limitations of the model
DE.9.4.4 Analyze: Analyze the validity of statistical conclusions on both one-
and two-variable data
DE.9.4.3 Represent: Find an appropriate mathematical model of a linear or
Fit a function to the data; use functions fitted to data to solve problems in the
exponential function and use the model to make predictions recognizing the
context of the data. Use given functions or choose a function suggested by the
limitations of the model
context. Emphasize linear, quadratic, and exponential models. CC.9-12.S.ID.6a
Informally assess the fit of a function by plotting and analyzing residuals. CC.9-       DE.11.4.3 Represent: Interpret least squares regression line as the line that
12.S.ID.6b                                                                               minimizes the sum of the squared errors
DE.9.4.3 Represent: Find an appropriate mathematical model of a linear or
Fit a linear function for a scatter plot that suggest a linear association. CC.9-
exponential function and use the model to make predictions recognizing the
12.S.ID.6c
limitations of the model
Interpret linear models.
DE.9.2.12 Representations: Analyze the interrelationship among the table,
Interpret the slope (rate of change) and the intercept (constant term) of a linear       graph and equation of both linear and exponential functions paying particular
model in the context of the data. CC.9-12.S.ID.7                                         attention to the meaning of intercept and slope in the context of the problem

DE.9.2.9 Representations: Analyze data sets using technology to find an
Compute (using technology) and interpret the correlation coefficient of a linear         appropriate linear or exponential mathematical model
fit CC.9-12.S.ID.8                                                                       DE.9.2.10 Representations: Demonstrate a conceptual understanding of
correlation
DE.9.2.9 Representations: Analyze data sets using technology to find an
appropriate linear or exponential mathematical model
Distinguish between correlation and causation CC.9-12.S.ID.9
DE.9.2.10 Representations: Demonstrate a conceptual understanding of
correlation

Page 2 of 74                                                                                    as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Statistics and Probability Overview

Domain                                                                                 Matched Common Core Standard                                                                Delaware Standards
represent, and interpret data on underlying statistical experiments.
Summarize, and evaluate random processes a single count or measurement variable.
Understand
DE.9.4.1 Collect: Describe and explain how the validity of predictions are
affected by number of trials, sample size, and the population
Grades 9-12: Interpreting Categorical and Quantitative Data
Grades 9-12: Making Inferences and Justifying Conclusions

Understand statistics as a process for making inferences about population          DE.11.4.1 Collect: Understand the differences among the various kinds of
parameters based on a random sample from that population. CC.9-12.S.IC.1           studies (e.g., survey, controlled experiment)
DE.12.4.1 Collect: Apply principles of data collection and experimental design
that aim to minimize bias and variability of resulting data
Decide if a specified model is consistent with results from a given data-          DE.9.4.6 Probability: Use and design simulations or experiments to determine
generating process, e.g., using simulation. For example, a model says a            probabilities of independent and dependent events
spinning coin falls heads up with probability 0. 5. Would a result of 5 tails in a DE.12.4.1 Collect: Apply principles of data collection and experimental design
row cause you to question the model? CC.9-12.S.IC.2                                that aim to minimize bias and variability of resulting data
Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
DE.9.4.1 Collect: Describe and explain how the validity of predictions are
Recognize the purposes of and differences among sample surveys,
affected by number of trials, sample size, and the population
experiments, and observational studies; explain how randomization relates to
DE.11.4.1 Collect: Understand the differences among the various kinds of
each. CC.9-12.S.IC.3
studies (e.g., survey, controlled experiment)
Use data from a sample survey to estimate a population mean or proportion;         DE.12.4.3 Represent: Interpret margin of error and confidence intervals
develop a margin of error through the use of simulation models for random
sampling. CC.9-12.S.IC.4
Use data from a randomized experiment to compare two treatments; use               No Delaware Match
simulations to decide if differences between parameters are significant. CC.9-
12.S.IC.5
DE.9.4.4 Analyze: Analyze the validity of statistical conclusions on both one-
and two-variable data
DE.11.4.4 Analyze: Compute and use standard deviation to analyze data
Evaluate reports based on data. CC.9-12.S.IC.6                                     variability
DE.11.4.5 Analyze: Apply benchmark percents described by the "empirical rule"
(68%-95%-99.7% rule) in a normal distribution
DE.12.4.3 Represent: Interpret margin of error and confidence intervals

Page 3 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Statistics and Probability Overview

Domain                                                                                                Matched Common Core Standard                                                            Delaware Standards
represent, and interpret data on a single count or them to interpret data.
Summarize, independence and conditional probability and usemeasurement variable.
Understand
Describe events as subsets of a sample space (the set of outcomes) using         No Delaware Match
characteristics (or categories) of the outcomes, or as unions, intersections, or
Grades 9-12: Interpreting Categorical and Quantitative Data

complements of other events ("or," "and," "not"). CC.9-12.S.CP.1
DE.11.4.7 Probability: Understand and use the addition rule to calculate
Understand that two events A and B are independent if the probability of A and probabilities for mutually exclusive and non-mutually exclusive events
B occurring together is the product of their probabilities, and use this
Grades 9-12: Conditional Porbability and the Rules of Probability

DE.12.4.5 Probability: Use conditional probabilities to solve problems from
characterization to determine if they are independent. CC.9-12.S.CP.2
health, public policy, and other areas
DE.10.4.4 Probability: Compute the probability of both independent and
Understand the conditional probability of A given B as P(A and B)/P(B), and          dependent events
interpret independence of A and B as saying that the conditional probability of A    DE.11.4.7 Probability: Understand and use the addition rule to calculate
given B is the same as the probability of A, and the conditional probability of B    probabilities for mutually exclusive and non-mutually exclusive events
given A is the same as the probability of B. CC.9-12.S.CP.3                          DE.12.4.5 Probability: Use conditional probabilities to solve problems from
health, public policy, and other areas
Construct and interpret two-way frequency tables of data when two categories         DE.8.4.5 Analyze: Analyze a representative sample to make inferences about a
are associated with each object being classified. Use the two-way table as a         population
sample space to decide if events are independent and to approximate                  DE.9.4.8 Probability: Compare event experimental probability with theoretical
conditional probabilities. For example, collect data from a random sample of         probability (Law of Large Numbers)
students in your school on their favorite subject among math, science, and
English. Estimate the probability that a randomly selected student from your
school will favor science given that the student is in tenth grade. Do the same
for other subjects and compare the results. CC.9-12.S.CP.4
Recognize and explain the concepts of conditional probability and                  DE.12.4.5 Probability: Use conditional probabilities to solve problems from
independence in everyday language and everyday situations. For example,            health, public policy, and other areas
compare the chance of having lung cancer if you are a smoker with the chance
of being a smoker if you have lung cancer. CC.9-12.S.CP.5
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Find the conditional probability of A given B as the fraction of B's outcomes that DE.11.4.7 Probability: Understand and use the addition rule to calculate
also belong to A, and interpret the answer in terms of the model. CC.9-            probabilities for mutually exclusive and non-mutually exclusive events
12.S.CP.6
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the DE.11.4.7 Probability: Understand and use the addition rule to calculate
answer in terms of the model. CC.9-12.S.CP.7                                       probabilities for mutually exclusive and non-mutually exclusive events
(+) Apply the general Multiplication Rule in a uniform probability model, P(A and DE.10.4.4 Probability: Compute the probability of both independent and
B) = [P(A)]*[P(B|A)] =[P(B)]*[P(A|B)], and interpret the answer in terms of the    dependent events
model. CC.9-12.S.CP.8
(+) Use permutations and combinations to compute probabilities of compound         DE.10.4.1 Collect: Use permutations and combinations as counting techniques
events and solve problems. CC.9-12.S.CP.9

Page 4 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Statistics and Probability Overview

Domain                                                                                   Matched Common Core Standard                                                            Delaware Standards
interpret data on a single count
Summarize, represent, andand use them to solve problems.or measurement variable.
Calculate expected values
(+) Define a random variable for a quantity of interest by assigning a numerical DE.10.4.3 Probability: Compute and interpret expected value
value to each event in a sample space; graph the corresponding probability          DE.12.4.4 Analyze: Use discrete probability models such as the binomial model
Interpreting Categorical and Quantitative Data

distribution using the same graphical displays as for data distributions. CC.9-     to represent real world phenomena
(+) Calculate the expected value of a random variable; interpret it as the mean     DE.10.4.3 Probability: Compute and interpret expected value
of the probability distribution. CC.9-12.S.MD.2
(+) Develop a probability distribution for a random variable defined for a sample DE.10.4.3 Probability: Compute and interpret expected value
Grades 9-12: Using Probability to Make Decisions

space in which theoretical probabilities can be calculated; find the expected
value. For example, find the theoretical probability distribution for the number of
correct answers obtained by guessing on all five questions of a multiple-choice
test where each question has four choices, and find the expected grade under
(+) Develop a probability distribution for a random variable defined for a sample DE.10.4.3 Probability: Compute and interpret expected value
space in which probabilities are assigned empirically; find the expected value.
For example, find a current data distribution on the number of TV sets per
household in the United States, and calculate the expected number of sets per DE.12.4.6 Probability: Use the normal distribution to calculate probabilities
household. How many T V sets would you expect to find in 100 randomly
selected households? CC.9-12.S.MD.4
Use probability to evaluate outcomes of decisions.
(+) Weigh the possible outcomes of a decision by assigning probabilities to         DE.10.4.3 Probability: Compute and interpret expected value
payoff values and finding expected values. CC.9-12.S.MD.5
(+) Find the expected payoff for a game of chance. For example, find the            DE.10.4.3 Probability: Compute and interpret expected value
expected winnings from a state lottery ticket or a game at a fast-food restaurant.
CC.9-12.S.MD.5a
(+) Evaluate and compare strategies on the basis of expected values. For            DE.10.4.3 Probability: Compute and interpret expected value
example, compare a high-deductible versus a low- deductible automobile
insurance policy using various, but reasonable, chances of having a minor or a
major accident. CC.9-12.S.MD.5b
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a        DE.10.4.3 Probability: Compute and interpret expected value
random number generator). CC.9-12.S.MD.6
(+) Analyze decisions and strategies using probability concepts (e.g., product      DE.10.4.3 Probability: Compute and interpret expected value
testing, medical testing, pulling a hockey goalie at the end of a game). CC.9-
12.S.MD.7

Page 5 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grades 9–12

Domain                                          Matched Common Core Standard                                                                     Delaware Standards
Experiment with transformations in the plane.
DE.9.3.1 Classification: Represent and verify parallel and perpendicular
relationships in linear functions
Know precise definitions of angle, circle, perpendicular line, parallel line, and
DE.10.3.4 Classification: Use and justify angle relationships created by
line segment, based on the undefined notions of point, line, distance along a
intersecting and parallel lines
line, and distance around a circular arc. CC.9-12.G.CO.1
DE.11.3.3 Classification: Identify and apply the properties of circles as they
relate to central angles, inscribed angles, and tangents
Represent transformations in the plane using, e.g., transparencies and              DE.10.3.6 Location and transformation: Determine the results of multiple
geometry software; describe transformations as functions that take points in the transformations and determine the transformations required to obtain the
plane as inputs and give other points as outputs. Compare transformations that finished product from the original shape
preserve distance and angle to those that do not (e.g., translation versus
horizontal stretch). CC.9-12.G.CO.2

DE.10.3.6 Location and transformation: Determine the results of multiple
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
transformations and determine the transformations required to obtain the
rotations and reflections that carry it onto itself. CC.9-12.G.CO.3
finished product from the original shape
Develop definitions of rotations, reflections, and translations in terms of angles, DE.10.3.7 Location and transformation: Use appropriate technologies to model
circles, perpendicular lines, parallel lines, and line segments. CC.9-12.G.CO.4     geometric figures and to develop conjectures about them
Given a geometric figure and a rotation, reflection, or translation, draw the       DE.10.3.6 Location and transformation: Determine the results of multiple
transformed figure using, e.g., graph paper, tracing paper, or geometry             transformations and determine the transformations required to obtain the
software. Specify a sequence of transformations that will carry a given figure      finished product from the original shape
DE.10.3.7 Location and transformation: Use appropriate technologies to model
onto another. CC.9-12.G.CO.5
geometric figures and to develop conjectures about them
Understand congruence in terms of rigid motions.
Use geometric descriptions of rigid motions to transform figures and to predict     DE.10.3.3 Classification: Justify whether two figures are similar or congruent
the effect of a given rigid motion on a given figure; given two figures, use the
definition of congruence in terms of rigid motions to decide if they are
congruent. CC.9-12.G.CO.6
DE.10.3.3 Classification: Justify whether two figures are similar or congruent
Use the definition of congruence in terms of rigid motions to show that two
DE.10.3.8 Location and transformation: Draw geometric figures in the
triangles are congruent if and only if corresponding pairs of sides and
coordinate plane and justify the properties of the figure (e.g., slope, side length)
corresponding pairs of angles are congruent. CC.9-12.G.CO.7
Understand congruence in terms of rigid motions. Explain how the criteria for          DE.10.3.3 Classification: Justify whether two figures are similar or congruent
triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions. CC.9-12.G.CO.8

Page 6 of 74                                                                                    as of 1/31/11
Common Core-Delaware Standards – Grades 9–12

Domain                                                                                                            Matched Common Core Standard                                                                  Delaware Standards
Experiment with transformations in the plane.
Prove geometric theorems.
Prove theorems about lines and angles. Theorems include: vertical angles are           DE.10.3.4 Classification: Use and justify angle relationships created by

congruent; when a transversal crosses parallel lines, alternate interior angles        intersecting and parallel lines
are congruent and corresponding angles are congruent; points on a
perpendicular bisector of a line segment are exactly those equidistant from the
segment's endpoints. CC.9-12.G.CO.9
Prove theorems about triangles. Theorems include: measures of interior angles          DE.9.3.3 Location and transformation: Use properties of triangles and
of a triangle sum to 180 degrees; base angles of isosceles triangles are               quadrilaterals to construct them in the coordinate plane
congruent; the segment joining midpoints of two sides of a triangle is parallel to     DE.10.3.2 Classification: Identify necessary and sufficient conditions that define
the third side and half the length; the medians of a triangle meet at a point.         parallelograms or triangles
CC.9-12.G.CO.10
DE.9.3.3 Location and transformation: Use properties of triangles and
Prove theorems about parallelograms. Theorems include: opposite sides are              quadrilaterals to construct them in the coordinate plane

congruent, opposite angles are congruent, the diagonals of a parallelogram             DE.10.3.2 Classification: Identify necessary and sufficient conditions that define
bisect each other, and conversely, rectangles are parallelograms with                  parallelograms or triangles
DE.10.3.8 Location and transformation: Draw geometric figures in the
congruent diagonals. CC.9-12.G.CO.11
coordinate plane and justify the properties of the figure (e.g., slope, side length)

Make geometric constructions.
No Delaware Match
Understand similarity in terms of similarity transformations.
Grades 9-12: Similarity, Right Triangles, and

Verify experimentally the properties of dilations given by a center and a scale        No Delaware Match
factor:
a. A dilation takes a line not passing through the center of the dilation to a
parallel line, and leaves a line passing through the center unchanged.
b. The dilation of a line segment is longer or shorter in the ratio given by the
scale factor. CC.9-12.G.SRT.1
Given two figures, use the definition of similarity in terms of similarity             DE.10.3.3 Classification: Justify whether two figures are similar or congruent
Trigonometry

transformations to decide if they are similar; explain using similarity
transformations the meaning of similarity for triangles as the equality of all
corresponding pairs of angles and the proportionality of all corresponding pairs
of sides. CC.9-12.G.SRT.2
Use the properties of similarity transformations to establish the AA criterion for     DE.10.3.3 Classification: Justify whether two figures are similar or congruent
two triangles to be similar. CC.9-12.G.SRT.3
Prove theorems involving similarity.
Prove theorems about triangles. Theorems include: a line parallel to one side of       DE.10.3.5 Classification: Reason deductively to justify a conclusion or to create
a triangle divides the other two proportionally, and conversely; the Pythagorean       a counter-example
Theorem proved using triangle similarity. CC.9-12.G.SRT.4
Use congruence and similarity criteria for triangles to solve problems and to          DE.10.3.5 Classification: Reason deductively to justify a conclusion or to create
prove relationships in geometric figures. CC.9-12.G.SRT.5                              a counter-example

Page 7 of 74                                                                                    as of 1/31/11
Common Core-Delaware Standards – Grades 9–12

Domain                                                                             Matched Common Core Standard                                                                      Delaware Standards
Experiment with transformations in the plane. involving right triangles.
Define trigonometric ratios and solve problems
Grades 9-12: Similarity, Right Triangles, and Trigonometry

DE.10.3.9 Measurement: Apply trigonometric relationships to determine side
Understand that by similarity, side ratios in right triangles are properties of the
lengths and angle measures of right triangle
angles in the triangle, leading to definitions of trigonometric ratios for acute
DE.11.3.8 Measurement: Use trigonometric relationships to determine side
angles. CC.9-12.G.SRT.6
lengths and angle measures of any triangle
DE.10.3.9 Measurement: Apply trigonometric relationships to determine side
Explain and use the relationship between the sine and cosine of complementary lengths and angle measures of right triangle
angles. CC.9-12.G.SRT.7                                                       DE.11.3.8 Measurement: Use trigonometric relationships to determine side
lengths and angle measures of any triangle
DE.9.3.5 Measurement: Solve problems which require an understanding of the
(continued)

Pythagorean Theorem relationships.
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles DE.10.3.9 Measurement: Apply trigonometric relationships to determine side

in applied problems. CC.9-12.G.SRT.8                                          lengths and angle measures of right triangle
DE.10.3.12 Measurement: Apply the Pythagorean Theorem and its converse

Apply trigonometry to general triangles.
No Delaware Match
(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an
auxiliary line from a vertex perpendicular to the opposite side. CC.9-12.G.SRT.9
(+) Prove the Laws of Sines and Cosines and use them to solve problems.                  DE.11.3.8 Measurement: Use trigonometric relationships to determine side
CC.9-12.G.SRT.10                                                                         lengths and angle measures of any triangle
(+) Understand and apply the Law of Sines and the Law of Cosines to find                 DE.11.3.8 Measurement: Use trigonometric relationships to determine side
unknown measurements in right and non-right triangles (e.g., surveying                   lengths and angle measures of any triangle
problems, resultant forces). CC.9-12.G.SRT.11
Understand and apply theorems about circles.
Prove that all circles are similar. CC.9-12.G.C.1                                        No Delaware Match
Identify and describe relationships among inscribed angles, radii, and chords.           DE.11.3.3 Classification: Identify and apply the properties of circles as they
Include the relationship between central, inscribed, and circumscribed angles;           relate to central angles, inscribed angles, and tangents

inscribed angles on a diameter are right angles; the radius of a circle is
perpendicular to the tangent where the radius intersects the circle. CC.9-
12.G.C.2
Construct the inscribed and circumscribed circles of a triangle, and prove               No Delaware Match
properties of angles for a quadrilateral inscribed in a circle. CC.9-12.G.C.3
(+) Understand and apply theorems about circles. Construct a tangent line from           DE.11.3.3 Classification: Identify and apply the properties of circles as they
a point outside a given circle to the circle. CC.9-12.G.C.4                              relate to central angles, inscribed angles, and tangents
Find arc lengths and areas of sectors of circles.
Derive using similarity the fact that the length of the arc intercepted by an angle      No Delaware Match
is proportional to the radius, and define the radian measure of the angle as the
constant of proportionality; derive the formula for the area of a sector. CC.9-
12.G.C.5

Page 8 of 74                                                                                    as of 1/31/11
Common Core-Delaware Standards – Grades 9–12

Domain                                                                      Matched Common Core Standard                                                                   Delaware Standards
Experiment with transformations description and the equation for a conic section.
Translate between the geometric in the plane.
Derive the equation of a circle of given center and radius using the Pythagorean No Delaware Match
Grades 9-12: Expressing Geometric Properties with

Theorem; complete the square to find the center and radius of a circle given by
an equation. CC.9-12.G.GPE.1
Derive the equation of a parabola given a focus and directrix. CC.9-12.G.GPE.2 No Delaware Match
(+) Derive the equations of ellipses and hyperbolas given the foci, using the fact
No Delaware Match
that the sum or difference of distances from the foci is constant. CC.9-
12.G.GPE.3
Use coordinates to prove simple geometric theorems algebraically.
For example, prove or disprove that a figure defined by four given points in the       DE.10.3.8 Location and transformation: Draw geometric figures in the
Equations

coordinate plane is a rectangle; prove or disprove that the point (1, ?3) lies on      coordinate plane and justify the properties of the figure (e.g., slope, side length)
the circle centered at the origin and containing the point (0, 2). CC.9-

12.G.GPE.4
Prove the slope criteria for parallel and perpendicular lines and use them to          DE.9.2.15 Symbols: Determine symbolically the equation of a line given
solve geometric problems (e.g., find the equation of a line parallel or                combinations of point, slope, and intercept information
perpendicular to a given line that passes through a given point). CC.9-                DE.9.3.1 Classification: Represent and verify parallel and perpendicular
12.G.GPE.5                                                                             relationships in linear functions
Find the point on a directed line segment between two given points that                No Delaware Match
partitions the segment in a given ratio. CC.9-12.G.GPE.6
DE.9.3.3 Location and transformation: Use properties of triangles and
Use coordinates to compute perimeters of polygons and areas of triangles and           quadrilaterals to construct them in the coordinate plane
rectangles, e.g., using the distance formula.* CC.9-12.G.GPE.7                         DE.10.3.13 Measurement: Develop and apply the distance and midpoint
formulas
Explain volume formulas and use them to solve problems.
Give an informal argument for the formulas for the circumference of a circle,          DE.9.3.4 Measurement: Demonstrate an understanding of and apply formulas
Measurement and Dimension

area of a circle, volume of a cylinder, pyramid, and cone. Use dissection              for area, surface area, and volume of geometric figures including pyramids,

arguments, Cavalieri's principle, and informal limit arguments. CC.9-                  cones, spheres, and cylinders
12.G.GMD.1
(+) Give an informal argument using Cavalieri's principle for the formulas for the     No Delaware Match
volume of a sphere and other solid figures. CC.9-12.G.GMD.2
DE.9.3.4 Measurement: Demonstrate an understanding of and apply formulas
Use volume formulas for cylinders, pyramids, cones, and spheres to solve
for area, surface area, and volume of geometric figures including pyramids,
problems.* CC.9-12.G.GMD.3
cones, spheres, and cylinders
Visualize relationships between two-dimensional and three-dimensional objects.
CC.9-12.G.GMD.4 Identify the shapes of two-dimensional cross-sections of       DE.9.3.2 Classification: Classify 3-dimensional figures according to the shapes
three-dimensional objects, and identify three-dimensional objects generated by of their base(s) and faces
rotations of two-dimensional objects.                                          DE.11.3.5 Location and transformation: Visualize three-dimensional objects
from different perspectives

Page 9 of 74                                                                                   as of 1/31/11
Common Core-Delaware Standards – Grades 9–12

Domain                                                Matched Common Core Standard                                                          Delaware Standards
Experiment with transformations in the situations.
Apply geometric concepts in modeling plane.
Use geometric shapes, their measures, and their properties to describe objects   DE.12.3.3 Location and transformation: Use perspective, proportionality, and
Modeling with

(e.g., modeling a tree trunk or a human torso as a cylinder).* CC.9-12.G.MG.1    patterning to explore real world geometric applications
Geometry

Apply concepts of density based on area and volume in modeling situations      No Delaware Match
(e.g., persons per square mile, BTUs per cubic foot).* CC.9-12.G.MG.2
Apply geometric methods to solve design problems (e.g., designing an object or No Delaware Match
structure to satisfy physical constraints or minimize cost; working with
typographic grid systems based on ratios).* CC.9-12.G.MG.3

Page 10 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Functions Overview

Domain                                                          Matched Common Core Standard                                                                Delaware Standards
Understand the concept of a function and use function notation.
Understand that a function from one set (called the domain) to another set         DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
(called the range) assigns to each element of the domain exactly one element of
the range. If f is a function and x is an element of its domain, then f(x) denotes
the output of f corresponding to the input x. The graph of f is the graph of the
equation y = f(x). CC.9-12.F.IF.1
Use function notation, evaluate functions for inputs in their domains, and         DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
interpret statements that use function notation in terms of a context. CC.9-
12.F.IF.2
Recognize that sequences are functions, sometimes defined recursively, whose No Delaware match
domain is a subset of the integers. For example, the Fibonacci sequence is
defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1. CC.9-
12.F.IF.3
Interpret functions that arise in applications in terms of the context.

DE.9.2.3 Patterns and change: Describe the effect of parameter changes on
linear and exponential functions within a context, table, graph, and equation

DE.9.2.12 Representations: Analyze the interrelationship among the table, graph
For a function that models a relationship between two quantities, interpret key
and equation of both linear and exponential functions paying particular attention
features of graphs and tables in terms of the quantities, and sketch graphs
to the meaning of intercept and slope in the context of the problem
showing key features given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is increasing, decreasing,
DE.10.2.8 Representations: Convert flexibly among relationships expressed in
positive, or negative; relative maximums and minimums; symmetries; end
tables, graphs, and equations for exponential and quadratic functions
behavior; and periodicity.* CC.9-12.F.IF.4
DE.11.2.6 Representations: Understand the relationship between the solution to
a quadratic equation and its graph
DE.12.2.3 Representations: Interpret maximum and minimum values of
functions in problem situations
Relate the domain of a function to its graph and, where applicable, to the            DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
quantitative relationship it describes. For example, if the function h(n) gives the   polynomial, rational, exponential, logarithmic, and/or step functions, absolute
number of person-hours it takes to assemble n engines in a factory, then the          value and square roots
positive integers would be an appropriate domain for the function.* CC.9-
12.F.IF.5
DE.9.2.1 Patterns and change: Explain slope as a rate of change between
dependent and independent variables
DE.12.2.1 Patterns and change: Apply and use an understanding of rates of
Calculate and interpret the average rate of change of a function (presented           change to solve real world problems involving applications of finance such as
symbolically or as a table) over a specified interval. Estimate the rate of change    but not limited to, savings, compound interest, continuous interest, depreciation,
from a graph.* CC.9-12.F.IF.6                                                         loans, credit cards, mortgages, reading amortization tables, home buying, etc.

DE.12.2.2 Patterns and change: Explore and analyze real world problem
situations involving non-financial applications of rates

Page 11 of 74                                                                                as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Functions Overview

Domain                                                                         Matched Common Core Standard                                                               Delaware Standards
Understand the concept different representations.
Analyze functions using of a function and use function notation.
DE.12.1.3 Operations: Select and use appropriate methods and tools for
computing from among mental computation, estimation, calculators, paper and
Graph functions expressed symbolically and show key features of the graph, by       pencil, and computers according to the context and nature of the computation
hand in simple cases and using technology for more complicated cases.* CC.9-
12.F.IF.7                                                                      DE.11.2.5 Representations: Analyze linear, quadratic, exponential, periodic,
trigonometric, or inverse relationships in graphs using best fit lines and curves
(regression lines and curve fitting)
DE.9.2.7 Representations: Model and solve real-world linear situations, including
linear inequalities, using tables, graphs, and symbols
DE.10.2.9 Representations: Estimate solutions to exponential and quadratic
Graph linear and quadratic functions and show intercepts, maxima, and minima. function using tables and graphs

CC.9-12.F.IF.7a                                                                DE.11.2.6 Representations: Understand the relationship between the solution to
a quadratic equation and its graph

DE.12.2.3 Representations: Interpret maximum and minimum values of
functions in problem situations
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
Graph square root, cube root, and piecewise-defined functions, including step
polynomial, rational, exponential, logarithmic, and/or step functions, absolute
functions and absolute value functions. CC.9-12.F.IF.7b
value and square roots
Graph polynomial functions, identifying zeros when suitable factorizations are DE.12.2.4 Representations: Understand the relationship between the zeros
available, and showing end behavior. CC.9-12.F.IF.7c                           (roots) of a polynomial function and its factors
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
(+) Graph rational functions, identifying zeros and asymptotes when suitable
polynomial, rational, exponential, logarithmic, and/or step functions, absolute
factorizations are available, and showing end behavior. CC.9-12.F.IF.7d
value and square roots
DE.11.2.3 Patterns and change: Develop the conceptual understanding that
logarithmic and exponential functions are inverse functions
Graph exponential and logarithmic functions, showing intercepts and end        DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
behavior, and trigonometric functions, showing period, midline, and amplitude. polynomial, rational, exponential, logarithmic, and/or step functions, absolute
CC.9-12.F.IF.7e                                                                value and square roots
DE.11.3.4 Location and transformation: Stretch and shrink periodic functions by
changing parameters
DE.9.2.16 Symbols: Convert between equivalent forms of linear functions
Write a function defined by an expression in different but equivalent forms to
DE.11.2.8 Symbols: Write equivalent symbolic forms of linear, quadratic, or
reveal and explain different properties of the function. CC.9-12.F.IF.8
exponential functions
DE.10.2.9 Representations: Estimate solutions to exponential and quadratic
function using tables and graphs
Use the process of factoring and completing the square in a quadratic function DE.11.2.9 Symbols: Use geometric models and/or algebraic symbols to multiply
to show zeros, extreme values, and symmetry of the graph, and interpret these binomials and complete the square
DE.11.2.10 Symbols: Use algebraic techniques to identify the vertex and
in terms of a context. CC.9-12.F.IF.8a
DE.11.2.11 Symbols: Apply the quadratic formula and/or factor to solve problems

DE.9.2.3 Patterns and change: Describe the effect of parameter changes on
linear and exponential functions within a context, table, graph, and equation
rpreting Functions

DE.9.2.5 Patterns and change: Demonstrate and apply recursive thinking to
classify linear and exponential functions
Use the properties of exponents to interpret expressions for exponential
Page y of
functions. For example, identify percent rate of change in functions such as12 = 74                                                                                 as of 1/31/11
tinued)

(1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as
representing exponential. CC.9-12.F.IF.8b
Common Core-Delaware Standards – Grades 9–12 – Functions Overview

Domain                                                                    Matched Common Core Standard                                                                Delaware Standards
Understand the concept of a function and use function notation.
Use the properties of exponents to interpret expressions for exponential              DE.10.2.3 Patterns and change: Compare linear with exponential and quadratic
functions. For example, identify percent rate of change in functions such as y =      functions using the context, table, graph, or equation
(continued)

(1.02)^t, y = (0.97)^t, y = (1.01)^(12t), y = (1.2)^(t/10), and classify them as      DE.12.2.1 Patterns and change: Apply and use an understanding of rates of
representing exponential. CC.9-12.F.IF.8b                                             change to solve real world problems involving applications of finance such as
but not limited to, savings, compound interest, continuous interest, depreciation,

DE.12.2.2 Patterns and change: Explore and analyze real world problem
situations involving non-financial applications of rates
Compare properties of two functions each represented in a different way               DE.10.2.8 Representations: Convert flexibly among relationships expressed in
(algebraically, graphically, numerically in tables, or by verbal descriptions). For   tables, graphs, and equations for exponential and quadratic functions
example, given a graph of one quadratic function and an algebraic expression
for another, say which has the larger maximum. CC.9-12.F.IF.9
Build a function that models a relationship between two quantities.

DE.9.2.7 Representations: Model and solve real-world linear situations, including
linear inequalities, using tables, graphs, and symbols

Write a function that describes a relationship between two quantities.* CC.9-         DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
12.F.BF.1
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, and/or step functions, absolute
value and square roots
DE.9.2.5 Patterns and change: Demonstrate and apply recursive thinking to
classify linear and exponential functions
DE.9.2.6 Patterns and change: Use a variety of strategies to write expressions
Determine an explicit expression, a recursive process, or steps for calculation       that generate the nth term of arithmetic (linear) and geometric (exponential)
from a context. CC.9-12.F.BF.1a                                                       patterns
DE.9.2.7 Representations: Model and solve real-world linear situations, including
linear inequalities, using tables, graphs, and symbols
DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions

Determine an explicit expression, a recursive process, or steps for calculation       DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
from a context. CC.9-12.F.BF.1b                                                       polynomial, rational, exponential, logarithmic, and/or step functions, absolute
value and square roots

Page 13 of 74                                                                                 as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Functions Overview

Domain                                                                           Matched Common Core Standard                                                                    Delaware Standards
(+) Compose functions. For example, if and use temperature in the
Understand the concept of a functionT(y) is the function notation.                         DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
atmosphere as a function of height, and h(t) is the height of a weather balloon
as a function of time, then T(h(t)) is the temperature at the location of the
weather balloon as a function of time. CC.9-12.F.BF.1c
DE.9.2.6 Patterns and change: Use a variety of strategies to write expressions
that generate the nth term of arithmetic (linear) and geometric (exponential)
Write arithmetic and geometric sequences both recursively and with an explicit
patterns
formula, use them to model situations, and translate between the two forms.*

DE.11.2.12 Symbols: Use expressions or equations to describe arithmetic and
CC.9-12.F.BF.2
geometric sequences (nth term) and series (using sigma notation) to represent
the sum
Build new functions from existing functions.
DE.9.2.3 Patterns and change: Describe the effect of parameter changes on
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x +   linear and exponential functions within a context, table, graph, and equation
k) for specific values of k (both positive and negative); find the value of k given
9-12: Interpreting Functions

the graphs. Experiment with cases and illustrate an explanation of the effects on          DE.10.2.2 Patterns and change: Describe and predict the effect of parameter
the graph using technology. Include recognizing even and odd functions from                changes on functions
their graphs and algebraic expressions for them. CC.9-12.F.BF.3                            DE.11.3.4 Location and transformation: Stretch and shrink periodic functions by
changing parameters
DE.11.2.3 Patterns and change: Develop the conceptual understanding that
Find inverse functions. CC.9-12.F.BF.4
logarithmic and exponential functions are inverse functions
Solve an equation of the form f(x) = c for a simple function f that has an inverse         DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
and write an expression for the inverse. For example, f(x) =2(x^3) for x > 0 or
f(x) Verify by composition 1 (x not equal to 1). the inverse of another. CC.9-
(+) = (x+1)/(x-1) for x =? that one function is CC.9-12.F.BF.4a                            DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
12.F.BF.4b
(+) Read values of an inverse function from a graph or a table, given that the             DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
function has an inverse. CC.9-12.F.BF.4c
(+) Produce an invertible function from a non-invertible function by restricting the       DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
domain. CC.9-12.F.BF.4d
(+) Understand the inverse relationship between exponents and logarithms and               DE.11.2.3 Patterns and change: Develop the conceptual understanding that
use this relationship to solve problems involving logarithms and exponents.                logarithmic and exponential functions are inverse functions
CC.9-12.F.BF.5

Page 14 of 74                                                                                  as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Functions Overview

Domain                                                                              Matched Common Core Standard                                                             Delaware Standards
Understand the concept linear, quadratic, and exponential models and solve problems.
Construct and compare of a function and use function notation.
DE.9.2.4 Patterns and change: Compare linear with exponential functions using,
the context, table, graph, or equation
Distinguish between situations that can be modeled with linear functions and   DE.10.2.3 Patterns and change: Compare linear with exponential and quadratic
with exponential functions.* CC.9-12.F.LE.1                                    functions using the context, table, graph, or equation
DE.10.2.7 Representations: Determine the appropriateness of linear,
exponential or quadratic models given a real-world situation
Prove that linear functions grow by equal differences over equal intervals and DE.9.2.5 Patterns and change: Demonstrate and apply recursive thinking to
that exponential functions grow by equal factors over equal intervals.* CC.9-  classify linear and exponential functions
12.F.LE.1a

DE.9.2.5 Patterns and change: Demonstrate and apply recursive thinking to
classify linear and exponential functions
DE.11.2.1 Patterns and change: Use rates of change to classify families of
functions

DE.12.2.1 Patterns and change: Apply and use an understanding of rates of
Recognize situations in which one quantity changes at a constant rate per unit
change to solve real world problems involving applications of finance such as
interval relative to another.* CC.9-12.F.LE.1b.
but not limited to, savings, compound interest, continuous interest, depreciation,

DE.12.2.2 Patterns and change: Explore and analyze real world problem
situations involving non-financial applications of rates
DE.9.2.5 Patterns and change: Demonstrate and apply recursive thinking to
classify linear and exponential functions
DE.11.2.1 Patterns and change: Use rates of change to classify families of
functions
DE.12.2.1 Patterns and change: Apply and use an understanding of rates of
Recognize situations in which a quantity grows or decays by a constant percent
change to solve real world problems involving applications of finance such as
rate per unit interval relative to another.* CC.9-12.F.LE.1c
but not limited to, savings, compound interest, continuous interest, depreciation,

DE.12.2.2 Patterns and change: Explore and analyze real world problem
situations involving non-financial applications of rates
DE.9.2.6 Patterns and change: Use a variety of strategies to write expressions
that generate the nth term of arithmetic (linear) and geometric (exponential)
patterns
Construct linear and exponential functions, including arithmetic and geometric   DE.10.2.4 Patterns and change: Use a variety of strategies to write expressions
sequences, given a graph, a description of a relationship, or two input-output   that generate the nth term of linear, exponential, and quadratic functions
pairs (include reading these from a table).* CC.9-12.F.LE.2
DE.11.2.12 Symbols: Use expressions or equations to describe arithmetic and
geometric sequences (nth term) and series (using sigma notation) to represent
the sum
DE.9.2.4 Patterns and change: Compare linear with exponential functions using,
the context, table, graph, or equation
and Exponential

DE.10.2.3 Patterns and change: Compare linear with exponential and quadratic
functions using the context, table, graph, or equation

Page
Observe using graphs and tables that a quantity increasing exponentially 15 of 74                                                                                as of 1/31/11
eventually exceeds a quantity increasing linearly, quadratically, or (more
generally) as a polynomial function.* CC.9-12.F.LE.3
d)
Common Core-Delaware Standards – Grades 9–12 – Functions Overview

Domain                                                                                                                  Matched Common Core Standard                                                                 Delaware Standards
Understand the concept of a function and use function notation.                      DE.11.2.1 Patterns and change: Use rates of change to classify families of
Observe using graphs and tables that a quantity increasing exponentially             functions
eventually exceeds a quantity increasing linearly, quadratically, or (more           DE.12.2.1 Patterns and change: Apply and use an understanding of rates of
generally) as a polynomial function.* CC.9-12.F.LE.3                                 change to solve real world problems involving applications of finance such as
Models (continued)

but not limited to, savings, compound interest, continuous interest, depreciation,

DE.12.2.2 Patterns and change: Explore and analyze real world problem
situations involving non-financial applications of rates
DE.9.2.3 Patterns and change: Describe the effect of parameter changes on
linear and exponential functions within a context, table, graph, and equation

DE.9.2.7 Representations: Model and solve real-world linear situations, including
Interpret the parameters in a linear, quadratic, or exponential function in terms of
linear inequalities, using tables, graphs, and symbols

a context.* CC.9-12.F.LE.5
DE.10.2.2 Patterns and change: Describe and predict the effect of parameter
changes on functions
DE.10.2.7 Representations: Determine the appropriateness of linear,
exponential or quadratic models given a real-world situation
Extend the domain of trigonometric functions using the unit circle.
Understand radian measure of an angle as the length of the arc on the unit circle DE.11.3.6 Measurement: Develop the conceptual understanding of a radian.

subtended by the angle. CC.9-12.F.TF.1
DE.11.3.1 Classification: Connect the right angle relationships with the unit circle
Explain how the unit circle in the coordinate plane enables the extension of         and periodic functions for any angle
trigonometric functions to all real numbers, interpreted as radian measures of       DE.11.3.7 Measurement: Understand the relationship between degree
angles traversed counterclockwise around the unit circle. CC.9-12.F.TF.2             measures and radian measures of benchmark angles such as 0°, 30°, 45°, 60°,
90°, and multiples of these angles
(+) Use special triangles to determine geometrically the values of sine, cosine,     DE.10.3.9 Measurement: Apply trigonometric relationships to determine side
tangent for ?/3, ?/4 and ?/6, and use the unit circle to express the values of sine, lengths and angle measures of right triangle
cosine, and tangent for ? - x, ? + x, and 2? - x in terms of their values for x,     DE.11.3.1 Classification: Connect the right angle relationships with the unit circle
where x is any real number. CC.9-12.F.TF.3                                           and periodic functions for any angle
Model periodic phenomena with trigonometric functions.
DE.11.3.2 Classification: Use Sine and Cosine functions to explore periodic real
Choose trigonometric functions to model periodic phenomena with specified            world phenomena
amplitude, frequency, and midline.* CC.9-12.F.TF.5                                   DE.12.3.1 Classification: Understand and use periodic functions to model real
world phenomena
Prove and apply trigonometric identies

Page 16 of 74                                                                                 as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Algebra

Domain                                                                    Matched Common Core Standard                                                              Delaware Standards
Interpret the structure of expressions.
Interpret expressions that represent a quantity in terms of its context.* CC.9-     DE.9.2.7 Representations: Model and solve real-world linear situations, including
12.A.SSE.1                                                                          linear inequalities, using tables, graphs, and symbols
DE.9.2.12 Representations: Analyze the interrelationship among the table, graph
and equation of both linear and exponential functions paying particular attention
to the meaning of intercept and slope in the context of the problem
Interpret parts of an expression, such as terms, factors, and coefficients. CC.9-
12.A.SSE.1a                                                                         DE.10.2.8 Representations: Convert flexibly among relationships expressed in
tables, graphs, and equations for exponential and quadratic functions
DE.11.2.8 Symbols: Write equivalent symbolic forms of linear, quadratic, or
exponential functions
DE.9.1.8 Operations: Use properties of the real number system to simplify
expressions (Associative, Commutative, Identity, Inverse, and Distributive)
Interpret complicated expressions by viewing one or more of their parts as a
Grades 9-12: Seeing Structure in Expressions

DE.9.2.12 Representations: Analyze the interrelationship among the table, graph
single entity. For example, interpret P(1+r)^n as the product of P and a factor not
and equation of both linear and exponential functions paying particular attention
depending on P. CC.9-12.A.SSE.1b
to the meaning of intercept and slope in the context of the problem

DE.10.1.3 Number sense: Simplify numeric and symbolic expressions involving
Use the structure of an expression to identify ways to rewrite it. For example, see absolute value, square roots, and exponents
x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as a difference of squares that DE.9.2.16 Symbols: Convert between equivalent forms of linear functions
can be factored as (x^2 - y^2)(x^2 + y^2). CC.9-12.A.SSE.2                          DE.11.2.8 Symbols: Write equivalent symbolic forms of linear, quadratic, or
exponential functions
Write expressions in equivalent forms to solve problems.
DE.10.2.7 Representations: Determine the appropriateness of linear,
exponential or quadratic models given a real-world situation
DE.11.2.8 Symbols: Write equivalent symbolic forms of linear, quadratic, or
Choose and produce an equivalent form of an expression to reveal and explain
exponential functions
properties of the quantity represented by the expression. CC.9-12.A.SSE.3
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, and/or step functions, absolute
value and square roots
Factor a quadratic expression to reveal the zeros of the function it defines. CC.9- DE.11.2.11 Symbols: Apply the quadratic formula and/or factor to solve problems
12.A.SSE.3a
DE.11.2.9 Symbols: Use geometric models and/or algebraic symbols to multiply
Complete the square in a quadratic expression to reveal the maximum or              binomials and complete the square
minimum value of the function it defines. CC.9-12.A.SSE.3b                          DE.11.2.10 Symbols: Use algebraic techniques to identify the vertex and
Use the properties of exponents to transform expressions for exponential            DE.9.2.9 Representations: Analyze data sets using technology to find an
functions. For example the expression 1.15^t can be rewritten as                    appropriate linear or exponential mathematical model
[1.15^(1/12)]^(12t) ? 1.012^(12t) to reveal the approximate equivalent monthly      DE.10.2.8 Representations: Convert flexibly among relationships expressed in
interest rate if the annual rate is 15%. CC.9-12.A.SSE.3c                           tables, graphs, and equations for exponential and quadratic functions
Derive the formula for the sum of a finite geometric series (when the common        DE.11.2.12 Symbols: Use expressions or equations to describe arithmetic and
ratio is not 1), and use the formula to solve problems. For example, calculate      geometric sequences (nth term) and series (using sigma notation) to represent
mortgage payments. CC.9-12.A.SSE.4                                                  the sum
Perform arithmetic operations on polynomials.
lynomials and

Page 17 of 74                                                                          as of 1/31/11
ns
Common Core-Delaware Standards – Grades 9–12 – Algebra

Domain                                                                                                    Matched Common Core Standard                                                               Delaware Standards
Grades 9-12: Arithmetic with Polynomials and   Interpret the structure of expressions. analogous to the integers, namely,
Understand that polynomials form a system                                             DE.11.1.4 Operations: Perform addition, subtraction, and multiplication on
they are closed under the operations of addition, subtraction, and multiplication;    polynomial expressions
add, subtract, and multiply polynomials. CC.9-12.A.APR.1
Understand the relationship between zeros and factors of polynomial.
Rational Expressions

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a,           DE.12.2.4 Representations: Understand the relationship between the zeros
the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a   (roots) of a polynomial function and its factors
factor of p(x). CC.9-12.A.APR.2
Identify zeros of polynomials when suitable factorizations are available, and use     DE.12.2.4 Representations: Understand the relationship between the zeros
the zeros to construct a rough graph of the function defined by the polynomial.       (roots) of a polynomial function and its factors
CC.9-12.A.APR.3
Rewrite rational expressions.
DE.9.1.8 Operations: Use properties of the real number system to simplify
(+) Understand that rational expressions form a system analogous to the rational      expressions (Associative, Commutative, Identity, Inverse, and Distributive)
Grades 9-12: Seeing Structure in Expressions

numbers, closed under addition, subtraction, multiplication, and division by a        DE.10.1.1 Number sense: Compare and contrast the properties of numbers in
nonzero rational expression; add, subtract, multiply, and divide rational             the real number system
expressions. CC.9-12.A.APR.7                                                          DE.11.1.1 Number sense: Extend the development of the properties of numbers
in the real number system

Page 18 of 74                                                                               as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Algebra

Domain                                                                              Matched Common Core Standard                                                               Delaware Standards
Interpret the structure describe numbers or relationship.
Create equations that of expressions.
DE.9.2.7 Representations: Model and solve real-world linear situations, including
linear inequalities, using tables, graphs, and symbols
DE.10.2.6 Representations: Model and solve situations involving systems of
Create equations and inequalities in one variable and use them to solve             equations and inequalities
problems. Include equations arising from linear and quadratic functions, and        DE.11.2.7 Symbols: Use functional notation to represent and evaluate functions
simple rational and exponential functions.* CC.9-12.A.CED.1
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using

polynomial, rational, exponential, logarithmic, and/or step functions, absolute
value and square roots
DE.9.2.7 Representations: Model and solve real-world linear situations, including
linear inequalities, using tables, graphs, and symbols
Create equations in two or more variables to represent relationships between
DE.9.2.8 Representations: Model and solve situations involving systems of
quantities; graph equations on coordinate axes with labels and scales.* CC.9-
Grades 9-12: Seeing Structure in Expressions

equations with tables or graphs using technology
12.A.CED.2
DE.10.2.8 Representations: Convert flexibly among relationships expressed in
tables, graphs, and equations for exponential and quadratic functions
DE.9.2.8 Representations: Model and solve situations involving systems of
equations with tables or graphs using technology
Represent constraints by equations or inequalities, and by systems of equations     DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
and/or inequalities, and interpret solutions as viable or non-viable options in a   algebraically and using technology
modeling context. For example, represent inequalities describing nutritional and    DE.11.2.4 Representations: Model constraints to solve linear programming
cost constraints on combinations of different foods.* CC.9-12.A.CED.3               problems
DE.12.2.5 Symbols: Use symbolic, numeric or graphical methods to solve
systems of equations and/or inequalities involving linear and nonlinear contexts
Rearrange formulas to highlight a quantity of interest, using the same reasoning    DE.9.2.16 Symbols: Convert between equivalent forms of linear functions
as in solving equations. For example, rearrange Ohm's law V = IR to highlight       DE.11.2.8 Symbols: Write equivalent symbolic forms of linear, quadratic, or
resistance R.* CC.9-12.A.CED.4                                                      exponential functions

Page 19 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Algebra

Domain                                                                                 Matched Common Core Standard                                                                  Delaware Standards
Understand structure of expressions.
Interpret thesolving equations as a process of reasoning and explain the reasoning.
DE.K-12.6 Standard 6 - Reasoning and Proof: Students will develop their
Reasoning and Proof ability by solving problems in which there is a need to
Explain each step in solving a simple equation as following from the equality of    investigate significant mathematical ideas in all content areas; to justify their
numbers asserted at the previous step, starting from the assumption that the        thinking; to reinforce and extend their logical reasoning abilities; to reflect on and
original equation has a solution. Construct a viable argument to justify a solution clarify their own thinking; to ask questions to extend their thinking; and to
method. CC.9-12.A.REI.1                                                             construct their own learning.
Grades 9-12:9-12: Reasoning with Equations and Inequalities

DE.9.2.17 Symbols: Solve single variable equations and inequalities
algebraically
DE.10.1.5 Operations: Solve problems that involve using inverse operations
Solve simple rational and radical equations in one variable, and give examples      including powers and roots
DE.11.1.6 Operations: Recognize and use inverse operations to solve
showing how extraneous solutions may arise. CC.9-12.A.REI.2
equations, powers, and their corresponding roots

Solve equations and inequalities in one variable.
Solve linear equations and inequalities in one variable, including equations with    DE.9.2.7 Representations: Model and solve real-world linear situations, including
coefficients represented by letters. CC.9-12.A.REI.3                                 linear inequalities, using tables, graphs, and symbols
DE.11.2.10 Symbols: Use algebraic techniques to identify the vertex and
DE.11.2.11 Symbols: Apply the quadratic formula and/or factor to solve problems
Solve quadratic equations in one variable. CC.9-12.A.REI.4
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
polynomial, rational, exponential, logarithmic, and/or step functions, absolute
value and square roots
DE.11.2.9 Symbols: Use geometric models and/or algebraic symbols to multiply
Use the method of completing the square to transforms any quadratic equation
binomials and complete the square
in x into an equation of the form (x - p)^2 = q that has the same solutions. Derive
DE.11.2.10 Symbols: Use algebraic techniques to identify the vertex and
the quadratic formula from this form. CC.9-12.A.REI.4a
DE.12.1.1 Number sense: Use i = ?(-1) to develop an awareness of other
number systems
Solve quadratic equations by inspection (e.g., for x^2 = 49), taking square roots, DE.11.2.9 Symbols: Use geometric models and/or algebraic symbols to multiply
completing the square, the quadratic formula and factoring, as appropriate to the binomials and complete the square
initial form of the equation. Recognize when the quadratic formula gives complex DE.11.2.10 Symbols: Use algebraic techniques to identify the vertex and
solutions and write them as a ± bi for real numbers a and b. CC.9-12.A.REI.4b       intercepts for quadratic functions
DE.11.2.11 Symbols: Apply the quadratic formula and/or factor to solve problems

Page 20 of 74                                                                               as of 1/31/11
Common Core-Delaware Standards – Grades 9–12 – Algebra

Domain                                                                                         Matched Common Core Standard                                                                  Delaware Standards
Interpret the structure of expressions.
Solve systems of equations.
Prove that, given a system of two equations in two variables, replacing one           DE.10.2.6 Representations: Model and solve situations involving systems of
equation by the sum of that equation and a multiple of the other produces a           equations and inequalities
DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
system with the same solutions. CC.9-12.A.REI.5
algebraically and using technology
Solve systems of linear equations exactly and approximately (e.g., with graphs),      DE.9.2.8 Representations: Model and solve situations involving systems of
focusing on pairs of linear equations in two variables. CC.9-12.A.REI.6               equations with tables or graphs using technology

Solve a simple system consisting of a linear equation and a quadratic equation        DE.12.2.5 Symbols: Use symbolic, numeric or graphical methods to solve
in two variables algebraically and graphically. For example, find the points of       systems of equations and/or inequalities involving linear and nonlinear contexts
intersection between the line y = -3x and the circle x^2 + y^2 = 3. CC.9-
12.A.REI.7
DE.10.2.6 Representations: Model and solve situations involving systems of
equations and inequalities
9-12: Reasoning with Equations Expressions

(+) Represent a system of linear equations as a single matrix equation in a           DE.10.2.10 Representations: Represent and analyze problem situations using
vector variable. CC.9-12.A.REI.8                                                      matrices
DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
algebraically and using technology
DE.10.2.6 Representations: Model and solve situations involving systems of
(+) Find the inverse of a matrix if it exists and use it to solve systems of linear   equations and inequalities
DE.10.2.10 Representations: Represent and analyze problem situations using
equations (using technology for matrices of dimension 3 × 3 or greater). CC.9-
matrices
12.A.REI.9
DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
algebraically and using technology
Represent and solve equations and inequalities graphically.
DE.9.2.7 Representations: Model and solve real-world linear situations, including
linear inequalities, using tables, graphs, and symbols
Understand that the graph of an equation in two variables is the set of all its
DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
solutions plotted in the coordinate plane, often forming a curve (which could be a
algebraically and using technology
line). CC.9-12.A.REI.10
DE.12.2.5 Symbols: Use symbolic, numeric or graphical methods to solve
systems of equations and/or inequalities involving linear and nonlinear contexts
Explain why the x-coordinates of the points where the graphs of the equations y DE.12.2.5 Symbols: Use symbolic, numeric or graphical methods to solve
= f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the systems of equations and/or inequalities involving linear and nonlinear contexts
solutions approximately, e.g., using technology to graph the functions, make
DE.12.2.6 Symbols: Solve everyday problems that can be modeled using
tables of values, or find successive approximations. Include cases where f(x)
polynomial, rational, exponential, logarithmic, and/or step functions, absolute
and/or g(x) are linear, polynomial, rational, absolute value, exponential, and
value and square roots
logarithmic functions.* CC.9-12.A.REI.11
DE.9.2.7 Representations: Model and solve real-world linear situations, including
Graph the solutions to a linear inequality in two variables as a half-plane           linear inequalities, using tables, graphs, and symbols
(excluding the boundary in the case of a strict inequality), and graph the solution DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
set to a system of linear inequalities in two variables as the intersection of the    algebraically and using technology
corresponding half-planes. CC.9-12.A.REI.12                                           DE.12.2.5 Symbols: Use symbolic, numeric or graphical methods to solve
systems of equations and/or inequalities involving linear and nonlinear contexts

Page 21 of 74                                                                          as of 1/31/11
Common Core-Delaware Standards – Grades 9–12
Number and Quantity
Domain                                                      Matched Common Core Standard                                                               Delaware Standards
Extend the properties of exponents to rational exponents.
DE.10.1.3 Number sense: Simplify numeric and symbolic expressions involving
absolute value, square roots, and exponents
Grades 9-12: The Real Number System

Explain how the definition of the meaning of rational exponents follows from
DE.10.1.5 Operations: Solve problems that involve using inverse operations
extending the properties of integer exponents to those values, allowing for a
including powers and roots
notation for radicals in terms of rational exponents. For example, we define
DE.11.1.2 Number sense: Simplify expressions with negative and fractional
5^(1/3) to be the cube root of 5 because we want [5^(1/3)]^3 = 5^[(1/3) x 3] to
exponents
hold, so [5^(1/3)]^3 must equal 5. CC.9-12.N.RN.1
DE.11.1.6 Operations: Recognize and use inverse operations to solve
equations, powers, and their corresponding roots
DE.11.1.2 Number sense: Simplify expressions with negative and fractional
Rewrite expressions involving radicals and rational exponents using the            exponents
properties of exponents. CC.9-12.N.RN.2                                            DE.11.1.6 Operations: Recognize and use inverse operations to solve
equations, powers, and their corresponding roots
Use properties of rational and irrational numbers.
DE.11.1.3 Operations: Make generalizations about the effect of operations on
real numbers
Explain why the sum or product of rational numbers is rational; that the sum of a
DE.11.1.5 Operations: Perform addition, subtraction, and multiplication on
rational number and an irrational number is irrational; and that the product of a
irrational expressions
nonzero rational number and an irrational number is irrational. CC.9-12.N.RN.3
DE.11.1.7 Operations: Analyze the reasonableness of computational strategies
and the results
Reason quantitatively and use units to solve problems.

Use units as a way to understand problems and to guide the solution of multi-     DE.9.2.14 Representations: Make strategic selection of graphing calculator
step problems; choose and interpret units consistently in formulas; choose and viewing window and scale to solve problems
interpret the scale and the origin in graphs and data displays. CC.9-12.N.Q.1     DE.12.3.5 Measurement: Use appropriate units to measure a given quantity
Define appropriate quantities for the purpose of descriptive modeling. CC.9-      DE.11.1.7 Operations: Analyze the reasonableness of computational strategies
12.N.Q.2                                                                          and the results
DE.10.1.2 Number sense: Determine the effect of using exact values or
estimates for repeating decimals and irrational numbers (e.g. 2/3 or .67, I or
Choose a level of accuracy appropriate to limitations on measurement when
3.14) in a problem solving situation
reporting quantities. CC.9-12.N.Q.3
DE.11.1.7 Operations: Analyze the reasonableness of computational strategies
and the results

Page 22 of 74                                                                       as of 1/31/11
Common Core-Delaware Standards – Grades 9–12
Number and Quantity
Domain                                                               Matched Common Core Standard                                                             Delaware Standards
Grades 9-12: The Complex Number System      Perform arithmetic operations with complex numbers.
Know there is a complex number i such that i^2 = ?1, and every complex              DE.12.1.1 Number sense: Use i = ?(-1) to develop an awareness of other
number has the form a + bi with a and b real. CC.9-12.N.CN.1                        number systems
Grades 9-12: The Real Number System

Use the relation i^2 = -1 and the commutative, associative, and distributive        DE.12.1.1 Number sense: Use i = ?(-1) to develop an awareness of other
properties to add, subtract, and multiply complex numbers. CC.9-12.N.CN.2           number systems
(+) Find the conjugate of a complex number; use conjugates to find moduli and       DE.12.1.1 Number sense: Use i = ?(-1) to develop an awareness of other
quotients of complex numbers. CC.9-12.N.CN.3                                        number systems
Represent complex numbers and their operations on the complex plane.
(+) Represent complex numbers on the complex plane in rectangular and polar         DE.12.1.1 Number sense: Use i = ?(-1) to develop an awareness of other
form (including real and imaginary numbers), and explain why the rectangular        number systems
and polar forms of a given complex number represent the same number. CC.9-
12.N.CN.4
Use complex numbers in polynomial identities and equations.
DE.12.1.1 Number sense: Use i = ?(-1) to develop an awareness of other
number systems
Solve quadratic equations with real coefficients that have complex solutions.       DE.11.2.10 Symbols: Use algebraic techniques to identify the vertex and
DE.11.2.11 Symbols: Apply the quadratic formula and/or factor to solve
problems
Perform operations on matrices and use matrices in applications.
(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or    DE.10.2.10 Representations: Represent and analyze problem situations using
Grades 9-12: Vector and Matrix Quantities

incidence relationships in a network. CC.9-12.N.VM.6                                matrices
(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of      DE.10.1.4 Operations: Use technology to add, subtract, and multiply with
the payoffs in a game are doubled. CC.9-12.N.VM.7                                   matrices in problem solving situations
(+) Add, subtract, and multiply matrices of appropriate dimensions. CC.9-           DE.10.1.4 Operations: Use technology to add, subtract, and multiply with
12.N.VM.8                                                                           matrices in problem solving situations
DE.10.1.1 Number sense: Compare and contrast the properties of numbers in
(+) Understand that, unlike multiplication of numbers, matrix multiplication for
the real number system
square matrices is not a commutative operation, but still satisfies the
DE.10.1.4 Operations: Use technology to add, subtract, and multiply with
associative and distributive properties. CC.9-12.N.VM.9
matrices in problem solving situations
(+) Understand that the zero and identity matrices play a role in matrix addition   DE.10.2.11 Symbols: Solve systems of linear equations and inequalities both
and multiplication similar to the role of 0 and 1 in the real numbers. The          algebraically and using technology
determinant of a square matrix is nonzero if and only if the matrix has a
multiplicative inverse. CC.9-12.N.VM.10
DE.10.1.4 Operations: Use technology to add, subtract, and multiply with
(+) Work with 2 X 2 matrices as transformations of the plane, and interpret the     matrices in problem solving situations
absolute value of the determinant in terms of area. CC.9-12.N.VM.12                 DE.10.2.10 Representations: Represent and analyze problem situations using
matrices

Page 23 of 74                                                                         as of 1/31/11
Common Core-Delaware Standards – Grade 8
Domain                          Matched Common Core Standard                                                               Delaware Standards
Know that numbers that are not rational are called irrational.
Understand informally that every number has a decimal ex-pansion; rational          DE.8.1.4 Number sense: Explore the meaning of irrational numbers such as ?,
numbers have decimal expansions that terminate in 0s or eventually repeat, and or ?3
conversely. CC.8.NS.1
System

Use rational approximations of irrational numbers to compare the size of            DE.8.1.4 Number sense: Explore the meaning of irrational numbers such as ?,
irrational numbers, locate them approximately on a number line diagram, and         or ?3
estimate the value of expressions (e.g., ?^2). For example, by truncating the       DE.9.1.3 Number sense: Estimate square roots
decimal expansion of ?2 (square root of 2), show that ?2 is between 1 and 2,
then between 1.4 and 1.5, and explain how to continue on to get better
approximations. CC.8.NS.2
Work with radicals and integer exponents.
Know and apply the properties of integer exponents to generate equivalent           DE.8.1.5 Operations: Perform computations with exponents, powers of 10, and
numerical expressions. For example, 3^2 × 3^(-5) = 3^(-3) = 1/(3^3) = 1/27.         scientific notation
CC.8.EE.1
Use square root and cube root symbols to represent solutions to equations of        DE.10.1.3 Number sense: Simplify numeric and symbolic expressions involving
the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate       absolute value, square roots, and exponents
square roots of small perfect squares and cube roots of small perfect cubes.        DE.10.1.5 Operations: Solve problems that involve using inverse operations

Know that ?2 is irrational. CC.8.EE.2                                               including powers and roots
Use numbers expressed in the form of a single digit times an integer power of       DE.7.1.1 Number sense: Use scientific notation to represent large numbers and
10 to estimate very large or very small quantities, and to express how many         decimals
times as much one is than the other. For example, estimate the population of        DE.7.1.2 Number sense: Use powers of ten to represent place value
the United States as 3 × 10^8 and the population of the world as 7 × 10^9, and
determine that the world population is more than 20 times larger. CC.8.EE.3
Perform operations with numbers expressed in scientific notation, including         DE.8.1.5 Operations: Perform computations with exponents, powers of 10, and
problems where both decimal and scientific notation are used. Use scientific        scientific notation
notation and choose units of appropriate size for measurements of very large or DE.8.1.7 Operations: Demonstrate the reasonableness of an exact calculation
very small quantities (e.g., use millimeters per year for seafloor spreading).      by using an estimation or mental math strategy
Interpret scientific notation that has been generated by technology. CC.8.EE.4
Understand the connections between proportional relationships, lines, and linear equations.
Graph proportional relationships, interpreting the unit rate as the slope of the    DE.8.2.7 Representations: Analyze the interrelationships among tables, graphs,
graph. Compare two different proportional relationships represented in different and equations of lines, paying particular attention to the meaning of intercept
ways. For example, compare a distance-time graph to a distance-time equation and slope in the context of the problem
to determine which of two moving objects has greater speed. CC.8.EE.5               DE.9.2.2 Patterns and change: Understand and compare the graphs, tables,
and equations within linear contexts that are direct variations (proportional) and
those that are not
Use similar triangles to explain why the slope m is the same between any two        DE.8.2.1 Patterns and change: Determine the slope of a line given two points on
distinct points on a non-vertical line in the coordinate plane; derive the equation the line (as coordinates, in a graph, in a table)
y =mx for a line through the origin and the equation y = mx + b for a line          DE.8.2.2 Patterns and change: Use y-intercept and slope to graph the equation
intercepting the vertical axis at b. CC.8.EE.6                                      of a line

Page 24 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grade 8
Domain                         Matched Common Core Standard                                                             Delaware Standards
are of simultaneous
Know that numbers that are not rationalpairscalled irrational. linear equations.
Analyze and solve linear equations and
DE.7.2.8 Symbols: Solve linear equations using a variety of strategies
Solve linear equations in one variable. CC.8.EE.7                                 DE.8.2.15 Symbols: Solve linear equations using inverse operations and
properties of equality
System
Grade 8: Expressions and Equations (continued)

Give examples of linear equations in one variable with one solution, infinitely   DE.7.2.8 Symbols: Solve linear equations using a variety of strategies
many solutions, or no solutions. Show which of these possibilities is the case by DE.8.2.15 Symbols: Solve linear equations using inverse operations and
successively transforming the given equation into simpler forms, until an         properties of equality
equivalent equation of the form x = a, a = a, or a = b results (where a and b are
different numbers). CC.8.EE.7a
DE.7.2.8 Symbols: Solve linear equations using a variety of strategies
Solve linear equations with rational number coefficients, including equations     DE.8.2.13 Symbols: Combine two algebraic expressions to form a new
whose solutions require expanding expressions using the distributive property     expression
and collecting like terms. CC.8.EE.7b                                             DE.8.2.15 Symbols: Solve linear equations using inverse operations and
properties of equality
DE.9.2.8 Representations: Model and solve situations involving systems of
Analyze and solve pairs of simultaneous linear equations. CC.8.EE.8
equations with tables or graphs using technology
Understand that solutions to a system of two linear equations in two variables    DE.9.2.8 Representations: Model and solve situations involving systems of
correspond to points of intersection of their graphs, because points of           equations with tables or graphs using technology
intersection satisfy both equations simultaneously. CC.8.EE.8a
Solve systems of two linear equations in two variables algebraically, and         DE.9.2.8 Representations: Model and solve situations involving systems of
estimate solutions by graphing the equations. Solve simple cases by inspection. equations with tables or graphs using technology
For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y
cannot simultaneously be 5 and 6. CC.8.EE.8b
Solve real-world and mathematical problems leading to two linear equations in     DE.9.3.1 Classification: Represent and verify parallel and perpendicular
two variables. For example, given coordinates for two pairs of points, determine relationships in linear functions
whether the line through the first pair of points intersects the line through the
second pair. CC.8.EE.8c

Page 25 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grade 8
Domain                      Matched Common Core Standard                                                                                       Delaware Standards
Define, evaluate, and compare rational are
Know that numbers that are notfunctions. called irrational.
DE.8.2.3 Patterns and change: Compare the rates of change in tables and
Understand that a function is a rule that assigns to each input exactly one            graphs and classify them as linear or nonlinear
output. The graph of a function is the set of ordered pairs consisting of an input     DE.8.2.4 Patterns and change: Recognize exponential rates of growth and
System

and the corresponding output. (Function notation is not required in Grade 8.)          decay in tables and graphs
CC.8.F.1                                                                               DE.8.2.9 Representations: Use tables, graphs and symbolic reasoning to identify
functions as linear or nonlinear
Compare properties of two functions each represented in a different way                DE.8.2.3 Patterns and change: Compare the rates of change in tables and
(algebraically, graphically, numerically in tables, or by verbal descriptions). For    graphs and classify them as linear or nonlinear
example, given a linear function represented by a table of values and a linear         DE.8.2.9 Representations: Use tables, graphs and symbolic reasoning to identify
function represented by an algebraic expression, determine which function has          functions as linear or nonlinear
the greater rate of change. CC.8.F.2

Interpret the equation y = mx + b as defining a linear function, whose graph is a      DE.8.2.3 Patterns and change: Compare the rates of change in tables and
straight line; give examples of functions that are not linear. For example, the        graphs and classify them as linear or nonlinear
function A = s^2 giving the area of a square as a function of its side length is not
linear because its graph contains the points (1,1), (2,4) and (3,9), which are not     DE.8.2.9 Representations: Use tables, graphs and symbolic reasoning to identify
on a straight line. CC.8.F.3                                                           functions as linear or nonlinear
Use functions to model relationships between quantities.
Construct a function to model a linear relationship between two quantities.            DE.8.2.6 Representations: Write an equation given the tabular or graphic form
Determine the rate of change and initial value of the function from a description      of a linear problem
of a relationship or from two (x, y) values, including reading these from a table or   DE.8.2.7 Representations: Analyze the interrelationships among tables, graphs,
from a graph. Interpret the rate of change and initial value of a linear function in   and equations of lines, paying particular attention to the meaning of intercept
terms of the situation it models, and in terms of its graph or a table of values.      and slope in the context of the problem
CC.8.F.4
DE.8.2.3 Patterns and change: Compare the rates of change in tables and
graphs and classify them as linear or nonlinear
Describe qualitatively the functional relationship between two quantities by
DE.8.2.7 Representations: Analyze the interrelationships among tables, graphs,
analyzing a graph (e.g., where the function is increasing or decreasing, linear or
and equations of lines, paying particular attention to the meaning of intercept
nonlinear). Sketch a graph that exhibits the qualitative features of a function that
and slope in the context of the problem
has been described verbally. CC.8.F.5
DE.8.2.9 Representations: Use tables, graphs and symbolic reasoning to identify
functions as linear or nonlinear

Page 26 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 8
Domain                           Matched Common Core Standard                                                                 Delaware Standards
are similarity using physical models,
Know that numbers that andnot rational are called irrational. transparencies, or geometry software.
Understand congruence
Verify experimentally the properties of rotations, reflections, and translations:    DE.7.3.5 Location and transformation: Describe the effects that transformations
-- a. Lines are taken to lines, and line segments to line segments of the same (i.e., reflections, translations, and rotations) and changes in scale have on
similarity and congruence
System

length.
DE.8.3.3 Location and transformation: Develop and evaluate mathematical
-- b. Angles are taken to angles of the same measure.
arguments to demonstrate geometric relationships such as similarity,
-- c. Parallel lines are taken to parallel lines. CC.8.G.1
congruence, or symmetry
DE.7.3.5 Location and transformation: Describe the effects that transformations
Understand congruence and similarity using physical models, transparencies, or
(i.e., reflections, translations, and rotations) and changes in scale have on
geometry software. Understand that a two-dimensional figure is congruent to
similarity and congruence
another if the second can be obtained from the first by a sequence of rotations,
DE.8.3.3 Location and transformation: Develop and evaluate mathematical
reflections, and translations; given two congruent figures, describe a sequence
arguments to demonstrate geometric relationships such as similarity,
that exhibits the congruence between them. CC.8.G.2
congruence, or symmetry
DE.7.3.5 Location and transformation: Describe the effects that transformations
(i.e., reflections, translations, and rotations) and changes in scale have on
similarity and congruence

DE.7.3.6 Location and transformation: Demonstrate dilations of scale on the
Describe the effect of dilations, translations, rotations and reflections on two-    coordinate plane
dimensional figures using coordinates. CC.8.G.3                                      DE.7.3.7 Location and transformation: Represent reflections, rotations, and
translations on the coordinate plane
DE.8.3.3 Location and transformation: Develop and evaluate mathematical
arguments to demonstrate geometric relationships such as similarity,
congruence, or symmetry
DE.7.3.5 Location and transformation: Describe the effects that transformations
(i.e., reflections, translations, and rotations) and changes in scale have on
similarity and congruence
Understand that a two-dimensional figure is similar to another if the second can DE.7.3.6 Location and transformation: Demonstrate dilations of scale on the
be obtained from the first by a sequence of rotations, reflections, translations,    coordinate plane
and dilations; given two similar two-dimensional figures, describe a sequence        DE.7.3.7 Location and transformation: Represent reflections, rotations, and
that exhibits the similarity between them. CC.8.G.4                                  translations on the coordinate plane
DE.8.3.3 Location and transformation: Develop and evaluate mathematical
arguments to demonstrate geometric relationships such as similarity,
congruence, or symmetry
Use informal arguments to establish facts about the angle sum and exterior           DE.8.3.1 Classification: Apply angle relationships to solve problems
angle of triangles, about the angles created when parallel lines are cut by a
transversal, and the angle-angle criterion for similarity of triangles. For example,
arrange three copies of the same triangle so that the three angles appear to
form a line, and give an argument in terms of transversals why this is so.
CC.8.G.5

Page 27 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grade 8
Domain                    Matched Common Core Standard                                                                                                          Delaware Standards
Know that numbers that are not rational are called irrational.
Understand and apply the Pythagorean Theorem.
DE.8.3.4 Location and transformation: Use the Pythagorean Theorem to find
missing sides of right triangles
DE.9.3.5 Measurement: Solve problems which require an understanding of the
System

Explain a proof of the Pythagorean Theorem and its converse. CC.8.G.6             Pythagorean Theorem relationships.
DE.10.3.1 Classification: Determine whether a triangle is a right triangle (e.g.,
Converse of Pythagorean Theorem, slopes of adjacent sides)
DE.10.3.12 Measurement: Apply the Pythagorean Theorem and its converse
Apply the Pythagorean Theorem to determine unknown side lengths in right          DE.8.3.4 Location and transformation: Use the Pythagorean Theorem to find
triangles in real-world and mathematical problems in two and three dimensions.    missing sides of right triangles
CC.8.G.7
DE.9.3.5 Measurement: Solve problems which require an understanding of the
Apply the Pythagorean Theorem to find the distance between two points in a          Pythagorean Theorem relationships.
coordinate system. CC.8.G.8                                                         DE.10.3.13 Measurement: Develop and apply the distance and midpoint
formulas
Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.
DE.8.3.8 Measurement: Compare the relationship between the volume of
Know the formulas for the volume of cones, cylinders and spheres and use them
different shapes with the same base and height (e.g., cylinder and cone, prism
to solve real-world and mathematical problems. CC.8.G.9
and pyramid)
Investigate patterns of association in bivariate data.
Construct and interpret scatter plots for bivariate measurement data to             DE.8.4.4 Analyze: Defend or dispute conclusions drawn from the interpretation
investigate patterns of association between two quantities. Describe patterns       of data by comparing sets of data or exploring possible relationships based upon
such as clustering, outliers, positive or negative association, linear association, scatter plots of related data and approximate lines of fit
and nonlinear association. CC.8.SP.1

Know that straight lines are widely used to model relationships between two         DE.8.4.4 Analyze: Defend or dispute conclusions drawn from the interpretation
quantitative variables. For scatter plots that suggest a linear association,        of data by comparing sets of data or exploring possible relationships based upon
informally fit a straight line, and informally assess the model fit by judging the  scatter plots of related data and approximate lines of fit
closeness of the data points to the line. CC.8.SP.2
Use the equation of a linear model to solve problems in the context of bivariate    DE.8.4.4 Analyze: Defend or dispute conclusions drawn from the interpretation
measurement data, interpreting the slope and intercept. For example, in a linear of data by comparing sets of data or exploring possible relationships based upon
model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that      scatter plots of related data and approximate lines of fit
an additional hour of sunlight each day is associated with an additional 1.5 cm in
mature plant height. CC.8.SP.3
Understand that patterns of association can also be seen in bivariate categorical DE.8.4.4 Analyze: Defend or dispute conclusions drawn from the interpretation
data by displaying frequencies and relative frequencies in a two-way table.         of data by comparing sets of data or exploring possible relationships based upon
Construct and interpret a two-way table summarizing data on two categorical         scatter plots of related data and approximate lines of fit
variables collected from the same subjects. Use relative frequencies calculated
for rows or columns to describe possible association between the two variables. DE.9.2.10 Representations: Demonstrate a conceptual understanding of
For example, collect data from students in your class on whether or not they        correlation
have a curfew on school nights and whether or not they have assigned chores at
home. Is there evidence that those who have a curfew also tend to have
chores? CC.8.SP.4

Page 28 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 7
Domain                          Matched Common Core Standard                                                                  Delaware Standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
DE.7.1.12 Operations: Calculate unit rate to solve real-world problems (e.g.,
Compute unit rates associated with ratios of fractions, including ratios of lengths, speed of a car, unit price of food, etc.)
areas and other quantities measured in like or different units. For example, If a      DE.7.1.14 Operations: Use ratios, proportions and percents to solve
person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex           contextualized problems
fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour. CC.7.RP.1          DE.8.1.10 Operations: Apply proportional reasoning strategies to solve real-
world problems
DE.7.1.14 Operations: Use ratios, proportions and percents to solve
Recognize and represent proportional relationships between quantities.                 contextualized problems
Grade 7: Ratios and Proportional Relationships

CC.7.RP.2                                                                              DE.8.1.10 Operations: Apply proportional reasoning strategies to solve real-
world problems
DE.6.2.2 Representations: Demonstrate that a given situation may be
Decide whether two quantities are in a proportional relationship, e.g., by testing represented by a table, graph or equation
for equivalent ratios in a table or graphing on a coordinate plane and observing       DE.7.2.4 Representations: Model and solve contextualized linear problems using
whether the graph is a straight line through the origin. CC.7.RP.2a                    various representations (e.g., tables, graphs, equations) with respect to starting
point and rate of change
DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
measurements (e.g., recipes)
Identify the constant of proportionality (unit rate) in tables, graphs, equations,     DE.7.1.6 Number sense: Explore the effects of scaling up and scaling down on
diagrams, and verbal descriptions of proportional relationships. CC.7.RP.2b            the coordinate plane
DE.7.1.12 Operations: Calculate unit rate to solve real-world problems (e.g.,
speed of a car, unit price of food, etc.)
DE.7.1.14 Operations: Use ratios, proportions and percents to solve
Represent proportional relationships by equations. For example,if total cost t is      contextualized problems
proportional to the number n of items purchased at a constant price p, the             DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
relationship between the total cost and the number of items can be expressed           operations with rational numbers
as t = pn. CC.7.RP.2c                                                                  DE.8.1.10 Operations: Apply proportional reasoning strategies to solve real-
world problems
DE.7.2.2 Patterns and change: Interpret rate of change in tables and graphs
Explain what a point (x, y) on the graph of a proportional relationship means in       based on the context of the problem
terms of the situation, with special attention to the points (0, 0) and (1, r) where r DE.7.2.4 Representations: Model and solve contextualized linear problems using
is the unit rate. CC.7.RP.2d                                                           various representations (e.g., tables, graphs, equations) with respect to starting
point and rate of change
Use proportional relationships to solve multistep ratio and percent problems.          DE.7.1.14 Operations: Use ratios, proportions and percents to solve
Examples: simple interest, tax, markups and markdowns, gratuities and                  contextualized problems
commissions, fees, percent increase and decrease, percent error. CC.7.RP.3

Page 29 of 74                                                                              as of 1/31/11
Common Core-Delaware Standards – Grade 7
Domain                          Matched Common Core Standard                                                                  Delaware Standards
real-world and mathematical problems.
Analyze proportional relationships and use them to solve with fractions to add, subtract, multiply, and divide rational numbers.
Apply and extend previous understandings of operations
Apply and extend previous understandings of addition and subtraction to add            DE.7.1.8 Number sense: Explain the relationship of a number to its additive
and subtract rational numbers; represent addition and subtraction on a                 inverse
DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
horizontal or vertical number line diagram. CC.7.NS.1
operations with rational numbers
Describe situations in which opposite quantities combine to make 0. For                DE.7.1.8 Number sense: Explain the relationship of a number to its additive
example, a hydrogen atom has 0 charge because its two constituents are                 inverse
oppositely charged. CC.7.NS.1a
Understand p + q as the number located a distance |q| from p, in the positive or DE.7.1.8 Number sense: Explain the relationship of a number to its additive
negative direction depending on whether q is positive or negative. Show that a         inverse

number and its opposite have a sum of 0 (are additive inverses). Interpret sums DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
of rational numbers by describing real-world contexts. CC.7.NS.1b                      operations with rational numbers
DE.7.1.8 Number sense: Explain the relationship of a number to its additive
Understand subtraction of rational numbers as adding the additive inverse, p - q inverse
= p + (-q). Show that the distance between two rational numbers on the number DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
line is the absolute value of their difference, and apply this principle in real-world operations with rational numbers
contexts. CC.7.NS.1c                                                                   DE.8.1.9 Operations: Use meaningful relationships between addition,
subtraction, multiplication, and division of integers to justify the rules of

operations
DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
Apply properties of operations as strategies to add and subtract rational              operations with rational numbers
numbers. CC.7.NS.1d                                                                    DE.8.1.9 Operations: Use meaningful relationships between addition,
subtraction, multiplication, and division of integers to justify the rules of
operations
Apply and extend previous understandings of multiplication and division and of         DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
fractions to multiply and divide rational numbers. CC.7.NS.2                           operations with rational numbers
DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
Understand that multiplication is extended from fractions to rational numbers by
operations with rational numbers
requiring that operations continue to satisfy the properties of operations,            DE.8.1.8 Operations: Explain how the distributive property is used to multiply
particularly the distributive property, leading to products such as (-1)(-1) = 1 and (e.g., partial products, mixed numbers)
the rules for multiplying signed numbers. Interpret products of rational numbers DE.8.1.9 Operations: Use meaningful relationships between addition,
by describing real-world contexts. CC.7.NS.2a                                          subtraction, multiplication, and division of integers to justify the rules of
operations
Understand that integers can be divided, provided that the divisor is not zero,        DE.8.1.9 Operations: Use meaningful relationships between addition,
and every quotient of integers (with non-zero divisor) is a rational number. If p      subtraction, multiplication, and division of integers to justify the rules of
and q are integers then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational      operations Apply and adapt a variety of appropriate strategies to solve
DE.K-12.5.3
numbers by describing real-world contexts. CC.7.NS.2b                                  problems
DE.5.1.21 Operations: Connect multiplication by 1/3, 1/4, 1/5 to division by its
Apply properties of operations as strategies to multiply and divide rational           inverse (3, 4, 5) (e.g., 12 × 1/4 = 12 ÷ 4)
numbers. CC.7.NS.2c                                                                    DE.8.1.6 Operations: Use inverse operations to "do and undo" mathematical
operations with rational numbers
Convert a rational number to a decimal using long division; know that the              DE.6.1.11 Operations: Calculate the decimal equivalent of fractions
decimal form of a rational number terminates in 0s or eventually repeats.
CC.7.NS.2d
Solve real-world and mathematical problems involving the four operations with          DE.K-12.5.2 Solve problems that arise in mathematics and in other contexts
rational numbers. (Computations with rational numbers extend the rules for             DE.K-12.8.3 Recognize and apply mathematics in contexts outside of
manipulating fractions to complex fractions.) CC.7.NS.3                                mathematics
Use properties of operations to generate equivalent expressions.
DE.8.2.8 Representations: Demonstrate the equivalence of two algebraic
Apply properties of operations as strategies to add, subtract, factor, and expand
expressions using physical models
linear expressions with rational coefficients. CC.7.EE.1
DE.8.2.10 Symbols: Apply the order of operations

Page 30 of 74                                                                               as of 1/31/11
Common Core-Delaware Standards – Grade 7
Domain                          Matched Common Core Standard                                                               Delaware Standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Understand that rewriting an expression in different forms in a problem context      DE.8.2.8 Representations: Demonstrate the equivalence of two algebraic
can shed light on the problem and how the quantities in it are related. For          expressions using physical models
example, a + 0.05a = 1.05a means that "increase by 5%" is the same as
"multiply by 1.05." CC.7.EE.2
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Solve multi-step real-life and mathematical problems posed with positive and         DE.7.1.17 Operations: Use an estimation or mental math strategy to
negative rational numbers in any form (whole numbers, fractions, and decimals), demonstrate the reasonableness on an exact answer

using tools strategically. Apply properties of operations as strategies to calculate DE.7.1.18 Operations: Select and use appropriate methods and tools for
with numbers in any form; convert between forms as appropriate; and assess           computing (e.g., mental computation, estimation, calculators, paper and pencil)
Grade 7: Ratios and Proportional Relationships

the reasonableness of answers using mental computation and estimation                depending on the context and nature of the computation
strategies. For example: If a woman making \$25 an hour gets a 10% raise, she
DE.8.2.8 Representations: Demonstrate the equivalence of two algebraic
will make an additional 1/10 of her salary an hour, or \$2.50, for a new salary of
expressions using physical models
\$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door
that is 27 1/2 inches wide, you will need to place the bar about 9 inches from       DE.8.2.10 Symbols: Apply the order of operations
each edge; this estimate can be used as a check on the exact computation.
DE.7.2.4 Representations: Model and solve contextualized linear problems using
Solve real-life and mathematical problems using numerical and algebraic              various representations (e.g., tables, graphs, equations) with respect to starting
expressions and equations. Use variables to represent quantities in a real-world point and rate of change
or mathematical problem, and construct simple equations and inequalities to          DE.7.2.6 Symbols: Write an equation to show how two variables are related
solve problems by reasoning about the quantities. CC.7.EE.4                          DE.9.2.13 Representations: Determine if a given value is a solution to a given
equation or inequality
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, DE.7.2.4 Representations: Model and solve contextualized linear problems using
where p, q, and r are specific rational numbers. Solve equations of these forms various representations (e.g., tables, graphs, equations) with respect to starting
fluently. Compare an algebraic solution to an arithmetic solution, identifying the   point and rate of change
sequence of the operations used in each approach. For example, The perimeter
of a rectangle is 54 cm. Its length is 6 cm. What is its width? CC.7.EE.4a
Solve word problems leading to inequalities of the form px + q > r or px + q < r,   DE.K-12.5.2 Solve problems that arise in mathematics and in other contexts
where p, q, and r are specific rational numbers. Graph the solution set of the      DE.K-12.8.3 Recognize and apply mathematics in contexts outside of
inequality and interpret it in the context of the problem. For example, As a        mathematics
salesperson, you are paid \$50 per week plus \$3 per sale. This week you want         DE.9.2.17 Symbols: Solve single variable equations and inequalities algebraically
your pay to be at least \$100. Write an inequality for the number of sales you
need to make, and describe the solutions. CC.7.EE.4b

Page 31 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 7
Domain                         Matched Common Core Standard                                                               Delaware Standards
them to solve real-world and mathematical problems.
Analyze proportional relationships and use figures and describe the relationships between them.
Draw, construct, and describe geometrical
DE.6.3.2 Classification: Identify geometric relationships in the real world (e.g.,
Solve problems involving scale drawings of geometric figures, including
parallel lines, perpendicular lines, etc.)
computing actual lengths and areas from a scale drawing and reproducing a
DE.7.3.6 Location and transformation: Demonstrate dilations of scale on the
scale drawing at a different scale. CC.7.G.1
coordinate plane
Draw (freehand, with ruler and protractor, and with technology) geometric         DE.7.3.1 Classification: Demonstrate geometric relationships between the
shapes with given conditions. Focus on constructing triangles from three          measures of angles and sides of triangles and other polygons
measures of angles or sides, noticing when the conditions determine a unique
triangle, more than one triangle, or no triangle. CC.7.G.2

Describe the two-dimensional figures that result from slicing three-dimensional   DE.7.3.3 Classification: Build three-dimensional objects from two-dimensional
Grade 7: Ratios and Proportional 7: Geometry

figures, as in plane sections of right rectangular prisms and right rectangular   representations and draw two-dimensional representations of three-dimensional
pyramids. CC.7.G.3                                                                objects
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Know the formulas for the area and circumference of a circle and use them to      DE.7.3.8 Measurement: Find the area and circumference of circles.
solve problems; give an informal derivation of the relationship between the
circumference and area of a circle. CC.7.G.4
DE.7.3.1 Classification: Demonstrate geometric relationships between the
Use facts about supplementary, complementary, vertical, and adjacent angles in measures of angles and sides of triangles and other polygons
a multi-step problem to write and solve simple equations for an unknown angle     DE.7.3.2 Classification: Find the measure of the sum of the angles of a closed
in a figure. CC.7.G.5                                                             figure
DE.8.3.1 Classification: Apply angle relationships to solve problems
DE.7.3.10 Measurement: Find the surface area of prisms using physical models
Solve real-world and mathematical problems involving area, volume and surface DE.7.3.12 Measurement: Determine the volume and surface areas of cylinders
area of two- and three-dimensional objects composed of triangles,             and prisms
quadrilaterals, polygons, cubes, and right prisms. CC.7.G.6                   DE.7.3.13 Measurement: Demonstrate the relationship between the area of the
base and volume of prisms and cylinders

Page 32 of 74                                                                        as of 1/31/11
Common Core-Delaware Standards – Grade 7
Domain                         Matched Common Core Standard                                                           Delaware Standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
Use random sampling to draw inferences about a population.
Understand that statistics can be used to gain information about a population by DE.8.4.2 Collect: Use random sampling methods to collect the necessary
examining a sample of the population; generalizations about a population from a information to answer questions
sample are valid only if the sample is representative of that population.        DE.8.4.5 Analyze: Analyze a representative sample to make inferences about a
Understand that random sampling tends to produce representative samples and population
support valid inferences. CC.7.SP.1                                              DE.8.4.11 Probability: Explore the concepts of randomness and random sample

Use data from a random sample to draw inferences about a population with an          DE.8.4.5 Analyze: Analyze a representative sample to make inferences about a
unknown characteristic of interest. Generate multiple samples (or simulated          population
Grade 7: Ratios and Proportional Relationships

samples) of the same size to gauge the variation in estimates or predictions. For
example, estimate the mean word length in a book by randomly sampling words
from the book; predict the winner of a school election based on randomly
sampled survey data. Gauge how far off the estimate or prediction might be.

CC.7.SP.2
Draw informal comparative inferences about two populations.
DE.7.4.2 Represent: Construct displays of data for single data sets (e.g., stem-
Informally assess the degree of visual overlap of two numerical data                 and-leaf plots) or in order to study the relationship between related data sets
distributions with similar variabilities, measuring the difference between the       (scatter plots)
centers by expressing it as a multiple of a measure of variability. For example,     DE.7.4.3 Analyze: Defend or dispute conclusions drawn from the interpretation
the mean height of players on the basketball team is 10 cm greater than the          of data by comparing one data set to another
mean height of players on the soccer team, about twice the variability (mean         DE.8.4.3 Represent: Construct displays of data to represent individual sets of
absolute deviation) on either team; on a dot plot, the separation between the two data (e.g., histograms, box plots) or to explore the relationship between related
distributions of heights is noticeable. CC.7.SP.3                                    sets of data (scatter plots, line graphs); describe the correspondence between
data sets and their graphical displays
Use measures of center and measures of variability for numerical data from           DE.7.4.3 Analyze: Defend or dispute conclusions drawn from the interpretation
random samples to draw informal comparative inferences about two                     of data by comparing one data set to another
populations. For example, decide whether the words in a chapter of a seventh-        DE.7.4.4 Analyze: Choose an appropriate measures of center (mean, median,
grade science book are generally longer than the words in a chapter of a fourth- mode) and spread (range) to interpret data set(s)
Investigate chance processes and develop, use, and evaluate probability models.
Understand that the probability of a chance event is a number between 0 and 1 DE.5.4.6 Probability: Conduct a probability experiment, represent the result as a
that expresses the likelihood of the event occurring. Larger numbers indicate        number (fraction, decimal, percent) between 0 and 1, and draw conclusions
greater likelihood. A probability near 0 indicates an unlikely event, a probability  from the results
around 1/2 indicates an event that is neither unlikely nor likely, and a probability
near 1 indicates a likely event. CC.7.SP.5
Approximate the probability of a chance event by collecting data on the chance       DE.7.4.6 Probability: Use proportional reasoning to predict how often a simple
process that produces it and observing its long-run relative frequency, and          probability event will occur in a given number of trials
predict the approximate relative frequency given the probability. For example,
when rolling a number cube 600 times, predict that a 3 or 6 would be rolled
roughly 200 times, but probably not exactly 200 times. CC.7.SP.6

Page 33 of 74                                                                               as of 1/31/11
Common Core-Delaware Standards – Grade 7
Domain                        Matched Common Core Standard                                                             Delaware Standards
Analyze proportional relationships and use them to solve real-world and mathematical problems.
DE.7.4.5 Probability: Construct a sample space (organized list, counting tree) to
determine theoretical probabilities of an event
Develop a probability model and use it to find probabilities of events. Compare DE.7.4.6 Probability: Use proportional reasoning to predict how often a simple
probabilities from a model to observed frequencies; if the agreement is not     probability event will occur in a given number of trials
good, explain possible sources of the discrepancy. CC.7.SP.7                    DE.8.4.10 Probability: Investigate and describe the difference between the event
experimental probability of a simulated event (experiment) and the theoretical
probability of the same event
Develop a uniform probability model by assigning equal probability to all       DE.8.4.9 Probability: Construct an appropriate sample space and apply
outcomes, and use the model to determine probabilities of events. For example, principles of probability for a simple or compound event
Grade 7:7:Ratios and and Probability (continued)

if a student is selected at random from a class, find the probability that Jane will
be selected and the probability that a girl will be selected. CC.7.SP.7a

Develop a probability model (which may not be uniform) by observing               DE.8.4.8 Probability: Compare and make predictions based on theoretical and
frequencies in data generated from a chance process. For example, find the        experimental probabilities, using sample data generated through actual
approximate probability that a spinning penny will land heads up or that a tossed experiments or computer simulations
paper cup will land open-end down. Do the outcomes for the spinning penny
appear to be equally likely based on the observed frequencies? CC.7.SP.7b
DE.7.4.5 Probability: Construct a sample space (organized list, counting tree) to
Find probabilities of compound events using organized lists, tables, tree          determine theoretical probabilities of an event
diagrams, and simulation. CC.7.SP.8                                                DE.8.4.9 Probability: Construct an appropriate sample space and apply
principles of probability for a simple or compound event
DE.7.4.5 Probability: Construct a sample space (organized list, counting tree) to
CC.7.SP.8a Understand that, just as with simple events, the probability of a
determine theoretical probabilities of an event
compound event is the fraction of outcomes in the sample space for which the
DE.8.4.9 Probability: Construct an appropriate sample space and apply
compound event occurs.
principles of probability for a simple or compound event
Represent sample spaces for compound events using methods such as                  DE.7.4.5 Probability: Construct a sample space (organized list, counting tree) to
organized lists, tables and tree diagrams. For an event described in everyday      determine theoretical probabilities of an event
language (e.g., "rolling double sixes"), identify the outcomes in the sample space DE.8.4.9 Probability: Construct an appropriate sample space and apply
which compose the event. CC.7.SP.8b                                                principles of probability for a simple or compound event
DE.8.4.8 Probability: Compare and make predictions based on theoretical and
Design and use a simulation to generate frequencies for compound events. For experimental probabilities, using sample data generated through actual
example, use random digits as a simulation tool to approximate the answer to       experiments or computer simulations
the question: if 40% of donors have type A blood, what is the probability that it  DE.8.4.10 Probability: Investigate and describe the difference between the event
will take at least 4 donors to find one with type A blood? CC.7.SP.8c              experimental probability of a simulated event (experiment) and the theoretical
probability of the same event

Page 34 of 74                                                                          as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                     Matched Common Core Standard                                                                                                                 Delaware Standards
Understand ratio concepts and use ratio reasoning to solve problems.
DE.7.1.14 Operations: Use ratios, proportions and percents to solve
Understand the concept of a ratio and use ratio language to describe a ratio         contextualized problems
relationship between two quantities. For example, "The ratio of wings to beaks in    DE.6.2.3 Representations: Explore informal methods to model and solve real-
the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak."      world situations that involve equivalent fractions (e.g., use a table of equivalent
"For every vote candidate A received, candidate C received nearly three votes."      ratios to solve proportional reasoning problems)
CC.6.RP.1                                                                            DE.6.3.9 Measurement: Find the ratio of the circumference o the diameter of a
Grade 6: Ratios and Proportional Relationships

circular objects to obtain an estimate of ?
Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0     DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
(b not equal to zero), and use rate language in the context of a ratio relationship. measurements (e.g., recipes)
For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so
there is 3/4 cup of flour for each cup of sugar." "We paid \$75 for 15 hamburgers, DE.7.1.12 Operations: Calculate unit rate to solve real-world problems (e.g.,
which is a rate of \$5 per hamburger." (Expectations for unit rates in this grade     speed of a car, unit price of food, etc.)
are limited to non-complex fractions.) CC.6.RP.2
DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
measurements (e.g., recipes)
DE.7.1.4 Number sense: Use proportional reasoning to express rates (e.g.,
speed, density, mpg)
Use ratio and rate reasoning to solve real-world and mathematical problems,          DE.7.1.14 Operations: Use ratios, proportions and percents to solve
e.g., by reasoning about tables of equivalent ratios, tape diagrams, double          contextualized problems
number line diagrams, or equations. CC.6.RP.3                                        DE.6.2.2 Representations: Demonstrate that a given situation may be
represented by a table, graph or equation
DE.6.2.3 Representations: Explore informal methods to model and solve real-
world situations that involve equivalent fractions (e.g., use a table of equivalent
ratios to solve proportional reasoning problems)
DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
measurements (e.g., recipes)
Make tables of equivalent ratios relating quantities with whole-number               DE.6.2.2 Representations: Demonstrate that a given situation may be
measurements, find missing values in the tables, and plot the pairs of values on represented by a table, graph or equation
the coordinate plane. Use tables to compare ratios. CC.6.RP.3a                       DE.6.2.3 Representations: Explore informal methods to model and solve real-
world situations that involve equivalent fractions (e.g., use a table of equivalent
ratios to solve proportional reasoning problems)

Page 35 of 74                                                                                as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                     Matched Common Core Standard                                                                                                                  Delaware Standards
Understand ratio concepts and use ratio reasoning to solve problems.                                                                   DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
measurements (e.g., recipes)

Solve unit rate problems including those involving unit pricing and constant     DE.7.1.4 Number sense: Use proportional reasoning to express rates (e.g.,
speed. For example, If it took 7 hours to mow 4 lawns, then at that rate, how
Relationships (continued)

speed, density, mpg)
many lawns could be mowed in 35 hours? At what rate were lawns being             DE.7.1.12 Operations: Calculate unit rate to solve real-world problems (e.g.,
mowed? CC.6.RP.3b                                                                speed of a car, unit price of food, etc.)
DE.7.1.14 Operations: Use ratios, proportions and percents to solve
Grade 6: Ratios and Proportional Relationships

contextualized problems
DE.5.1.9 Number sense: Develop the meaning of percent as a ratio of a number
Find a percentage of a quantity as a rate per 100 (e.g., 30% of a quantity means out of 100
30/100 times the quantity); solve problems involving finding the whole given a   DE.6.1.6 Number sense: Demonstrate equivalence of decimals, fractions, and
part and the percentage. CC.6.RP.3c                                              percents using multiple models
DE.6.1.12 Operations: Use benchmark percents to solve problems
DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
Use ratio reasoning to convert measurement units; manipulate and transform       measurements (e.g., recipes)
units appropriately when multiplying or dividing quantities. CC.6.RP.3d          DE.5.3.14 Measurement: Convert a measurement from feet to inches, or from
meters to centimeters

Page 36 of 74                                                                         as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                          Matched Common Core Standard                                                                Delaware Standards
Understand ratio concepts and use ratio reasoning to solve problems.
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
Interpret and compute quotients of fractions, and solve word problems involving DE.6.1.9 Operations: Connect multiplication by a unit fraction (such as 1/3,1/4,
division of fractions by fractions, e.g., by using visual fraction models and       1/5, 1/10, 1/100) to division by its multiplicative inverse (3, 4, 5, 10, 100) using
equations to represent the problem. For example, create a story context for (2/3) models
÷ (3/4) and use a visual fraction model to show the quotient; use the relationship DE.7.1.10 Operations: Multiply and divide fractions and use models to justify
between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 your solution
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.). How much chocolate will each
Grade 6: Ratios and Proportional Relationships

DE.7.1.11 Operations: Use a variety of strategies to add, subtract, multiply, and
person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup
divide fractions
servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land
with length 3/4 mi and area 1/2 square mi? CC.6.NS.1
Compute fluently with multi-digit numbers and find common factors and multiples.

DE.5.1.13 Operations: Multiply and divide by large numbers (e.g., two digits by
two digits) and show why the operation works
Fluently divide multi-digit numbers using the standard algorithm. CC.6.NS.2         DE.6.1.16 Operations: Select and use appropriate methods and tools for
computing (e.g., mental computation, estimation, calculators, paper, and pencil)
depending on the context and nature of the computation
DE.5.1.23 Operations: Add and subtract decimals using models
DE.6.1.13 Operations: Explain the role of place value in adding and subtracting
decimals
DE.6.1.14 Operations: Multiply decimals to solve real-world problems (e.g., find
Fluently add, subtract, multiply, and divide multi-digit decimals using the         the cost of 3 1/2 pounds of grapes at \$1.95 per pound)
standard algorithm for each operation. CC.6.NS.3                                    DE.6.1.16 Operations: Select and use appropriate methods and tools for
computing (e.g., mental computation, estimation, calculators, paper, and pencil)
depending on the context and nature of the computation
DE.7.1.13 Operations: Justify the placement of the decimal point in the solution
to a multiplication or division problem
DE.5.1.3 Number sense: Describe numbers according to characteristics such as
Find the greatest common factor of two whole numbers less than or equal to          evens, odds, factors, multiples, and squares
100 and the least common multiple of two whole numbers less than or equal to        DE.8.1.3 Number sense: Apply knowledge of factors and multiples, evens and
12. Use the distributive property to express a sum of two whole numbers 1-100 odds, primes and composites, to generalizations
with a common factor as a multiple of a sum of two whole numbers with no            DE.5.2.6 Symbols: Develop an understanding of the Distributive Properties of
common factor. For example, express 36 + 8 as 4 (9 + 2). CC.6.NS.4                  whole number operations as a tool to solve problems (e.g., is 24 × 32 ever the
same as 20 × 30 + 4 × 2?)

Page 37 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                        Matched Common Core Standard                                                               Delaware Standards
Understand ratio concepts and use ratio reasoning to solve problems.of rational numbers.
Apply and extend previous understandings of numbers to the system
DE.4.1.7 Number sense: Explore negative numbers by extending the number
Understand that positive and negative numbers are used together to describe
line using familiar applications (elevator, temperature, sea level, debt)
quantities having opposite directions or values (e.g., temperature above/below
zero, elevation above/below sea level, debits/credits, positive/negative electric DE.5.1.10 Number sense: Use a variety of familiar applications to represent
charge); use positive and negative numbers to represent quantities in real-world positive and negative numbers as opposites
contexts, explaining the meaning of 0 in each situation. CC.6.NS.5                DE.5.1.24 Operations: Add and subtract integers using familiar applications
such as sea level, elevators, etc.
Grade 6: Ratios and Proportional Relationships

DE.5.1.6 Number sense: Use multiple models and methods to compare decimals
Grade 6: The Number System (continued)

DE.6.1.5 Number sense: Use place value structure to describe the size of
decimals
Understand a rational number as a point on the number line. Extend number line
DE.6.1.6 Number sense: Demonstrate equivalence of decimals, fractions, and
diagrams and coordinate axes familiar from previous grades to represent points
percents using multiple models
on the line and in the plane with negative number coordinates. CC.6.NS.6
DE.7.1.5 Number sense: Compare fractions, decimals, and percents using
multiple models
DE.7.1.7 Number sense: Compare integers on the number line
DE.7.1.9 Number sense: Apply knowledge of integers to the coordinate plane
DE.5.1.10 Number sense: Use a variety of familiar applications to represent
Recognize opposite signs of numbers as indicating locations on opposite sides
positive and negative numbers as opposites
of 0 on the number line; recognize that the opposite of the opposite of a number
is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. CC.6.NS.6a   DE.7.1.8 Number sense: Explain the relationship of a number to its additive
inverse
Understand signs of numbers in ordered pairs as indicating locations in             DE.5.3.5 Location and transformation: Use the coordinate system to specify
quadrants of the coordinate plane; recognize that when two ordered pairs differ locations and to describe paths between locations
only by signs, the locations of the points are related by reflections across one or DE.7.3.7 Location and transformation: Represent reflections, rotations, and
both axes. CC.6.NS.6b                                                               translations on the coordinate plane
DE.5.1.2 Number sense: Develop understanding of fractions as parts of unit
wholes, as part of a collection, as locations on number lines, and as division of
whole numbers
Find and position integers and other rational numbers on a horizontal or vertical DE.7.1.5 Number sense: Compare fractions, decimals, and percents using
number line diagram; find and position pairs of integers and other rational         multiple models
numbers on a coordinate plane. CC.6.NS.6c                                           DE.7.1.7 Number sense: Compare integers on the number line
DE.7.1.9 Number sense: Apply knowledge of integers to the coordinate plane
DE.5.3.5 Location and transformation: Use the coordinate system to specify
locations and to describe paths between locations

Page 38 of 74                                                                              as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                     Matched Common Core Standard                                                                                                                  Delaware Standards
Understand ratio concepts and use ratio reasoning to solve problems.                                                                DE.5.1.2 Number sense: Develop understanding of fractions as parts of unit
wholes, as part of a collection, as locations on number lines, and as division of
whole numbers
DE.7.1.5 Number sense: Compare fractions, decimals, and percents using
Understand the ordering and the absolute value of rational numbers. CC.6.NS.7
multiple models
Grade 6: Ratios andThe Number System (continued)

DE.7.1.8 Number sense: Explain the relationship of a number to its additive
inverse

DE.9.1.2 Number sense: Compare relative sizes of real numbers
Interpret statements of inequality as statements about the relative position of       DE.9.1.2 Number sense: Compare relative sizes of real numbers
two numbers on a number line diagram. For example, interpret -3 > -7 as a
statement that -3 is located to the right of -7 on a number line oriented from left
to right. CC.6.NS.7a
Write, interpret, and explain statements of order for rational numbers in real-       DE.7.1.5 Number sense: Compare fractions, decimals, and percents using
world contexts. For example, write -3 degrees C > -7 degrees C to express the         multiple models
fact that -3 degrees C is warmer than -7 degrees C. CC.6.NS.7b                        DE.9.1.2 Number sense: Compare relative sizes of real numbers
Understand the absolute value of a rational number as its distance from 0 on the      DE.9.1.2 Number sense: Compare relative sizes of real numbers
number line; interpret absolute value as magnitude for a positive or negative
quantity in a real-world situation. For example, for an account balance of -30
dollars, write |-30| = 30 to describe the size of the debt in dollars. CC.6.NS.7c
Distinguish comparisons of absolute value from statements about order. For            DE.9.1.2 Number sense: Compare relative sizes of real numbers
example, recognize that an account balance less than -30 dollars represents a
debt greater than 30 dollars. CC.6.NS.7d
Solve real-world and mathematical problems by graphing points in all four             DE.5.3.5 Location and transformation: Use the coordinate system to specify
quadrants of the coordinate plane. Include use of coordinates and absolute            locations and to describe paths between locations
value to find distances between points with the same first coordinate or the
same second coordinate. CC.6.NS.8

Page 39 of 74                                                                                as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                          Matched Common Core Standard                                                           Delaware Standards
problems.
Understand ratio concepts and use ratio reasoning to solvealgebraic expressions.
Apply and extend previous understandings of arithmetic to
DE.8.1.1 Number sense: Use exponential notation to represent whole numbers
Write and evaluate numerical expressions involving whole-number exponents.
CC.6.EE.1                                                                           DE.8.1.5 Operations: Perform computations with exponents, powers of 10, and
scientific notation
DE.6.2.1 Patterns and change: Use an expression or rule to describe patterns of
Write, read, and evaluate expressions in which letters stand for numbers.           change in numeric and geometric patterns
CC.6.EE.2                                                                           DE.7.2.7 Symbols: Evaluate an algebraic expression for a given value of the
Grade 6: Ratios and Proportional Relationships

variable
Write expressions that record operations with numbers and with letters standing DE.6.2.1 Patterns and change: Use an expression or rule to describe patterns of
for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.     change in numeric and geometric patterns
CC.6.EE.2a

DE.5.2.6 Symbols: Develop an understanding of the Distributive Properties of
Identify parts of an expression using mathematical terms (sum, term, product,
whole number operations as a tool to solve problems (e.g., is 24 × 32 ever the
factor, quotient, coefficient); view one or more parts of an expression as a single
same as 20 × 30 + 4 × 2?)
entity. For example, describe the expression 2(8 + 7) as a product of two
factors; view (8 + 7) as both a single entity and a sum of two terms. CC.6.EE.2b
Evaluate expressions by substituting values for their variables. Include          DE.7.2.7 Symbols: Evaluate an algebraic expression for a given value of the
expressions that arise from formulas in real-world problems. Perform arithmetic   variable
operations, including those involving whole-number exponents, in the
conventional order when there are no parentheses to specify a particular order
(Order of Operations). For example, use the formulas V = s^3 and A = 6 s^2 to
find the volume and surface area of a cube with sides of length s = 1/2.
DE.8.2.10 Symbols: Apply the order of operations
CC.6.EE.2c
DE.8.1.8 Operations: Explain how the distributive property is used to multiply
(e.g., partial products, mixed numbers)
Apply the properties of operations as strategies to generate equivalent           DE.5.2.6 Symbols: Develop an understanding of the Distributive Properties of
expressions. For example, apply the distributive property to the expression 3(2 + whole number operations as a tool to solve problems (e.g., is 24 × 32 ever the
x) to produce the equivalent expression 6 + 3x; apply properties of operations to same as 20 × 30 + 4 × 2?)
y + y + y to produce the equivalent expression 3y. CC.6.EE.3                      DE.8.2.8 Representations: Demonstrate the equivalence of two algebraic
expressions using physical models
CC.6.EE.4 Apply and extend previous understandings of arithmetic to algebraic     DE.8.2.8 Representations: Demonstrate the equivalence of two algebraic
expressions. Identify when two expressions are equivalent (i.e., when the two     expressions using physical models
expressions name the same number regardless of which value is substituted
into them). For example, the expressions y + y + y and 3y are equivalent
because they name the same number regardless of which number y stands for.

Page 40 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                     Matched Common Core Standard                                                                                                                 Delaware Standards
Understand ratio concepts and use ratio reasoning to solve problems.
Reason about and solve one-variable equations and inequalities.
DE.6.2.5 Symbols: Use inverse operations to "do and undo" number sentences
Understand solving an equation or inequality as a process of answering a
question: which values from a specified set, if any, make the equation or          DE.7.2.4 Representations: Model and solve contextualized linear problems using
inequality true? Use substitution to determine whether a given number in a         various representations (e.g., tables, graphs, equations) with respect to starting
Grade 6: Expressions and Equations (continued)

specified set makes an equation or inequality true. CC.6.EE.5                      point and rate of change
DE.7.2.8 Symbols: Solve linear equations using a variety of strategies
Use variables to represent numbers and write expressions when solving a real-      DE.5.2.5 Symbols: Use equations to express mathematical relationships
Grade 6: Ratios and Proportional Relationships

world or mathematical problem; understand that a variable can represent an
unknown number, or, depending on the purpose at hand, any number in a
specified set. CC.6.EE.6                                                            DE.7.2.6 Symbols: Write an equation to show how two variables are related
Solve real-world and mathematical problems by writing and solving equations of DE.6.2.5 Symbols: Use inverse operations to "do and undo" number sentences
the form x + p = q and px = q for cases in which p, q and x are all nonnegative
rational numbers. CC.6.EE.7                                                         DE.7.2.8 Symbols: Solve linear equations using a variety of strategies
Write an inequality of the form x > c or x < c to represent a constraint or         DE.9.2.7 Representations: Model and solve real-world linear situations, including
condition in a real-world or mathematical problem. Recognize that inequalities of linear inequalities, using tables, graphs, and symbols
the form x > c or x < c have infinitely many solutions; represent solutions of such
inequalities on number line diagrams. CC.6.EE.8
Represent and analyze quantitative relationships between dependent and independent variables.
DE.6.2.2 Representations: Demonstrate that a given situation may be
Use variables to represent two quantities in a real-world problem that change in represented by a table, graph or equation
relationship to one another; write an equation to express one quantity, thought of DE.6.2.4 Representations: Create a table and scatter plot to represent the
as the dependent variable, in terms of the other quantity, thought of as the        relationship between two variables
independent variable. Analyze the relationship between the dependent and            DE.7.2.3 Representations: Connect different representations of the same
independent variables using graphs and tables, and relate these to the equation. situation to one another using tables, graphs, and rules
DE.7.2.4 Representations: Model and solve contextualized linear problems using
For example, in a problem involving motion at constant speed, list and graph
various representations (e.g., tables, graphs, equations) with respect to starting
ordered pairs of distances and times, and write the equation d = 65t to represent
point and rate of change
the relationship between distance and time. CC.6.EE.9                               DE.7.2.5 Representations: Describe how the dependent and independent
variables are related in a given situation

Page 41 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                          Matched Common Core Standard                                                                Delaware Standards
concepts and use ratio reasoning to area, surface area, and volume.
Understand ratioand mathematical problems involvingsolve problems.
Solve real-world
Find area of right triangles, other triangles, special quadrilaterals, and polygons DE.6.3.6 Measurement: Use the conceptual knowledge of the area of rectangles
by composing into rectangles or decomposing into triangles and other shapes;        to develop formulas for the areas of triangles and parallelograms
apply these techniques in the context of solving real-world and mathematical        DE.7.3.9 Measurement: Find the area of polygons by partitioning into rectangles
problems. CC.6.G.1                                                                  and triangles
Find the volume of a right rectangular prism with fractional edge lengths by        DE.4.3.12 Measurement: Count the number of cubes it takes to fill a three-

packing it with unit cubes of the appropriate unit fraction edge lengths, and show dimensional figure (volume)
Grade 6: Ratios and Proportional Relationships

that the volume is the same as would be found by multiplying the edge lengths       DE.5.3.12 Measurement: Find the volume of an object
of the prism. Apply the formulas V = l w h and V = b h to find volumes of right     DE.7.3.12 Measurement: Determine the volume and surface areas of cylinders
rectangular prisms with fractional edge lengths in the context of solving real-     and prisms
world and mathematical problems. CC.6.G.2
Draw polygons in the coordinate plane given coordinates for the vertices; use       DE.5.3.5 Location and transformation: Use the coordinate system to specify
coordinates to find the length of a side joining points with the same first         locations and to describe paths between locations
coordinate or the same second coordinate. Apply these techniques in the             DE.9.3.3 Location and transformation: Use properties of triangles and
context of solving real-world and mathematical problems. CC.6.G.3                   quadrilaterals to construct them in the coordinate plane
Represent three-dimensional figures using nets made up of rectangles and            DE.7.3.4 Classification: Create models of nets of three-dimensional figures (e.g.,
triangles, and use the nets to find the surface area of these figures. Apply these cube, rectangular prism, cylinder)
techniques in the context of solving real-world and mathematical problems.          DE.7.3.10 Measurement: Find the surface area of prisms using physical models
CC.6.G.4
Develop understanding of statistical variability.
Recognize a statistical question as one that anticipates variability in the data    DE.6.4.1 Collect: Collect and organize numerical (whole number or decimal)
related to the question and accounts for it in the answers. For example, "How       data in order to answer a question

old am I?" is not a statistical question, but "How old are the students in my
school?" is a statistical question because one anticipates variability in students'
ages. CC.6.SP.1
DE.5.4.2 Represent: Construct and use data displays (e.g., tables, scaled
pictographs, line plots, bar graphs) in order to answer a question
DE.7.4.2 Represent: Construct displays of data for single data sets (e.g., stem-
Understand that a set of data collected to answer a statistical question has a      and-leaf plots) or in order to study the relationship between related data sets
distribution which can be described by its center, spread, and overall shape.       (scatter plots)
CC.6.SP.2                                                                           DE.8.4.3 Represent: Construct displays of data to represent individual sets of
data (e.g., histograms, box plots) or to explore the relationship between related
sets of data (scatter plots, line graphs); describe the correspondence between
data sets and their graphical displays
Recognize that a measure of center for a numerical data set summarizes all of       DE.6.4.4 Analyze: Find and use summary measures of center (mean, median,
its values using a single number, while a measure of variation describes how its mode) and spread (range) to compare sets of single variable data
values vary using a single number. CC.6.SP.3

Page 42 of 74                                                              as of 1/31/11
Common Core-Delaware Standards – Grade 6
Domain                     Matched Common Core Standard                                                                                                                            Delaware Standards
ratio concepts and use ratio
Understand and describe distributions. reasoning to solve problems.
Summarize
Grade 6: Ratios and6: Statistics and Probability (continued)                                                                                        DE.5.4.2 Represent: Construct and use data displays (e.g., tables, scaled
pictographs, line plots, bar graphs) in order to answer a question
DE.7.4.2 Represent: Construct displays of data for single data sets (e.g., stem-
and-leaf plots) or in order to study the relationship between related data sets
Display numerical data in plots on a number line, including dot plots, histograms,
(scatter plots)
and box plots. CC.6.SP.4
DE.8.4.3 Represent: Construct displays of data to represent individual sets of

data (e.g., histograms, box plots) or to explore the relationship between related
sets of data (scatter plots, line graphs); describe the correspondence between
data sets and their graphical displays
DE.5.4.3 Analyze: Compare related data sets noting similarities and differences
Summarize numerical data sets in relation to their context, such as by:              in the distributions
-- a. Reporting the number of observations.                                        DE.6.4.3 Analyze: Defend conclusions drawn from the interpretation of data by
-- b. Describing the nature of the attribute under investigation, including how it comparing one data set to another
was measured and its units of measurement.                                           DE.8.4.4 Analyze: Defend or dispute conclusions drawn from the interpretation
-- c. Giving quantitative measures of center (median and/or mean) and              of data by comparing sets of data or exploring possible relationships based upon
variability (interquartile range and/or mean absolute deviation), as well as         scatter plots of related data and approximate lines of fit
describing any overall pattern and any striking deviations from the overall pattern DE.8.4.6 Analyze: Find and use appropriate measures of center (mean, media,
with reference to the context in which the data was gathered.                        mode) and spread (range, interquartile range) to interpret data
-- d. Relating the choice of measures of center and variability to the shape of    DE.8.4.7 Analyze: Compare the usefulness of the mean and median as
the data distribution and the context in which the data was gathered. CC.6.SP.5 measures of center; describe the effect of changes in the data on the mean and
median of the data set(s)

Page 43 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 5
Domain                          Matched Common Core Standard                                                                                               Delaware Standards

Grade 5: Operations and Algebraic Thinking
Write and interpret numerical expressions.
Use parentheses, brackets, or braces in numerical expressions and evaluate                                             DE.4.1.1 Number sense: Decompose and recompose whole numbers up to
expressions with these symbols. CC.5.OA.1                                                                              10,000 using a variety of one, two- and three-digit combinations
Write simple expressions that record calculations with numbers, and interpret                                          DE.4.1.1 Number sense: Decompose and recompose whole numbers up to
numerical expressions without evaluating them. For example, express the                                                10,000 using a variety of one, two- and three-digit combinations
calculation "add 8 and 7, then multiply by 2" as 2 × (8 + 7). Recognize that 3 ×
(18932 + 921) is three times as large as 18932 + 921, without having to
calculate the indicated sum or product. CC.5.OA.2
Analyze patterns and relationships.
Generate two numerical patterns using two given rules. Identify apparent                                               DE.4.2.2 Patterns and change: Record patterns of growth in tables and graphs
relationships between corresponding terms. Form ordered pairs consisting of
corresponding terms from the two patterns, and graph the ordered pairs on a                                            DE.4.2.3 Patterns and change: Interpret tables, graphs and real-world events
coordinate plane. For example, given the rule "Add 3" and the starting number 0,                                       based on how they change over time
and given the rule "Add 6" and the starting number 0, generate terms in the
resulting sequences, and observe that the terms in one sequence are twice the
corresponding terms in the other sequence. Explain informally why this is so.
CC.5.OA.3
Understand the place value system.
Grade 5: Number and Operations in Base Ten

Recognize that in a multi-digit number, a digit in one place represents 10 times                                       DE.5.1.1 Number sense: Describe whole numbers up to 100,000 using place
as much as it represents in the place to its right and 1/10 of what it represents in                                   value structure
the place to its left. CC.5.NBT.1                                                                                      DE.5.1.4 Number sense: Find 1/10 or 10 times a number using mental math
Explain patterns in the number of zeros of the product when multiplying a                                              DE.5.1.4 Number sense: Find 1/10 or 10 times a number using mental math
number by powers of 10, and explain patterns in the placement of the decimal
DE.7.1.2 Number sense: Use powers of ten to represent place value
point when a decimal is multiplied or divided by a power of 10. Use positive
integer exponents to denote powers of 10. CC.5.NBT.2
Read, write, and compare decimals to thousandths. CC.5.NBT.3                                                           DE.5.1.6 Number sense: Use multiple models and methods to compare decimals
Read and write decimals to thousandths using base-ten numerals, number        DE.6.1.5 Number sense: Use place value structure to describe the size of
names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 ×      decimals
(1/10) + 9 × (1/100) + 2 × (1/1000). CC.5.NBT.3a
Compare two decimals to thousandths based on meanings of the digits in each   DE.5.1.6 Number sense: Use multiple models and methods to compare decimals
place, using >, =, and < symbols to record the results of comparisons.
CC.5.NBT.3b                                                                   DE.5.1.25 Operations: Select and use appropriate methods and tools for
computing (e.g., mental computation, estimation, calculators, paper and pencil)
Use place value understanding to round decimals to any place. CC.5.NBT.4      depending on the context and nature of the computation
DE.6.1.5 Number sense: Use place value structure to describe the size of
decimals

Page 44 of 74                                                                          as of 1/31/11
Common Core-Delaware Standards – Grade 5
Domain                         Matched Common Core Standard                                                                 Delaware Standards

Grade 5: Operations and Algebraic Thinking
Write and interpret numerical expressions.numbers and with decimals to hundredths.
Perform operations with multi-digit whole
Fluently multiply multi-digit whole numbers using the standard algorithm.           DE.5.1.14 Operations: Use multiplication clusters to build mental math strategies
Grade 5: Number and Operations in

CC.5.NBT.5                                                                          (e.g., 5×2, 5×20, 50×2, 50×20)
Find whole-number quotients with up to four-digit dividends and two-digit           DE.5.1.13 Operations: Multiply and divide by large numbers (e.g., two digits by
Base Ten (continued)

divisors, using strategies based on place value, the properties of operations,      two digits) and show why the operation works
and/or the relationship between multiplication and division. Illustrate and explain DE.5.1.14 Operations: Use multiplication clusters to build mental math strategies
the calculation by using equations, rectangular arrays, and/or area models.         (e.g., 5×2, 5×20, 50×2, 50×20)
DE.5.1.15 Operations: Use partial products to verify how multiplication
CC.5.NBT.6
algorithms work
DE.5.1.18 Operations: Add and subtract benchmark fractions and fractions with
common denominators using physical models
Add, subtract, multiply, and divide decimals to hundredths, using concrete          DE.6.1.13 Operations: Explain the role of place value in adding and subtracting
models or drawings and strategies based on place value, properties of               decimals
operations, and/or the relationship between addition and subtraction; relate the    DE.6.1.14 Operations: Multiply decimals to solve real-world problems (e.g., find
strategy to a written method and explain the reasoning used. CC.5.NBT.7             the cost of 3 1/2 pounds of grapes at \$1.95 per pound)
DE.7.1.13 Operations: Justify the placement of the decimal point in the solution
to a multiplication or division problem
Use equivalent fractions as a strategy to add and subtract fractions.
Add and subtract fractions with unlike denominators (including mixed numbers) DE.5.1.18 Operations: Add and subtract benchmark fractions and fractions with
by replacing given fractions with equivalent fractions in such a way as to produce common denominators using physical models
an equivalent sum or difference of fractions with like denominators. For
DE.6.1.10 Operations: Add and subtract fractions with unlike denominators and
Operations—Fractions

example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) use physical models to justify your answer

CC.5.NF.1
DE.K-12.5 Standard 5 - Problem Solving: Students will develop their Problem
Solving ability by engaging in developmentally appropriate problem-solving
Solve word problems involving addition and subtraction of fractions referring to    opportunities in which there is a need to use various approaches to investigate
the same whole, including cases of unlike denominators, e.g., by using visual       and understand mathematical concepts; to formulate their own problems; to find
fraction models or equations to represent the problem. Use benchmark fractions solutions to problems from everyday situations; to develop and apply strategies
and number sense of fractions to estimate mentally and assess the                   to solve a wide variety of problems; and to integrate mathematical reasoning,
reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 communication and connections.
DE.5.1.18 Operations: Add and subtract benchmark fractions and fractions with
= 3/7 by observing that 3/7 < 1/2. CC.5.NF.2                                        common denominators using physical models
DE.6.1.10 Operations: Add and subtract fractions with unlike denominators and

Page 45 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grade 5
Domain                          Matched Common Core Standard                                                                Delaware Standards

Grade 5: Number and Operations—Fractions (continued) Algebraic Thinking
Write and interpret numerical expressions. of multiplication and division to multiply and divide fractions.
Apply and extend previous understandings
Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). DE.5.1.16 Operations: Use and apply various meanings of multiplication and
Solve word problems involving division of whole numbers leading to answers in division (e.g., fair share, repeated addition/subtraction, compare, rate)
the form of fractions or mixed numbers, e.g., by using visual fraction models or     DE.5.1.17 Operations: Develop and use strategies to estimate the results of
equations to represent the problem. For example, interpret 3/4 as the result of      operations on whole numbers
dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes
are shared equally among 4 people each person has a share of size 3/4. If 9          DE.5.1.21 Operations: Connect multiplication by 1/3, 1/4, 1/5 to division by its

people want to share a 50-pound sack of rice equally by weight, how many             inverse (3, 4, 5) (e.g., 12 × 1/4 = 12 ÷ 4)
pounds of rice should each person get? Between what two whole numbers does DE.K-12.5.2 Solve problems that arise in mathematics and in other contexts
DE.5.1.19 Operations: Multiply fractions by whole numbers using models such
as: clock fractions, number/ratio tables, number lines, fractions strips, skip
Apply and extend previous understandings of multiplication to multiply a fraction
counting or array models
or whole number by a fraction. CC.5.NF.4
DE.6.1.8 Operations: Multiply fractions by other fractions using physical models,
ratio/rate tables, and arrays
Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;   DE.5.1.19 Operations: Multiply fractions by whole numbers using models such
equivalently, as the result of a sequence of operations a × q ÷ b. For example,      as: clock fractions, number/ratio tables, number lines, fractions strips, skip
use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context      counting or array models
for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) DE.6.1.8 Operations: Multiply fractions by other fractions using physical models,
= ac/bd.) CC.5.NF.4a                                                                 ratio/rate tables, and arrays
Find the area of a rectangle with fractional side lengths by tiling it with unit     DE.6.1.8 Operations: Multiply fractions by other fractions using physical models,
squares of the appropriate unit fraction side lengths, and show that the area is     ratio/rate tables, and arrays
the same as would be found by multiplying the side lengths. Multiply fractional
side lengths to find areas of rectangles, and represent fraction products as
rectangular areas. CC.5.NF.4b
Interpret multiplication as scaling (resizing) by:                                   DE.5.1.14 Operations: Use multiplication clusters to build mental math strategies
-- a. Comparing the size of a product to the size of one factor on the basis of    (e.g., 5×2, 5×20, 50×2, 50×20)
the size of the other factor, without performing the indicated multiplication.
DE.6.1.4 Number sense: Scale up or scale down fraction and whole number
-- b. Explaining why multiplying a given number by a fraction greater than 1
measurements (e.g., recipes)
results in a product greater than the given number (recognizing multiplication by
whole numbers greater than 1 as a familiar case); explaining why multiplying a       DE.K-12.5.1 Build new mathematical knowledge
given number by a fraction less than 1 results in a product smaller than the         DE.K-12.6.2 Make and investigate mathematical conjectures
given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b)
to the effect of multiplying a/b by 1. CC.5.NF.5
Solve real world problems involving multiplication of fractions and mixed            DE.6.1.8 Operations: Multiply fractions by other fractions using physical models,
numbers, e.g., by using visual fraction models or equations to represent the         ratio/rate tables, and arrays
problem. CC.5.NF.6

Page 46 of 74                                                                as of 1/31/11
Common Core-Delaware Standards – Grade 5
Domain                       Matched Common Core Standard                                                                                                             Delaware Standards

Grade 5: Operations and Algebraic Thinking
and interpret numerical expressions.
Write and extend previous understandings of division to divide unit fractions by
Apply
Grade 5: Number and Operations—Fractions                                                                                            DE.5.1.21 Operations: Connect multiplication by 1/3, 1/4, 1/5 to division by its
whole numbers and whole numbers by unit fractions. (Students able to multiply      inverse (3, 4, 5) (e.g., 12 × 1/4 = 12 ÷ 4)
fractions in general can develop strategies to divide fractions in general, by
reasoning about the relationship between multiplication and division. But division
of a fraction by a fraction is not a requirement at this grade.) CC.5.NF.7
Interpret division of a unit fraction by a non-zero whole number, and compute      DE.5.1.21 Operations: Connect multiplication by 1/3, 1/4, 1/5 to division by its
such quotients. For example, create a story context for (1/3) ÷ 4 and use a visual inverse (3, 4, 5) (e.g., 12 × 1/4 = 12 ÷ 4)
(continued)

fraction model to show the quotient; use the relationship between multiplication
and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. CC.5.NF.7a
Interpret division of a whole number by a unit fraction, and compute such            DE.6.2.5 Symbols: Use inverse operations to "do and undo" number sentences
quotients. For example, create a story context for 4 ÷ (1/5) and use a visual
fraction model to show the quotient; use the relationship between multiplication
and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. CC.5.NF.7b
Solve real-world problems involving division of unit fractions by non-zero whole     DE.6.1.9 Operations: Connect multiplication by a unit fraction (such as 1/3,1/4,
numbers and division of whole numbers by unit fractions, e.g., by using visual       1/5, 1/10, 1/100) to division by its multiplicative inverse (3, 4, 5, 10, 100) using
fraction models and equations to represent the problem. For example, How             models
much chocolate will each person get if 3 people share 1/2 lb of chocolate
equally? How many 1/3-cup servings are in 2 cups of raisins? CC.5.NF.7c

Page 47 of 74                                                                                  as of 1/31/11
Common Core-Delaware Standards – Grade 5
Domain                          Matched Common Core Standard                                                               Delaware Standards

Grade 5: Operations and Algebraic Thinking
Write and interpret numerical expressions.
Convert like measurement units within a given measurement system.
Convert among different-sized standard measurement units within a given             DE.5.3.14 Measurement: Convert a measurement from feet to inches, or from
measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions meters to centimeters
in solving multi-step real world problems. CC.5.MD.1                                DE.K-12.5.2 Solve problems that arise in mathematics and in other contexts
Represent and interpret data.
DE.5.1.18 Operations: Add and subtract benchmark fractions and fractions with
Make a line plot to display a data set of measurements in fractions of a unit (1/2,
common denominators using physical models
1/4, 1/8). Use operations on fractions for this grade to solve problems involving
DE.5.4.2 Represent: Construct and use data displays (e.g., tables, scaled
information presented in line plots. For example, given different measurements
pictographs, line plots, bar graphs) in order to answer a question
of liquid in identical beakers, find the amount of liquid each beaker would contain
DE.5.4.4 Analyze: Find and use measures of center (mean, median, mode) and
if the total amount in all the beakers were redistributed equally. CC.5.MD.2
spread (range) to summarize and interpret data
Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Recognize volume as an attribute of solid figures and understand concepts of        DE.4.3.12 Measurement: Count the number of cubes it takes to fill a three-
volume measurement.                                                                 dimensional figure (volume)
-- a. A cube with side length 1 unit, called a "unit cube," is said to have "one
cubic unit" of volume, and can be used to measure volume.                           DE.5.3.12 Measurement: Find the volume of an object
-- b. A solid figure which can be packed without gaps or overlaps using n unit
cubes is said to have a volume of n cubic units. CC.5.MD.3
DE.4.3.12 Measurement: Count the number of cubes it takes to fill a three-
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and
dimensional figure (volume)
improvised units. CC.5.MD.4                                                         DE.5.3.12 Measurement: Find the volume of an object
Relate volume to the operations of multiplication and addition and solve real      DE.5.3.12 Measurement: Find the volume of an object
world and mathematical problems involving volume. CC.5.MD.5
DE.4.2.6 Symbols: Develop an understanding of the Commutative and
Find the volume of a right rectangular prism with whole-number side lengths by
Associative Properties of whole number multiplication as a tool to solve
packing it with unit cubes, and show that the volume is the same as would be
problems (e.g., is 4 × 5 always the same as 5 × 4?)
found by multiplying the edge lengths, equivalently by multiplying the height by
DE.5.3.12 Measurement: Find the volume of an object
the area of the base. Represent three-fold whole-number products as volumes,
DE.7.3.13 Measurement: Demonstrate the relationship between the area of the
e.g., to represent the associative property of multiplication. CC.5.MD.5a
base and volume of prisms and cylinders
Apply the formulas V =(l)(w)(h) and V = (b)(h) for rectangular prisms to find      DE.5.3.12 Measurement: Find the volume of an object
volumes of right rectangular prisms with whole-number edge lengths in the
context of solving real-world and mathematical problems. CC.5.MD.5b
Recognize volume as additive. Find volumes of solid figures composed of two        DE.5.3.12 Measurement: Find the volume of an object
non-overlapping right rectangular prisms by adding the volumes of the non-         DE.10.3.14 Measurement: Use partitioning and formulas to find the surface area
overlapping parts, applying this technique to solve real world problems.           and volume of complex shapes
CC.5.MD.5c

Page 48 of 74                                                                         as of 1/31/11
Common Core-Delaware Standards – Grade 5
Domain                        Matched Common Core Standard                                                            Delaware Standards

Grade 5: Operations and Algebraic Thinking
Write and interpret numerical expressions.
Graph points on the coordinate plane to solve real-world and mathematical problems.
Use a pair of perpendicular number lines, called axes, to define a coordinate     DE.5.2.4 Representations: Model problem situations with objects and use
system, with the intersection of the lines (the origin) arranged to coincide with representations such as graphs, tables or equations to draw conclusion
the 0 on each line and a given point in the plane located by using an ordered
pair of numbers, called its coordinates. Understand that the first number
indicates how far to travel from the origin in the direction of one axis, and the    DE.5.3.5 Location and transformation: Use the coordinate system to specify
second number indicates how far to travel in the direction of the second axis,       locations and to describe paths between locations

with the convention that the names of the two axes and the coordinates
correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate). CC.5.G.1
DE.5.2.4 Representations: Model problem situations with objects and use
Represent real world and mathematical problems by graphing points in the first
representations such as graphs, tables or equations to draw conclusion
quadrant of the coordinate plane, and interpret coordinate values of points in the
DE.5.3.5 Location and transformation: Use the coordinate system to specify
context of the situation. CC.5.G.2
locations and to describe paths between locations
Classify two-dimensional figures into categories based on their properties.
Understand that attributes belonging to a category of two-dimensional figures      DE.5.3.1 Classification: Analyze and classify two-dimensional shapes according
also belong to all subcategories of that category. For example, all rectangles     to their properties and develop definitions for classes of shapes (e.g., a square
have four right angles and squares are rectangles, so all squares have four right is a rectangle is a parallelogram is a quadrilateral)
angles. CC.5.G.3
DE.5.3.1 Classification: Analyze and classify two-dimensional shapes according
Classify two-dimensional figures in a hierarchy based on properties. CC.5.G.4      to their properties and develop definitions for classes of shapes (e.g., a square
is a rectangle is a parallelogram is a quadrilateral)

Page 49 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grade 4

Domain                                                              Matched Common Core Standard                                                                   Delaware Standards
Use the four operations with whole numbers to solve problems.
DE.3.1.9 Operations: Use pictures and number sentences to represent
multiplication and division problems
DE.3.1.10 Operations: Develop the concept of multiplication by using models to
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as represent and count the number of groups and the number of elements in each
a statement that 35 is 5 times as many as 7 and 7 times as many as 5.                   group (e.g., repeated addition, arrays, skip counting)
Represent verbal statements of multiplicative comparisons as multiplication             DE.4.1.11 Operations: Show how multiplication and division facts up to 50 are
equations. CC.4.OA.1                                                                    related, using arrays, skip counting, and area models
DE.4.2.4 Representations: Model situations that involve the addition,
subtraction, multiplication and division of whole numbers using objects,
pictures, geometric model, and symbols
DE.3.1.3 Number sense: Connect skip counting to multiplication
Grade 4: Operations and Algebraic Thinking

Multiply or divide to solve word problems involving multiplicative comparison,
DE.4.1.8 Operations: Choose the appropriate operation to solve a word problem
e.g., by using drawings and equations with a symbol for the unknown number to
and explain why
represent the problem, distinguishing multiplicative comparison from additive
DE.4.2.5 Symbols: Represent the idea of a variable as an unknown quantity
comparison. CC.4.OA.2
using a letter or symbol
DE.4.1.8 Operations: Choose the appropriate operation to solve a word problem
Solve multistep word problems posed with whole numbers and having whole-                and explain why
number answers using the four operations, including problems in which                   DE.4.1.10 Operations: Demonstrate mastery of mental math strategies for
remainders must be interpreted. Represent these problems using equations                multiplying numbers (e.g., 25 x 8)
with a letter standing for the unknown quantity. Assess the reasonableness of           DE.4.1.13 Operations: Explain the meaning of the remainder in a division
answers using mental computation and estimation strategies including                    problem based on the context of the problem
rounding. CC.4.OA.3                                                                     DE.4.2.5 Symbols: Represent the idea of a variable as an unknown quantity
using a letter or symbol
Gain familiarity with factors and multiples.
DE.3.1.3 Number sense: Connect skip counting to multiplication
DE.4.1.2 Number sense: Determine factor pairs that make up a given number
Find all factor pairs for a whole number in the range 1-100. Recognize that a
whole number is a multiple of each of its factors. Determine whether a given            DE.4.1.12 Operations: Master multiplication facts and the related division facts
whole number in the range 1-100 is a multiple of a given one-digit number.              up to the 10s tables
Determine whether a given whole number in the range 1-100 is prime or                   DE.5.1.3 Number sense: Describe numbers according to characteristics such
composite. CC.4.OA.4                                                                    as evens, odds, factors, multiples, and squares
DE.8.1.3 Number sense: Apply knowledge of factors and multiples, evens and
odds, primes and composites, to generalizations
Generate and analyze patterns.
Generate a number or shape pattern that follows a given rule. Identify apparent DE.4.2.2 Patterns and change: Record patterns of growth in tables and graphs
features of the pattern that were not explicit in the rule itself. For example:         DE.4.2.3 Patterns and change: Interpret tables, graphs and real-world events
Given the rule "Add 3" and the starting number 1, generate terms in the                 based on how they change over time
resulting sequence and observe that the terms appear to alternate between odd
and even numbers. Explain informally why the numbers will continue to                   DE.5.2.1 Patterns and change: Find a given term in an arithmetic sequence
alternate in this way. CC.4.OA.5
Generalize place value understanding for multi-digit whole numbers.
DE.4.1.1 Number sense: Decompose and recompose whole numbers up to
Recognize that in a multi-digit whole number, a digit in one place represents ten
10,000 using a variety of one, two- and three-digit combinations
times what it represents in the place to its right. For example, recognize that
DE.5.1.14 Operations: Use multiplication clusters to build mental math
700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4
strategies (e.g., 5×2, 5×20, 50×2, 50×20)
expectations in this domain are limited to whole numbers less than or equal to
1,000,000.) CC.4.NBT.1                                                     Page 50 of 74                                                                             as of 1/31/11
Common place represents ten
Recognize that in a multi-digit whole number, a digit in one Core-Delaware Standards – Grade 4
times what it represents in the place to its right. For example, recognize that
700 ÷ 70 = 10 by applying concepts of place value and division. (Grade 4
Matched Common Core Standard                                                               Delaware Standards
Domain
expectations in this domain are limited to whole numbers less than or equal to
Use the four operations with whole numbers to solve problems.                       DE.5.1.20 Operations: Multiply numbers by 10, 1/10th, 100 and 1/100th using
1,000,000.) CC.4.NBT.1
mental math
DE.3.1.1 Number sense: Demonstrate an understanding that our number
Read and write multi-digit whole numbers using base-ten numerals, number
system is based on combinations of 1s, 10s, and 100s-place value
names, and expanded form. Compare two multi-digit numbers based on
Grade Algebraic and Operations in Base Ten

DE.4.1.1 Number sense: Decompose and recompose whole numbers up to
meanings of the digits in each place, using >, =, and < symbols to record the
10,000 using a variety of one, two- and three-digit combinations
results of comparisons. (Grade 4 expectations in this domain are limited to
DE.5.1.1 Number sense: Describe whole numbers up to 100,000 using place
whole numbers less than or equal to 1,000,000.) CC.4.NBT.2
value structure
Use place value understanding to round multi-digit whole numbers to any place. DE.4.1.18 Operations: Select and use appropriate methods and tools for
(Grade 4 expectations in this domain are limited to whole numbers less than or computing (e.g., mental computation, estimation, calculators, paper and pencil)
equal to 1,000,000.) CC.4.NBT.3                                                     depending on the context and nature of the computation
Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4: Operations and 4: NumberThinking

Fluently dd and subtract multi-digit whole numbers using the standard               DE.4.1.9 Operations: Add and subtract larger numbers (e.g., three digits + two
algorithm. (Grade 4 expectations in this domain are limited to whole numbers        digits) and explain how the operation works
less than or equal to 1,000,000. A range of algorithms may be used.)
CC.4.NBT.4
DE.4.1.11 Operations: Show how multiplication and division facts up to 50 are
Multiply a whole number of up to four digits by a one-digit whole number, and
related, using arrays, skip counting, and area models
multiply two two-digit numbers, using strategies based on place value and the
DE.5.1.12 Operations: Apply more than one operation to solve a word problem
properties of operations. Illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models. (Grade 4 expectations in         DE.5.1.14 Operations: Use multiplication clusters to build mental math
this domain are limited to whole numbers less than or equal to 1,000,000. A         strategies (e.g., 5×2, 5×20, 50×2, 50×20)
range of algorithms may be used.) CC.4.NBT.5                                        DE.5.1.15 Operations: Use partial products to verify how multiplication
algorithms work
Find whole-number quotients and remainders with up to four-digit dividends and DE.4.1.11 Operations: Show how multiplication and division facts up to 50 are
one-digit divisors, using strategies based on place value, the properties of        related, using arrays, skip counting, and area models
operations, and/or the relationship between multiplication and division. Illustrate DE.5.1.12 Operations: Apply more than one operation to solve a word problem
and explain the calculation by using equations, rectangular arrays, and/or area DE.5.1.14 Operations: Use multiplication clusters to build mental math
models. (Grade 4 expectations in this domain are limited to whole numbers           strategies (e.g., 5×2, 5×20, 50×2, 50×20)
less than or equal to 1,000,000. A range of algorithms may be used.)                DE.5.1.15 Operations: Use partial products to verify how multiplication
CC.4.NBT.6                                                                          algorithms work

Page 51 of 74                                                                          as of 1/31/11
Common Core-Delaware Standards – Grade 4

Domain                                                                                   Matched Common Core Standard                                                             Delaware Standards
four operations with whole numbers to solve problems.
Use theunderstanding of fraction equivalence and ordering.
Extend
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using       DE.4.1.4 Number sense: Demonstrate equivalent forms of common fractions
visual fraction models, with attention to how the number and size of the parts        using physical models, pictures, and number lines
Operations—Fractions

differ even though the two fractions themselves are the same size. Use this

principle to recognize and generate equivalent fractions. (Grade 4 expectations
in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12,
100.) CC.4.NF.1
Compare two fractions with different numerators and different denominators,           DE.4.1.5 Number sense: Compare and order fractions using physical models,
e.g., by creating common denominators or numerators, or by comparing to a             pictures, and number lines
benchmark fraction such as 1/2. Recognize that comparisons are valid only
when the two fractions refer to the same whole. Record the results of
Grade 4: Operations and Algebraic Thinking

comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using
a visual fraction model. (Grade 4 expectations in this domain are limited to
fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.) CC.4.NF.2

Page 52 of 74                                                                       as of 1/31/11
Common Core-Delaware Standards – Grade 4

Domain                                                                         Matched Common Core Standard                                                               Delaware Standards
Use the four operations with whole numbers to solve problems.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
wholes
Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (Grade 4
DE.4.1.3 Number sense: Develop an understanding of fractions as parts of unit
expectations in this domain are limited to fractions with denominators 2, 3, 4, 5,
wholes and division of whole numbers
6, 8, 10, 12, 100.) CC.4.NF.3
DE.4.3.7 Measurement: Extend the precision of a standard measurement by
using fraction strips to develop 1/2, 1/4 or 1/10 as a "unit of measure."
Understand addition and subtraction of fractions as joining and separating parts DE.4.1.15 Operations: Use physical models and pictures to add and subtract
Grade 4: Number and Operations—Fractions (continued)

referring to the same whole. CC.4.NF.3a                                            benchmark fractions
Decompose a fraction into a sum of fractions with the same denominator in          DE.4.1.15 Operations: Use physical models and pictures to add and subtract
more than one way, recording each decomposition by an equation. Justify            benchmark fractions
decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 +      DE.3.3.11 Measurement: Make number lines and break each unit into smaller
Grade 4: Operations and Algebraic Thinking

1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8. CC.4.NF.3b    units (e.g., 1/2 units, 1/3 units, 1/4 units)
Add and subtract mixed numbers with like denominators, e.g., by replacing          DE.4.1.15 Operations: Use physical models and pictures to add and subtract
each mixed number with an equivalent fraction, and/or by using properties of       benchmark fractions
operations and the relationship between addition and subtraction. CC.4.NF.3c
Solve word problems involving addition and subtraction of fractions referring to   DE.4.1.15 Operations: Use physical models and pictures to add and subtract
the same whole and having like denominators, e.g., by using visual fraction        benchmark fractions
models and equations to represent the problem. CC.4.NF.3d
DE.4.1.16 Operations: Find 1/3, 1/4, and 1/5 of a given set or area using models
Apply and extend previous understandings of multiplication to multiply a fraction
by a whole number. (Grade 4 expectations in this domain are limited to fractions DE.5.1.19 Operations: Multiply fractions by whole numbers using models such
with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.) CC.4.NF.4                        as: clock fractions, number/ratio tables, number lines, fractions strips, skip
counting or array models
Understand a fraction a/b as a multiple of 1/b. For example, use a visual          DE.5.1.19 Operations: Multiply fractions by whole numbers using models such
fraction model to represent 5/4 as the product 5 × (1/4), recording the            as: clock fractions, number/ratio tables, number lines, fractions strips, skip
conclusion by the equation 5/4 = 5 × (1/4). CC.4.NF.4a                             counting or array models
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to DE.5.1.19 Operations: Multiply fractions by whole numbers using models such
multiply a fraction by a whole number. For example, use a visual fraction model as: clock fractions, number/ratio tables, number lines, fractions strips, skip
to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n counting or array models
× (a/b) = (n × a)/b.) CC.4.NF.4b
DE.5.1.19 Operations: Multiply fractions by whole numbers using models such
Solve word problems involving multiplication of a fraction by a whole number,      as: clock fractions, number/ratio tables, number lines, fractions strips, skip
e.g., by using visual fraction models and equations to represent the problem.      counting or array models
For example: If each person at a party will eat 3/8 of a pound of roast beef, and
there will be 5 people at the party, how many pounds of roast beef will be

Page 53 of 74                                                                         as of 1/31/11
Common Core-Delaware Standards – Grade 4

Domain                                                                                     Matched Common Core Standard                                                             Delaware Standards
operations with for fractions, and solve problems.
Use the fourdecimal notationwhole numbers to compare decimal fractions.
Understand
Express a fraction with denominator 10 as an equivalent fraction with               DE.5.1.5 Number sense: Generate and connect equivalent forms of benchmark

denominator 100, and use this technique to add two fractions with respective        fractions, decimals and percents
denominators 10 and 100. For example, express 3/10 as 30/100 and add 3/10
DE.5.1.8 Number sense: Use multiple methods and models to convert decimals
+ 4/100 = 34/100. (Students who can generate equivalent fractions can develop
to fractions and fractions to decimals
and subtraction with unlike denominators in general is not a requirement at this    DE.6.1.13 Operations: Explain the role of place value in adding and subtracting
(continued)

DE.5.1.5 Number sense: Generate and connect equivalent forms of benchmark
Use decimal notation for fractions with denominators 10 or 100. For example,
fractions, decimals and percents
rewrite 0.62 as 1 62/100 ; describe a length as 0.62 meters; locate 0.62 on a
number line diagram. (Grade 4 expectations in this domain are limited to            DE.5.1.8 Number sense: Use multiple methods and models to convert decimals
Grade 4: Operations and Algebraic Thinking

fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.) CC.4.NF.6               to fractions and fractions to decimals
Compare two decimals to hundredths by reasoning about their size. Recognize         DE.6.1.5 Number sense: Use place value structure to describe the size of
that comparisons comparisons are valid only when two decimals refer to the          decimals
same whole. Record the results of comparisons with the symbols >, =, or <, and
DE.6.1.6 Number sense: Demonstrate equivalence of decimals, fractions, and
justify the conclusions, e.g., by using a visual model. (Grade 4 expectations in
percents using multiple models
this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12,
100.) CC.4.NF.7

Page 54 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 4

Domain                                                                    Matched Common Core Standard                                                               Delaware Standards
to solve problems.
Use the four operations with whole numbers conversion of measurements from a larger unit to a smaller unit.
Solve problems involving measurement and
Know relative sizes of measurement units within one system of units including       DE.5.3.14 Measurement: Convert a measurement from feet to inches, or from
km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of           meters to centimeters
measurement, express measurements in a larger unit in terms of smaller unit.
Record measurement equivalents in a two-column table. For example: Know
that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in.
Generate a conversion table for feet and inches listing the number pairs (1, 12),
(2, 24), (3, 36), .... CC.4.MD.1
DE.K-12.5 Standard 5 - Problem Solving: Students will develop their Problem
Solving ability by engaging in developmentally appropriate problem-solving
opportunities in which there is a need to use various approaches to investigate
Use the four operations to solve word problems involving distances, intervals of
Grade 4: Operations 4: Measurement and Data

and understand mathematical concepts; to formulate their own problems; to find
time, liquid volumes, masses of objects, and money, including problems

solutions to problems from everyday situations; to develop and apply strategies
involving simple fractions or decimals, and problems that require expressing
to solve a wide variety of problems; and to integrate mathematical reasoning,
measurements given in a larger unit in terms of a smaller unit. Represent
communication and connections.
measurement quantities using diagrams such as number line diagrams that
DE.3.3.11 Measurement: Make number lines and break each unit into smaller
feature a measurement scale. CC.4.MD.2
units (e.g., 1/2 units, 1/3 units, 1/4 units)
DE.4.3.7 Measurement: Extend the precision of a standard measurement by
using fraction strips to develop 1/2, 1/4 or 1/10 as a "unit of measure."
DE.4.1.11 Operations: Show how multiplication and division facts up to 50 are
related, using arrays, skip counting, and area models
Apply the area and perimeter formulas for rectangles in real world and              DE.4.2.5 Symbols: Represent the idea of a variable as an unknown quantity
mathematical problems. For example, find the width of a rectangular room given using a letter or symbol
the area of the flooring and the length, by viewing the area formula as a           DE.4.3.10 Measurement: Find the distance around a geometric figure to the
multiplication equation with an unknown factor. CC.4.MD.3                           nearest whole number (perimeter)
DE.4.3.11 Measurement: Find the number of square units it takes to cover a
rectangle (area)
Represent and interpret data.
DE.4.1.15 Operations: Use physical models and pictures to add and subtract
Make a line plot to display a data set of measurements in fractions of a unit
benchmark fractions
(1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by
DE.4.4.3 Represent: Construct and use data displays (e.g., tables, scaled
using information presented in line plots. For example, from a line plot find and
pictographs, bar graphs, line plots) in order to answer a question
interpret the difference in length between the longest and shortest specimens in
DE.4.4.4 Analyze: Describe a set of data as a whole, noting important features
an insect collection. CC.4.MD.4
such as concentration of values, spread of the values, and extreme values

Page 55 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grade 4

Domain                                                                                               Matched Common Core Standard                                                        Delaware Standards
Use the four operations with whole numbers to solve problems.
Geometric measurement: understand concepts of angle and measure angles.
Recognize angles as geometric shapes that are formed wherever two rays           DE.4.3.9 Measurement: Use a ruler to draw lines or geometric figures with
Grade 4: Measurement and Data (continued)

share a common endpoint, and understand concepts of angle measurement:           given measurements
-- a. An angle is measured with reference to a circle with its center at the
common endpoint of the rays, by considering the fraction of the circular arc
between the points where the two rays intersect the circle. An angle that turns
through 1/360 of a circle is called a "one-degree angle," and can be used to
measure angles.
-- b. An angle that turns through n one-degree angles is said to have an angle
measure of n degrees. CC.4.MD.5
Geometric measurement: understand concepts of angle and measure angles.
Measure angles in whole-number degrees using a protractor. Sketch angles of DE.5.3.8 Measurement: Use measuring tools to find the size of turn angles in

specified measure. CC.4.MD.6                                                     degrees
Geometric measurement: understand concepts of angle and measure angles.          DE.4.2.5 Symbols: Represent the idea of a variable as an unknown quantity
Recognize angle measure as additive. When an angle is decomposed into non- using a letter or symbol
overlapping parts, the angle measure of the whole is the sum of the angle
measures of the parts. Solve addition and subtraction problems to find unknown DE.6.3.3 Classification: Explore the measure of a single angle and find the sum
angles on a diagram in real world and mathematical problems, e.g., by using an of the angles of a regular polygon
equation with a symbol for the unknown angle measure. CC.4.MD.7
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
DE.4.3.1 Classification: Identify and classify two-dimensional and three-
dimensional shapes according to their properties
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and     DE.5.3.3 Classification: Identify and classify angles as acute, right, obtuse, or
4: Geometry

perpendicular and parallel line. Identify these in two-dimensional figures.     straight
CC.4.G.1                                                                        DE.6.3.1 Classification: Estimate, measure, and classify angles
DE.6.3.2 Classification: Identify geometric relationships in the real world (e.g.,
parallel lines, perpendicular lines, etc.)
DE.4.3.1 Classification: Identify and classify two-dimensional and three-
Classify two-dimensional figures based on the presence or absence of parallel
dimensional shapes according to their properties
or perpendicular lines, or the presence or absence of angles of specified size.
DE.5.3.3 Classification: Identify and classify angles as acute, right, obtuse, or
Recognize right triangles as a category, and identify right triangles. CC.4.G.2
straight
Recognize a line of symmetry for a two-dimensional figure as a line across the  DE.4.3.3 Location and transformation: Identify line and rotational symmetry in
figure such that the figure can be folded along the line into matching parts.   two-dimensional shapes
Identify line-symmetric figures and draw lines of symmetry. CC.4.G.3

Page 56 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grade 3
Domain                                                               Matched Common Core Standard                                                              Delaware Standards
Represent and solve problems involving multiplication and division.
DE.3.1.3 Number sense: Connect skip counting to multiplication
DE.3.1.9 Operations: Use pictures and number sentences to represent
Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of
multiplication and division problems
objects in 5 groups of 7 objects each. For example, , describe a context in which
DE.3.1.10 Operations: Develop the concept of multiplication by using models to
a total number of objects can be expressed as 5 × 7. CC.3.OA.1
represent and count the number of groups and the number of elements in each
group (e.g., repeated addition, arrays, skip counting)
Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the DE.3.1.9 Operations: Use pictures and number sentences to represent
number of objects in each share when 56 objects are partitioned equally into 8    multiplication and division problems
shares, or as a number of shares when 56 objects are partitioned into equal
shares of 8 objects each. For example, describe a context in which a number of
Grade 3: Operations and Algebraic Thinking

shares or a number of groups can be expressed as 56 ÷ 8. CC.3.OA.2

DE.4.1.8 Operations: Choose the appropriate operation to solve a word problem
and explain why
Use multiplication and division within 100 to solve word problems in situations     DE.5.1.16 Operations: Use and apply various meanings of multiplication and
involving equal groups, arrays, and measurement quantities, e.g., by using          division (e.g., fair share, repeated addition/subtraction, compare, rate)
drawings and equations with a symbol for the unknown number to represent the DE.3.2.3 Representations: Model situations that involve the addition,
problem. CC.3.OA.3                                                                  subtraction, and multiplication of whole numbers using objects, pictures,
symbols, and geometric models
DE.3.2.4 Symbols: Represent the idea of an unknown quantity using a letter or a
symbol
Determine the unknown whole number in a multiplication or division equation         DE.3.2.4 Symbols: Represent the idea of an unknown quantity using a letter or a
relating three whole numbers. For example, determine the unknown number that symbol
makes the equation true in each of the equations 8 × ? = 48, 5 = __÷ 3, 6 × 6 =
?. CC.3.OA.4
Understand properties of multiplication and the relationship between multiplication and division.
Apply properties of operations as strategies to multiply and divide. Examples: If DE.4.1.10 Operations: Demonstrate mastery of mental math strategies for
6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of        multiplying numbers (e.g., 25 x 8)
multiplication.) 3 × 5 × 2 can be found by multiplying 3 × 5 = 15 then multiplying DE.4.2.6 Symbols: Develop an understanding of the Commutative and
15 × 2 = 30, or by multiplying 5 × 2 = 10 then multiplying 3 × 10 = 30.             Associative Properties of whole number multiplication as a tool to solve
(Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, problems (e.g., is 4 × 5 always the same as 5 × 4?)
one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive
property.) (Students need not use formal terms for these properties.) CC.3.OA.5

DE.4.1.2 Number sense: Determine factor pairs that make up a given number
Understand division as an unknown-factor problem. For example, divide 32 ÷ 8
by finding the number that makes 32 when multiplied by 8. CC.3.OA.6               DE.4.1.11 Operations: Show how multiplication and division facts up to 50 are
related, using arrays, skip counting, and area models

Page 57 of 74                                                                                    as of 1/31/11
Common Core-Delaware Standards – Grade 3
Domain                                                                                          Matched Common Core Standard                                                              Delaware Standards
Represent and solve problems involving multiplication and division.
Multiply and divide within 100.

Grade 3: Operations and Algebraic Thinking
Fluently multiply and divide within 100, using strategies such as the relationship DE.4.1.12 Operations: Master multiplication facts and the related division facts
between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 up to the 10s tables
÷ 5 = 8) or properties of operations. By end of Grade 3, know from memory all
products of one-digit numbers. CC.3.OA.7
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Solve two-step word problems using the four operations. Represent these            DE.3.1.8 Operations: Develop and use strategies to estimate the results of
problems using equations with a letter standing for the unknown quantity.          addition and subtraction operations on whole numbers
(continued)

Assess the reasonableness of answers using mental computation and                  DE.4.1.14 Operations: Develop and use strategies to estimate the results of
estimation strategies including rounding. (This standard is limited to problems    operations on whole numbers
Grade 3: Operations and Algebraic Thinking

posed with whole numbers and having whole-number answers; students should DE.3.2.4 Symbols: Represent the idea of an unknown quantity using a letter or a
know how to perform operations in the conventional order when there are no         symbol
parentheses to specify a particular order.) CC.3.OA.8
DE.2.2.3 Patterns and change: Create and extend patterns and then translate
Identify arithmetic patterns (including patterns in the addition table or          them into a rule or drawing
multiplication table), and explain them using properties of operations. For        DE.2.2.4 Patterns and change: Describe the rule for a pattern
example, observe that 4 times a number is always even, and explain why 4           DE.3.2.1 Patterns and change: Find numeric patterns in a hundreds table
times a number can be decomposed into two equal addends. CC.3.OA.9                 DE.3.2.2 Patterns and change: Describe the patterns that result when skip-
counting
Use place value understanding and properties of operations to perform multi-digit arithmetic.
DE.3.1.11 Operations: Select and use appropriate methods and tools for
Operations in Base Ten

Use place value understanding to round whole numbers to the nearest 10 or

computing (e.g., mental computation, estimation, calculators, paper and pencil)
100. CC.3.NBT.1
depending on the context and nature of the computation
DE.3.1.6 Operations: Add and subtract numbers up to 100 efficiently and explain
Fluently add and subtract within 1000 using strategies and algorithms based on
the strategies used
place value, properties of operations, and/or the relationship between addition
DE.4.1.9 Operations: Add and subtract larger numbers (e.g., three digits + two
and subtraction. (A range of algorithms may be used.) CC.3.NBT.2
digits) and explain how the operation works
DE.4.1.10 Operations: Demonstrate mastery of mental math strategies for
Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 ×
multiplying numbers (e.g., 25 x 8)
80, 5 × 60) using strategies based on place value and properties of operations.
DE.5.1.14 Operations: Use multiplication clusters to build mental math strategies
(A range of algorithms may be used.) CC.3.NBT.3
(e.g., 5×2, 5×20, 50×2, 50×20)

Page 58 of 74                                                                                    as of 1/31/11
Common Core-Delaware Standards – Grade 3
Domain                                                                  Matched Common Core Standard                                                              Delaware Standards
Represent and solve problems involving multiplication and division.
Develop understanding of fractions as numbers.
Understand a fraction 1/b as the quantity formed by 1 part when a whole is          DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
partitioned into b equal parts; understand a fraction a/b as the quantity formed    wholes
by a parts of size 1/b. CC.3.NF.1
Understand a fraction as a number on the number line; represent fractions on a      DE.3.3.11 Measurement: Make number lines and break each unit into smaller
number line diagram. CC.3.NF.2                                                      units (e.g., 1/2 units, 1/3 units, 1/4 units)
Represent a fraction 1/b on a number line diagram by defining the interval from     DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
0 to 1 as the whole and partitioning it into b equal parts. Recognize that each     wholes

part has size 1/b and that the endpoint of the part based at 0 locates the number   DE.3.3.11 Measurement: Make number lines and break each unit into smaller
1/b on the number line. CC.3.NF.2a                                                  units (e.g., 1/2 units, 1/3 units, 1/4 units)
Grade 3: Operations and Algebraic Thinking

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b      DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
from 0. Recognize that the resulting interval has size a/b and that its endpoint    wholes
locates the number a/b on the number line. CC.3.NF.2b                               DE.3.3.11 Measurement: Make number lines and break each unit into smaller
units (e.g., 1/2 units, 1/3 units, 1/4 units)
DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
Explain equivalence of fractions in special cases, and compare fractions by         wholes
DE.3.1.5 Number sense: Compare the size of common fractions using models
DE.4.1.4 Number sense: Demonstrate equivalent forms of common fractions
using physical models, pictures, and number lines
Understand two fractions as equivalent (equal) if they are the same size, or the    DE.4.1.4 Number sense: Demonstrate equivalent forms of common fractions
same point on a number line. CC.3.NF.3a                                             using physical models, pictures, and number lines
Recognize and generate simple equivalent fractions (e.g., 1/2 = 2/4, 4/6 = 2/3);    DE.4.1.4 Number sense: Demonstrate equivalent forms of common fractions
explain why the fractions are equivalent, e.g., by using a visual fraction model.   using physical models, pictures, and number lines
CC.3.NF.3b
DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
Express whole numbers as fractions, and recognize fractions that are equivalent
wholes
to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 =
DE.4.1.3 Number sense: Develop an understanding of fractions as parts of unit
6; locate 4/4 and 1 at the same point of a number line diagram. CC.3.NF.3c
wholes and division of whole numbers
Compare two fractions with the same numerator or the same denominator, by         DE.3.1.5 Number sense: Compare the size of common fractions using models
reasoning about their size; recognize that valid comparisons rely on the two      DE.4.1.4 Number sense: Demonstrate equivalent forms of common fractions
fractions referring to the same whole. Record the results of comparisons with the using physical models, pictures, and number lines
symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction DE.4.1.5 Number sense: Compare and order fractions using physical models,
model. CC.3.NF.3d                                                                 pictures, and number lines

Page 59 of 74                                                                              as of 1/31/11
Common Core-Delaware Standards – Grade 3
Domain                                                                          Matched Common Core Standard                                                                   Delaware Standards
Represent and solve problems involvingand estimation and division. time, liquid volumes, and masses of objects.
Solve problems involving measurement multiplication of intervals of
Tell and write time to the nearest minute and measure time intervals in minutes. DE.4.3.15 Measurement: Tell time to the nearest five minutes
Solve word problems involving addition and subtraction of time intervals in
minutes, e.g., by representing the problem on a number line diagram. CC.3.MD.1 DE.5.3.15 Measurement: Find elapsed time
Measure and estimate liquid volumes and masses of objects using standard                 DE.3.3.13 Measurement: Fill up measuring devices (e.g., measuring cups) to
units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide   informally find volume
Grade 3: Operations and Algebraic Thinking and Data

to solve one-step word problems involving masses or volumes that are given in
the same units, e.g., by using drawings (such as a beaker with a measurement             DE.4.3.13 Measurement: Use measuring cups and graduated cylinders to find
scale) to represent the problem. (Excludes compound units such as cm^3 and               volume
finding the geometric volume of a container.) CC.3.MD.2

Represent and interpret data.
DE.3.4.2 Represent: Demonstrate a variety of informal and conventional
Draw a scaled picture graph and a scaled bar graph to represent a data set with          techniques for representing and organizing categorical and numerical data (e.g.,
several categories. Solve one- and two-step "how many more" and "how many                tallies, tables, pictographs, bar graphs)
less" problems using information presented in scaled bar graphs. For example,            DE.3.4.3 Analyze: See and describe data as a whole, describing the shape of
draw a bar graph in which each square in the bar graph might represent 5 pets.           the distribution; reason about how individual pieces of data relate to the whole
CC.3.MD.3                                                                                DE.4.4.3 Represent: Construct and use data displays (e.g., tables, scaled
pictographs, bar graphs, line plots) in order to answer a question
DE.5.1.2 Number sense: Develop understanding of fractions as parts of unit
wholes, as part of a collection, as locations on number lines, and as division of
Generate measurement data by measuring lengths using rulers marked with
whole numbers
halves and fourths of an inch. Show the data by making a line plot, where the
DE.3.3.11 Measurement: Make number lines and break each unit into smaller
horizontal scale is marked off in appropriate units-whole numbers, halves, or
units (e.g., 1/2 units, 1/3 units, 1/4 units)
quarters. CC.3.MD.4
DE.4.4.3 Represent: Construct and use data displays (e.g., tables, scaled
pictographs, bar graphs, line plots) in order to answer a question

Page 60 of 74                                                                                      as of 1/31/11
Common Core-Delaware Standards – Grade 3
Domain                                                                       Matched Common Core Standard                                                             Delaware Standards
Represent and solve problems involving multiplication and division. to multiplication and to addition.
Geometric measurement: understand concepts of area                   relate area
Recognize area as an attribute of plane figures and understand concepts of area DE.3.3.12 Measurement: Find the area of a design by counting the number of
measurement.                                                                      units used to cover or fill it (e.g., pattern blocks, color tiles)
-- a. A square with side length 1 unit, called "a unit square," is said to have DE.4.3.11 Measurement: Find the number of square units it takes to cover a
"one square unit" of area, and can be used to measure area.                       rectangle (area)
-- b. A plane figure which can be covered without gaps or overlaps by n unit    DE.5.3.11 Measurement: Find the number of square units it takes to cover a
squares is said to have an area of n square units. CC.3.MD.5                      geometric figure (area)
DE.3.3.12 Measurement: Find the area of a design by counting the number of
units used to cover or fill it (e.g., pattern blocks, color tiles)
Measure areas by counting unit squares (square cm, square m, square in,           DE.4.3.11 Measurement: Find the number of square units it takes to cover a
Grade 3: Measurement and Data (continued) Thinking

square ft, and improvised units). CC.3.MD.6                                       rectangle (area)
DE.5.3.11 Measurement: Find the number of square units it takes to cover a
geometric figure (area)
DE.3.1.10 Operations: Develop the concept of multiplication by using models to

Relate area to the operations of multiplication and addition. CC.3.MD.7           represent and count the number of groups and the number of elements in each
group (e.g., repeated addition, arrays, skip counting)
DE.3.1.10 Operations: Develop the concept of multiplication by using models to
Find the area of a rectangle with whole-number side lengths by tiling it, and     represent and count the number of groups and the number of elements in each
show that the area is the same as would be found by multiplying the side          group (e.g., repeated addition, arrays, skip counting)
lengths. CC.3.MD.7a                                                               DE.3.3.12 Measurement: Find the area of a design by counting the number of
units used to cover or fill it (e.g., pattern blocks, color tiles)
DE.3.1.10 Operations: Develop the concept of multiplication by using models to
Multiply side lengths to find areas of rectangles with whole-number side lengths represent and count the number of groups and the number of elements in each
in the context of solving real-world and mathematical problems, and represent     group (e.g., repeated addition, arrays, skip counting)
whole-number products as rectangular areas in mathematical reasoning.             DE.3.3.12 Measurement: Find the area of a design by counting the number of
CC.3.MD.7b                                                                        units used to cover or fill it (e.g., pattern blocks, color tiles)
DE.K-12.5.2 Solve problems that arise in mathematics and in other contexts
Use tiling to show in a concrete case that the area of a rectangle with whole-    DE.5.2.6 Symbols: Develop an understanding of the Distributive Properties of
number side lengths a and b + c is the sum of a × b and a × c. Use area models whole number operations as a tool to solve problems (e.g., is 24 × 32 ever the
to represent the distributive property in mathematical reasoning. CC.3.MD.7c      same as 20 × 30 + 4 × 2?)
DE.3.3.3 Classification: Describe, and reason about the results of subdividing
and combining shapes
Recognize area as additive. Find areas of rectilinear figures by decomposing
DE.3.3.12 Measurement: Find the area of a design by counting the number of
them into non-overlapping rectangles and adding the areas of the non-
units used to cover or fill it (e.g., pattern blocks, color tiles)
overlapping parts, applying this technique to solve real-world problems.
DE.5.3.2 Classification: Draw the results of subdividing and combining shapes
CC.3.MD.7d
DE.5.3.11 Measurement: Find the number of square units it takes to cover a
geometric figure (area)
Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
DE.4.3.10 Measurement: Find the distance around a geometric figure to the
Solve real-world and mathematical problems involving perimeters of polygons,      nearest whole number (perimeter)
including finding the perimeter given the side lengths, finding an unknown side   DE.6.3.7 Measurement: Demonstrate an understanding that the perimeters of
length, and exhibiting rectangles with the same perimeter and different area or   rectangles with a fixed area can vary
with the same area and different perimeter. CC.3.MD.8                             DE.6.3.8 Measurement: Demonstrate an understanding that the areas of
rectangles with a fixed perimeter can vary

Page 61 of 74                                                                                 as of 1/31/11
Common Core-Delaware Standards – Grade 3
Domain                                                                Matched Common Core Standard                                                                Delaware Standards
Reason with shapes problems involving
Represent and solve and their attributes. multiplication and division.
Understand that shapes in different categories (e.g., rhombuses, rectangles, and     DE.4.3.1 Classification: Identify and classify two-dimensional and three-

others) may share attributes (e.g., having four sides), and that the shared          dimensional shapes according to their properties
attributes can define a larger category (e.g., quadrilaterals). Recognize            DE.5.3.1 Classification: Analyze and classify two-dimensional shapes according
rhombuses, rectangles, and squares as examples of quadrilaterals, and draw           to their properties and develop definitions for classes of shapes (e.g., a square
examples of quadrilaterals that do not belong to any of these subcategories.         is a rectangle is a parallelogram is a quadrilateral)
CC.3.G.1
Partition shapes into parts with equal areas. Express the area of each part as a     DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
unit fraction of the whole. For example, partition a shape into 4 parts with equal   wholes
area, and describe the area of each part is 1/4 of the area of the shape.            DE.3.1.5 Number sense: Compare the size of common fractions using models
CC.3.G.2
Grade 3: Operations and Algebraic Thinking

Page 62 of 74                                                                                      as of 1/31/11
Common Core-Delaware Standards – Grade 2
Domain                                                             Matched Common Core Standard                                                                 Delaware Standards
Represent and solve problems involving addition and subtraction.
DE.K-12.5 Standard 5 - Problem Solving: Students will develop their Problem
Solving ability by engaging in developmentally appropriate problem-solving
opportunities in which there is a need to use various approaches to investigate
and understand mathematical concepts; to formulate their own problems; to find
solutions to problems from everyday situations; to develop and apply strategies
to solve a wide variety of problems; and to integrate mathematical reasoning,
communication and connections.
DE.2.1.8 Operations: Use a variety of strategies to solve combination and
separation problems up to 100
Use addition and subtraction within 100 to solve one- and two-step word             DE.2.1.9 Operations: Show number sentences that demonstrate that addition
problems involving situations of adding to, taking from, putting together, taking   and subtraction are inverse operations (e.g., join, separate, part-part-whole,
apart, and comparing, with unknowns in all positions, e.g., by using drawings
Grade 2: Operations and Algebraic Thinking

compare)
and equations with a symbol for the unknown number to represent the problem.        DE.3.1.6 Operations: Add and subtract numbers up to 100 efficiently and explain
CC.2.OA.1                                                                           the strategies used
DE.3.1.11 Operations: Select and use appropriate methods and tools for
computing (e.g., mental computation, estimation, calculators, paper and pencil)
depending on the context and nature of the computation
DE.2.2.5 Representations: Model situations that involve the addition and
subtraction of whole numbers, using objects, pictures, geometric models and
symbols (e.g., multiplicative thinking may be represented by repeated addition
and fair shares by repeated subtraction)
DE.5.2.4 Symbols: Represent the idea of an unknown quantity using a letter or a
symbol
Fluently add and subtract within 20 using mental strategies. By end of Grade 2,     DE.3.1.7 Operations: Master addition and subtraction facts up to 20
know from memory all sums of two one-digit numbers. CC.2.OA.2
Work with equal groups of objects to gain foundations for multiplication.
Determine whether a group of objects (up to 20) has an odd or even number of        DE.1.1.7 Operations: Use manipulatives and models to demonstrate doubles
members, e.g., by pairing objects or counting them by 2s; write an equation to      DE.2.1.1 Number sense: Develop efficient strategies for counting (e.g., skip
express an even number as a sum of two equal addends. CC.2.OA.3                     counting by 1s, 2s, 5s and 10s)
DE.2.1.1 Number sense: Develop efficient strategies for counting (e.g., skip
counting by 1s, 2s, 5s and 10s)
DE.2.1.10 Operations: Represent repeated addition using pictures and models
DE.3.1.9 Operations: Use pictures and number sentences to represent
Use addition to find the total number of objects arranged in rectangular arrays     multiplication and division problems
with up to 5 rows and up to 5 columns; write an equation to express the total as    DE.3.1.10 Operations: Develop the concept of multiplication by using models to
a sum of equal addends. CC.2.OA.4                                                   represent and count the number of groups and the number of elements in each
group (e.g., repeated addition, arrays, skip counting)
DE.2.2.5 Representations: Model situations that involve the addition and
subtraction of whole numbers, using objects, pictures, geometric models and
symbols (e.g., multiplicative thinking may be represented by repeated addition
and fair shares by repeated subtraction)

Page 63 of 74                                                                            as of 1/31/11
Common Core-Delaware Standards – Grade 2
Domain                                                                                              Matched Common Core Standard                                                          Delaware Standards
Represent and solve problems involving addition and subtraction.
Understand place value.
Grade 2: Operations and Algebraic Thinking and Operations in Base Ten   Understand that the three digits of a three-digit number represent amounts of      DE.2.1.2 Number sense: Demonstrate an understanding that our number
hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.         system is based on combinations of ones and tens-place value
Understand the following as special cases:                                         DE.3.1.1 Number sense: Demonstrate an understanding that our number
-- a. 100 can be thought of as a bundle of ten tens - called a "hundred."         system is based on combinations of 1s, 10s, and 100s-place value
-- b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one,       DE.2.2.6 Symbols: Record mathematical thinking using conventional notation
two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0
ones). CC.2.NBT.1
DE.1.1.1 Number sense: Count sets of objects up to 50 by 1s, 2s, 5s, and 10s
DE.2.1.1 Number sense: Develop efficient strategies for counting (e.g., skip
Count within 1000; skip-count by 5s, 10s, and 100s. CC.2.NBT.2                     counting by 1s, 2s, 5s and 10s)
DE.3.1.1 Number sense: Demonstrate an understanding that our number
system is based on combinations of 1s, 10s, and 100s-place value

DE.3.1.1 Number sense: Demonstrate an understanding that our number
Read and write numbers to 1000 using base-ten numerals, number names, and          system is based on combinations of 1s, 10s, and 100s-place value
expanded form. CC.2.NBT.3                                                          DE.4.1.1 Number sense: Decompose and recompose whole numbers up to
10,000 using a variety of one, two- and three-digit combinations
Compare two three-digit numbers based on meanings of the hundreds, tens,           DE.2.1.4 Number sense: Use multiple strategies to compare size of two
and ones digits, using >, =, and < symbols to record the results of comparisons.   numbers (counting up, counting back)
CC.2.NBT.4                                                                         DE.2.2.7 Symbols: Use the = sign to connect equivalent parts in a number
sentence

Page 64 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 2
Domain                                                                             Matched Common Core Standard                                                               Delaware Standards
and solve problems and properties of and subtraction.
Use place
DE.2.1.3 Number sense: Use combinations of one- and two-digit numbers to
build larger (two-digit) numbers
DE.2.1.8 Operations: Use a variety of strategies to solve combination and
Fluently add and subtract within 100 using strategies based on place value,        separation problems up to 100
properties of operations, and/or the relationship between addition and             DE.2.1.9 Operations: Show number sentences that demonstrate that addition
subtraction. CC.2.NBT.5                                                            and subtraction are inverse operations (e.g., join, separate, part-part-whole,
compare)
DE.3.1.6 Operations: Add and subtract numbers up to 100 efficiently and explain
the strategies used
Grade 2: Number and Operations in Base Ten (continued)

DE.2.1.3 Number sense: Use combinations of one- and two-digit numbers to
build larger (two-digit) numbers
Grade 2: Operations and Algebraic Thinking

Add up to four two-digit numbers using strategies based on place value and         DE.3.1.6 Operations: Add and subtract numbers up to 100 efficiently and explain
properties of operations. CC.2.NBT.6                                               the strategies used
DE.4.1.9 Operations: Add and subtract larger numbers (e.g., three digits + two
digits) and explain how the operation works
DE.3.1.1 Number sense: Demonstrate an understanding that our number
system is based on combinations of 1s, 10s, and 100s-place value
Add and subtract within 1000, using concrete models or drawings and strategies DE.4.1.1 Number sense: Decompose and recompose whole numbers up to
based on place value, properties of operations, and/or the relationship between 10,000 using a variety of one, two- and three-digit combinations
addition and subtraction; relate the strategy to a written method. Understand that DE.4.1.9 Operations: Add and subtract larger numbers (e.g., three digits + two
in adding or subtracting three-digit numbers, one adds or subtracts hundreds       digits) and explain how the operation works
and hundreds, tens and tens, ones and ones; and sometimes it is necessary to DE.2.2.5 Representations: Model situations that involve the addition and
compose or decompose tens or hundreds. CC.2.NBT.7                                  subtraction of whole numbers, using objects, pictures, geometric models and
symbols (e.g., multiplicative thinking may be represented by repeated addition
and fair shares by repeated subtraction)
DE.2.1.2 Number sense: Demonstrate an understanding that our number
Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or system is based on combinations of ones and tens-place value
100 from a given number 100-900. CC.2.NBT.8                                        DE.3.1.2 Number sense: Connect counting up and counting back to addition and
subtraction
DE.K-12.7 Standard 7 - Communication: Students will develop their
mathematical Communication ability by solving problems in which there is a
need to obtain information from the real world through reading, listening and
observing; to translate this information into mathematical language and symbols;
Explain why addition and subtraction strategies work, using place value and the to process this information mathematically; and to present results in written, oral,
properties of operations. (Explanations may be supported by drawings or            and visual formats.
DE.3.1.6 Operations: Add and subtract numbers up to 100 efficiently and explain
objects.) CC.2.NBT.9
the strategies used
DE.2.2.5 Representations: Model situations that involve the addition and
subtraction of whole numbers, using objects, pictures, geometric models and
symbols (e.g., multiplicative thinking may be represented by repeated addition
and fair shares by repeated subtraction)
Measure and estimate lengths in standard units.
DE.2.3.6 Measurement: Measure an object by counting repetitions of the same
unit of measure (e.g., the length of the desk measured by an index card)
Measure the length of an object by selecting and using appropriate tools such as DE.2.3.7 Measurement: Measure a large object more than once using a
rulers, yardsticks, meter sticks, and measuring tapes. CC.2.MD.1                   different tool as the unit of measure each time- decide which one is the "best"
Page 65 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 2
Measure the length of an object by selecting and using appropriate tools such as
Domain rulers, yardsticks, meter sticks, and measuring tapes. CC.2.MD.1
Matched Common Core Standard                                                              Delaware Standards
Represent and solve problems involving addition and subtraction.                  DE.3.3.9 Measurement: Measure objects (height, length of arms, length of foot)
using standard measurement units (e.g., cm, inches, feet)
Measure and estimate lengths in standard units. Measure the length of an object DE.2.3.7 Measurement: Measure a large object more than once using a
twice, using length units of different lengths for the two measurements; describe different tool as the unit of measure each time- decide which one is the "best"
how the two measurements relate to the size of the unit chosen. CC.2.MD.2         for the task
Measure and estimate lengths in standard units. Estimate lengths using units of     DE.3.3.8 Measurement: Find objects that match a standard unit (e.g., one inch,
inches, feet, centimeters, and meters. CC.2.MD.3                                    one foot, one centimeter, one meter)
Measure and estimate lengths in standard units. Measure to determine how            DE.2.3.4 Measurement: Compare the length of two objects by counting the

much longer one object is than another, expressing the length difference in         number of nonstandard units used to measure them (e.g., linking cubes)
terms of a standard length unit. CC.2.MD.4
Relate addition and subtraction to length.
DE.K-12.5 Standard 5 - Problem Solving: Students will develop their Problem
Grade 2: Operations and Algebraic Thinking

Use addition and subtraction within 100 to solve word problems involving lengths    Solving ability by engaging in developmentally appropriate problem-solving
that are given in the same units, e.g., by using drawings (such as drawings of      opportunities in which there is a need to use various approaches to investigate
rulers) and equations with a symbol for the unknown number to represent the         and understand mathematical concepts; to formulate their own problems; to find
problem. CC.2.MD.5                                                                  solutions to problems from everyday situations; to develop and apply strategies
to solve a wide variety of problems; and to integrate mathematical reasoning,
communication and connections.
DE.2.1.4 Number sense: Use multiple strategies to compare size of two
Represent whole numbers as lengths from 0 on a number line diagram with             numbers (counting up, counting back)
equally spaced points corresponding to the numbers 0, 1, 2, ... , and represent     DE.2.2.5 Representations: Model situations that involve the addition and
whole-number sums and differences within 100 on a number line diagram.              subtraction of whole numbers, using objects, pictures, geometric models and
CC.2.MD.6                                                                           symbols (e.g., multiplicative thinking may be represented by repeated addition
and fair shares by repeated subtraction)
Work with time and money.
DE.4.1.6 Number sense: Use decimal notation to show the value of coins
Tell and write time from analog and digital clocks to the nearest five minutes,
DE.2.3.12 Measurement: Identify combinations of coin to make one dollar
using a.m. and p.m. CC.2.MD.7
DE.4.3.15 Measurement: Tell time to the nearest five minutes
DE.K-12.5 Standard 5 - Problem Solving: Students will develop their Problem
Solving ability by engaging in developmentally appropriate problem-solving
opportunities in which there is a need to use various approaches to investigate
Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, and understand mathematical concepts; to formulate their own problems; to find
using \$ (dollars) and ¢ (cents) symbols appropriately. Example: If you have 2      solutions to problems from everyday situations; to develop and apply strategies
dimes and 3 pennies, how many cents do you have? CC.2.MD.8                         to solve a wide variety of problems; and to integrate mathematical reasoning,
communication and connections.
DE.4.1.6 Number sense: Use decimal notation to show the value of coins
DE.2.3.12 Measurement: Identify combinations of coin to make one dollar
Represent and interpret data.
DE.2.4.1 Collect: Collect (e.g., observe, count, or survey) categorical data to

Generate measurement data by measuring lengths of several objects to the
answer a question posed by the teacher or students
nearest whole unit, or by making repeated measurements of the same object.
DE.2.4.2 Represent: Demonstrate a variety of informal techniques for organizing
Data (continued)

Show the measurements by making a line plot, where the horizontal scale is
and representing categorical data (e.g., tallies, pictures, or physical objects, bar
marked off in whole-number units. CC.2.MD.9
graph with scale provided, line plot)
DE.2.1.4 Number sense: Use multiple strategies to compare size of two
numbers (counting up, counting back)
Draw a picture graph and a bar graph (with single-unit scale) to represent a data
set with up to four categories. Solve simple put-together, take-apart, and
compare problems using information presented in a bar graph. CC.2.MD.10
Page 66 of 74                                                                                as of 1/31/11
Data (continued)
Common Core-Delaware Standards – Grade 2
Domain                                                                           Matched Common Core Standard                                                                   Delaware Standards
Represent and solveand a bar graph (with single-unit scale) to represent a data DE.2.4.2 Represent: Demonstrate a variety of informal techniques for organizing
Draw a picture graph
set with up to four categories. Solve simple put-together, take-apart, and           and representing categorical data (e.g., tallies, pictures, or physical objects, bar
compare problems using information presented in a bar graph. CC.2.MD.10              graph with scale provided, line plot)
DE.2.4.3 Analyze: Interpret data by noting characteristics of the graph (e.g.,
most, least, the same)
Reason with shapes and their attributes.
Recognize and draw shapes having specified attributes, such as a given number DE.2.3.1 Classification: Name and sort solid and plane figures by common
of angles or a given number of equal faces. Identify triangles, quadrilaterals,      attributes
pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not        DE.3.3.1 Classification: Name and sort solid and plane figures using several

compared by measuring.) CC.2.G.1                                                     attributes (e.g., number of corners, number of sides, size)
DE.2.3.8 Measurement: Cover up or "fill in" a design using manipulatives (e.g.,
pattern blocks, color tiles)
Grade 2: Operations and Algebraic Thinking

Partition a rectangle into rows and columns of same-size squares and count to        DE.3.3.12 Measurement: Find the area of a design by counting the number of
find the total number of them. CC.2.G.2                                              units used to cover or fill it (e.g., pattern blocks, color tiles)
DE.4.3.11 Measurement: Find the number of square units it takes to cover a
rectangle (area)
Partition circles and rectangles into two, three, or four equal shares, describe the DE.2.1.5 Number sense: Connect number words for fractions with pictures and
shares using the words halves, thirds, half of, a third of, etc., and describe the   numerals (1/2, 1/3, 1/4)
whole as two halves, three thirds, four fourths. Recognize that equal shares of      DE.3.1.4 Number sense: Develop understanding of fractions as parts of unit
identical wholes need not have the same shape. CC.2.G.3                              wholes

Page 67 of 74                                                                                as of 1/31/11
Common Core-Delaware Standards – Grade 1
Domain               Common Core Cluster and Related Standards                                                                                              Delaware Standards
Represent and solve problems involving addition and subtraction.
DE.1.1.5 Operations: Use manipulatives and pictures to model putting together
and taking apart numbers up to 20
DE.1.1.6 Operations: Write number sentences to represent addition
combinations up to 10
DE.1.1.8 Operations: Use direct models, manipulatives and pictures to
Use addition and subtraction within 20 to solve word problems involving
demonstrate joining and separating problems
situations of adding to, taking from, putting together, taking apart, and
DE.2.1.6 Operations: Use number sentences to represent number combinations
comparing, with unknowns in all positions, e.g., by using objects, drawings, and
Grade 1: Operations and Algebraic Thinking

up to 20
equations with a symbol for the unknown number to represent the problem.
DE.2.1.7 Operations: Use number sentences with missing addends to represent
CC.1.OA.1
number combinations up to 20
DE.1.2.5 Representations: Model situations in which there is a need to join,
separate, compare and use part-part-whole: using objects, pictures, geometric
models and symbols
DE.1.2.6 Symbols: Record mathematical thinking (i.e., invented notation)
DE.1.1.4 Number sense: Compose and decompose numbers up to 20
DE.1.1.6 Operations: Write number sentences to represent addition
Solve word problems that call for addition of three whole numbers whose sum is combinations up to 10
less than or equal to 20, e.g., by using objects, drawings, and equations with a DE.1.1.8 Operations: Use direct models, manipulatives and pictures to
symbol for the unknown number to represent the problem. CC.1.OA.2                demonstrate joining and separating problems
DE.2.1.6 Operations: Use number sentences to represent number combinations
up to 20
Understand and apply properties of operations and the relationship between addition and subtraction.
Apply properties of operations as strategies to add and subtract. Examples: If 8 DE.3.2.5 Symbols: Develop an understanding of the Commutative and
+ 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of       Associative properties of whole number addition as a tool to solve problems
addition.) To add 2 + 6 + 4, the second two numbers can be added to make a       (e.g., is 3+ (7 + 2) always the same as (3 + 7) + 2?)
ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) (Students
need not use formal terms for these properties.) CC.1.OA.3
DE.2.1.7 Operations: Use number sentences with missing addends to represent
number combinations up to 20
Understand subtraction as an unknown-addend problem. For example, subtract
DE.2.1.9 Operations: Show number sentences that demonstrate that addition
10 - 8 by finding the number that makes 10 when added to 8. CC.1.OA.4
and subtraction are inverse operations (e.g., join, separate, part-part-whole,
compare)

Page 68 of 74                                                                           as of 1/31/11
Common Core-Delaware Standards – Grade 1
Domain               Common Core Cluster and Related Standards                                                                                                                  Delaware Standards
Represent and solve problems involving addition and subtraction.
Grade 1: Operations and Algebraic Thinking (continued)                                                                                      DE.1.1.4 Number sense: Compose and decompose numbers up to 20
CC.1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to
DE.3.1.2 Number sense: Connect counting up and counting back to addition and
subtraction
DE.1.1.4 Number sense: Compose and decompose numbers up to 20
DE.1.1.6 Operations: Write number sentences to represent addition
combinations up to 10
within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 +
DE.1.1.7 Operations: Use manipulatives and models to demonstrate doubles
4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 -
Grade 1: Operations and Algebraic Thinking

1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g.,    DE.2.1.8 Operations: Use a variety of strategies to solve combination and
knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but        separation problems up to 100
DE.2.1.9 Operations: Show number sentences that demonstrate that addition
easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6
and subtraction are inverse operations (e.g., join, separate, part-part-whole,
+ 1 = 12 + 1 = 13). CC.1.OA.6
compare)
DE.3.1.7 Operations: Master addition and subtraction facts up to 20
Work with addition and subtraction equations.
DE.1.1.6 Operations: Write number sentences to represent addition
Understand the meaning of the equal sign, and determine if equations involving     combinations up to 10
addition and subtraction are true or false. For example, which of the following    DE.2.1.6 Operations: Use number sentences to represent number combinations
equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 =   up to 20
5 + 2. CC.1.OA.7                                                                   DE.2.2.7 Symbols: Use the = sign to connect equivalent parts in a number
sentence
Determine the unknown number in an addition or subtraction equation relating       DE.2.1.7 Operations: Use number sentences with missing addends to represent
three whole numbers. For example, determine the unknown number that makes          number combinations up to 20
the equation true in each of the equations 8 + ? = 11, 5 = __• 3, 6 + 6 = • _.
-           _        DE.2.2.7 Symbols: Use the = sign to connect equivalent parts in a number
CC.1.OA.8                                                                          sentence

Page 69 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 1
Domain               Common Core Cluster and Related Standards                                                                                                          Delaware Standards
Represent and solve sequence. involving addition and subtraction.
Extend the counting problems
DE.1.1.2 Number sense: Connect number words and numbers (up to 50) to the
Count to 120, starting at any number less than 120. In this range, read and write quantities they represent using physical models and representations
numerals and represent a number of objects with a written numeral. CC.1.NBT.1 DE.1.1.3 Number sense: Sequence numbers and explain which is larger, which
is smaller, and what is between other numbers up to 100
Understand place value.
Understand that the two digits of a two-digit number represent amounts of tens    DE.2.1.2 Number sense: Demonstrate an understanding that our number
and ones. Understand the following as special cases:                              system is based on combinations of ones and tens-place value
Grade 1: Number 1: Operations and Base Ten Thinking

-- a. 10 can be thought of as a bundle of ten ones - called a "ten."
-- b. The numbers from 11 to 19 are composed of a ten and one, two, three,
four, five, six, seven, eight, or nine ones.
-- c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three,

four, five, six, seven, eight, or nine tens (and 0 ones). CC.1.NBT.2
DE.1.1.3 Number sense: Sequence numbers and explain which is larger, which
is smaller, and what is between other numbers up to 100
Compare two two-digit numbers based on meanings of the tens and ones digits,
DE.2.1.2 Number sense: Demonstrate an understanding that our number
recording the results of comparisons with the symbols >, =, and <. CC.1.NBT.3
system is based on combinations of ones and tens-place value
DE.2.2.6 Symbols: Record mathematical thinking using conventional notation
Use place value understanding and properties of operations to add and subtract.
DE.2.1.2 Number sense: Demonstrate an understanding that our number
system is based on combinations of ones and tens-place value
Add within 100, including adding a two-digit number and a one-digit number, and DE.2.1.3 Number sense: Use combinations of one- and two-digit numbers to
adding a two-digit number and a multiple of 10, using concrete models or            build larger (two-digit) numbers
drawings and strategies based on place value, properties of operations, and/or      DE.2.1.8 Operations: Use a variety of strategies to solve combination and
the relationship between addition and subtraction; relate the strategy to a written separation problems up to 100
method and explain the reasoning used. Understand that in adding two-digit          DE.2.1.9 Operations: Show number sentences that demonstrate that addition
numbers, one adds tens and tens, ones and ones; and sometimes it is                 and subtraction are inverse operations (e.g., join, separate, part-part-whole,
necessary to compose a ten. CC.1.NBT.4                                              compare)
DE.3.1.6 Operations: Add and subtract numbers up to 100 efficiently and explain
the strategies used
Given a two-digit number, mentally find 10 more or 10 less than the number,         DE.2.1.3 Number sense: Use combinations of one- and two-digit numbers to
without having to count; explain the reasoning used.CC.1.NBT.5                      build larger (two-digit) numbers
DE.2.1.8 Operations: Use a variety of strategies to solve combination and
separation problems up to 100
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10- DE.2.1.9 Operations: Show number sentences that demonstrate that addition
90 (positive or zero differences), using concrete models or drawings and            and subtraction are inverse operations (e.g., join, separate, part-part-whole,
strategies based on place value, properties of operations, and/or the relationship compare)
DE.1.2.5 Representations: Model situations in which there is a need to join,
between addition and subtraction; relate the strategy to a written method and
separate, compare and use part-part-whole: using objects, pictures, geometric
explain the reasoning used. CC.1.NBT.6
models and symbols
DE.2.2.6 Symbols: Record mathematical thinking using conventional notation

Page 70 of 74                                                                             as of 1/31/11
Common Core-Delaware Standards – Grade 1
Domain               Common Core Cluster and Related Standards                                                                                                                             Delaware Standards
Represent and solve problems involving addition and subtraction.
Measure lengths indirectly and by iterating length units.
DE.1.3.6 Measurement: Compare the length of two objects by aligning them
Order three objects by length; compare the lengths of two objects indirectly by        DE.1.3.7 Measurement: Put objects in order according to their length
using a third object. CC.1.MD.1                                                        DE.1.3.9 Measurement: Use nonstandard units to represent how long an object
is

Express the length of an object as a whole number of length units, by laying           DE.1.3.9 Measurement: Use nonstandard units to represent how long an object
multiple copies of a shorter object (the length unit) end to end; understand that      is
the length measurement of an object is the number of same-size length units
and Algebraic Thinking

that span it with no gaps or overlaps. Limit to contexts where the object being
measured is spanned by a whole number of length units with no gaps or
overlaps. CC.1.MD.2
Tell and write time.
Tell and write time in hours and half-hours using analog and digital clocks.           DE.2.3.11 Measurement: Tell time to the hour
CC.1.MD.3                                                                              DE.3.3.15 Measurement: Tell time to the half hour
Represent and interpret data.
DE.1.4.1 Collect: Collect categorical data (observe and count frequencies) to
Organize, represent, and interpret data with up to three categories; ask and           answer a question posed by the teacher
answer questions about the total number of data points, how many in each               DE.1.4.2 Represent: Organize and informally represent categorical data (2 or 3
category, and how many more or less are in one category than in another.               categories) using drawings or physical objects
CC.1.MD.4                                                                              DE.1.4.3 Analyze: Interpret data by making comparisons between frequencies of
categorical data (e.g., how many more)
Reason with shapes and their attributes.
Distinguish between defining attributes (e.g., triangles are closed and three-         DE.1.3.3 Classification: Recognize and compare attributes and parts of two-
sided) versus non-defining attributes (e.g., color, orientation, overall size) for a   dimensional and three-dimensional shapes
wide variety of shapes; build and draw shapes to possess defining attributes.

CC.1.G.1
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles,            DE.1.3.2 Classification: Identify the new shape formed by combining two shapes
half-circles, and quarter-circles) or three-dimensional shapes (cubes, right
rectangular prisms, right circular cones, and right circular cylinders) to create a    DE.3.3.3 Classification: Describe, and reason about the results of subdividing
composite shape, and compose new shapes from the composite shape.                      and combining shapes
(Students do not need to learn formal names such as "right rectangular prism.")
CC.1.G.2
Partition circles and rectangles into two and four equal shares, describe the          DE.2.1.5 Number sense: Connect number words for fractions with pictures and
shares using the words halves, fourths, and quarters, and use the phrases half         numerals (1/2, 1/3, 1/4)
of, fourth of, and quarter of. Describe the whole as two of, or four of the shares.    DE.1.3.4 Location and transformation: Explore symmetry through drawings and
Understand for these examples that decomposing into more equal shares                  use of manipulatives

Page 71 of 74                                                                               as of 1/31/11
Common Core-Delaware Standards – Grade K
Domain                                              Common Core Cluster and Related Standards                                                             Delaware Standards
Know number names and the count sequence.
DE.K.1.2 Number sense: Connect number words and numerals (up to 10) to the
quantities they represent using various physical models and representations

Count to 100 by ones and by tens. CC.K.CC.1                                        DE.1.1.1 Number sense: Count sets of objects up to 50 by 1s, 2s, 5s, and 10s
DE.1.1.3 Number sense: Sequence numbers and explain which is larger, which
is smaller, and what is between other numbers up to 100
Count forward beginning from a given number within the known sequence              DE.K.1.3 Number sense: Sequence numbers and explain what comes before,
(instead of having to begin at 1). CC.K.CC.2                                       after and between other numbers
DE.K.1.2 Number sense: Connect number words and numerals (up to 10) to the
quantities they represent using various physical models and representations
Kindergarten: Counting and Cardinality

Write numbers from 0 to 20. Represent a number of objects with a written
DE.1.1.2 Number sense: Connect number words and numbers (up to 50) to the
numeral 0-20 (with 0 representing a count of no objects). CC.K.CC.3
quantities they represent using physical models and representations
DE.K.2.6 Symbols: Record mathematical thinking symbolically with teacher
assistance
Count to tell the number of objects.
Understand the relationship between numbers and quantities; connect counting       DE.K.1.1 Number sense: Count sets of objects up to 20
to cardinality. CC.K.CC.4
When counting objects, say the number names in the standard order, pairing         DE.K.1.1 Number sense: Count sets of objects up to 20
each object with one and only one number name and each number name with
one and only one object. CC.K.CC.4a
Understand that the last number name said tells the number of objects counted.     DE.K.1.1 Number sense: Count sets of objects up to 20
The number of objects is the same regardless of their arrangement or the order
in which they were counted. CC.K.CC.4b
Understand that each successive number name refers to a quantity that is one       DE.K.1.3 Number sense: Sequence numbers and explain what comes before,
larger. CC.K.CC.4c                                                                 after and between other numbers
Count to answer "how many?" questions about as many as 20 things arranged in       DE.K.1.1 Number sense: Count sets of objects up to 20
a line, a rectangular array, or a circle; or as many as 10 things in a scattered
configuration; given a number from 1-20, count out that many objects.
CC.K.CC.5
Compare numbers
DE.K.1.2 Number sense: Connect number words and numerals (up to 10) to the
Identify whether the number of objects in one group is greater than, less than, or quantities they represent using various physical models and representations
equal to the number of objects in another group, e.g., by using matching and
counting strategies. (Include groups with up to ten objects.) CC.K.CC.6.           DE.K.1.3 Number sense: Sequence numbers and explain what comes before,
after and between other numbers
Compare two numbers between 1 and 10 presented as written numerals.                DE.K.1.2 Number sense: Connect number words and numerals (up to 10) to the
CC.K.CC.7                                                                          quantities they represent using various physical models and representations

Page 72 of 74                                                                          as of 1/31/11
Common Core-Delaware Standards – Grade K
Domain                                                                        Common Core Cluster and Related Standards                                      Delaware Standards
and the count sequence.
Know number namesas putting together and adding to, and understand subtraction as taking apart and taking from.
Represent addition and subtraction with objects, fingers, mental images,           DE.K.1.5 Operations: Use manipulatives to model putting together and taking
drawings (drawings need not show details, but should show the mathematics in       apart (e.g., you have one cookie and you get two more cookies
Kindergarten: Counting Operations and Algebraic Thinking

the problem), sounds (e.g., claps), acting out situations, verbal explanations,    DE.K.2.5 Representations: Model join and separate situations with objects and
expressions, or equations. CC.K.OA.1                                               pictures
DE.K.1.5 Operations: Use manipulatives to model putting together and taking
Solve addition and subtraction word problems, and add and subtract within 10,      apart (e.g., you have one cookie and you get two more cookies
e.g., by using objects or drawings to represent the problem. CC.K.OA.2             DE.K.2.5 Representations: Model join and separate situations with objects and
pictures
DE.K.1.4 Number sense: Show more than one way to make numbers up to 10
Decompose numbers less than or equal to 10 into pairs in more than one way,
DE.K.1.6 Operations: Use manipulatives to show more than one way to make a
Kindergarten: and Cardinality

e.g., by using objects or drawings, and record each decomposition by a drawing
target number up to 6
or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). CC.K.OA.3
DE.K.2.5 Representations: Model join and separate situations with objects and
pictures
DE.K.1.4 Number sense: Show more than one way to make numbers up to 10
For any number from 1 to 9, find the number that makes 10 when added to the
DE.1.1.6 Operations: Write number sentences to represent addition
given number, e.g., by using objects or drawings, and record the answer with a
combinations up to 10
drawing or equation. CC.K.OA.4
DE.K.2.5 Representations: Model join and separate situations with objects and
pictures
DE.K.1.4 Number sense: Show more than one way to make numbers up to 10

Fluently add and subtract within 5. CC.K.OA.5                                      DE.K.1.6 Operations: Use manipulatives to show more than one way to make a
target number up to 6
DE.3.1.7 Operations: Master addition and subtraction facts up to 20
Work with numbers 11-19 to gain foundations for place value.
Operations in Base

DE.1.1.2 Number sense: Connect number words and numbers (up to 50) to the
Kindergarten:
Number and

Compose and decompose numbers from 11 to 19 into ten ones and some                 quantities they represent using physical models and representations
Ten

further ones, e.g., by using objects or drawings, and record each composition or
DE.1.1.4 Number sense: Compose and decompose numbers up to 20
decomposition by a drawing or equation (such as 18 = 10 + 8); understand that
these numbers are composed of ten ones and one, two, three, four, five, six,
seven, eight, or nine ones. CC.K.NBT.1                                             DE.2.1.2 Number sense: Demonstrate an understanding that our number system
is based on combinations of ones and tens-place value

Page 73 of 74                                                                          as of 1/31/11
Common Core-Delaware Standards – Grade K
Domain                                                                                   Common Core Cluster and Related Standards                                                             Delaware Standards
Kindergarten: Counting and Cardinality Measurement and Data   Know numbercompare measurable attributes.
Describe and names and the count sequence.
DE.K.3.5 Measurement: Compare the length of two objects by placing them side
by side
Describe measurable attributes of objects, such as length or weight. Describe    DE.K.3.8 Measurement: Describe and compare volume/capacity of two objects
several measurable attributes of a single object. CC.K.MD.1                      (e.g., full/empty, more/less)
DE.K.3.9 Measurement: Describe and compare the mass/weight of two objects
(e.g., light/heavy)
Directly compare two objects with a measurable attribute in common, to see       DE.K.3.5 Measurement: Compare the length of two objects by placing them side
which object has "more of"/"less of" the attribute, and describe the difference. by side
For example, directly compare the heights of two children and describe one child DE.K.3.6 Measurement: Find items that are longer than or shorter than a given
as taller/shorter. CC.K.MD.2                                                     measure (e.g., longer than 10 linker cubes)
Kindergarten:

Classify objects and count the number of objects in each category.
DE.K.1.1 Number sense: Count sets of objects up to 20
Classify objects into given categories; count the numbers of objects in each      DE.K.2.1 Patterns and change: Sort objects by a given attribute (e.g., size, color,
category and sort the categories by count. (Limit category counts to be less than shape)
or equal to 10.) CC.K.MD.3                                                        DE.K.3.1 Classification: Name and sort figures by shape (e.g., rectangle,
triangle, circle)
Identify and describe shapes (such as squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
DE.K.3.3 Classification: Recognize geometric shapes and structures in the
Describe objects in the environment using names of shapes, and describe the
environment
relative positions of these objects using terms such as above, below, beside, in
DE.K.3.4 Location and transformation: Find and name locations with simple
front of, behind, and next to. CC.K.G.1
relationships (e.g., near to, over, under, beside, between, outside, inside)
DE.K.3.1 Classification: Name and sort figures by shape (e.g., rectangle,
triangle, circle)
Kindergarten: Geometry

Correctly name shapes regardless of their orientations or overall size. CC.K.G.2
DE.2.3.1 Classification: Name and sort solid and plane figures by common
attributes
Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional   DE.K.3.2 Classification: Recognize attributes and parts of two-dimensional and
("solid"). CC.K.G.3                                                                  three-dimensional shapes
Analyze, compare, create, and compose shapes.
DE.K.3.2 Classification: Recognize attributes and parts of two-dimensional and
three-dimensional shapes
Analyze and compare two- and three-dimensional shapes, in different sizes and
DE.1.3.1 Classification: Name and sort plane figures by size and shape
orientations, using informal language to describe their similarities, differences,
DE.1.3.2 Classification: Identify the new shape formed by combining two shapes
parts (e.g., number of sides and vertices/"corners") and other attributes (e.g.,
having sides of equal length). CC.K.G.4
DE.1.3.3 Classification: Recognize and compare attributes and parts of two-
dimensional and three-dimensional shapes
Model shapes in the world by building shapes from components (e.g., sticks and DE.K.3.3 Classification: Recognize geometric shapes and structures in the
clay balls) and drawing shapes. CC.K.G.5                                       environment
Compose simple shapes to form larger shapes. For example, "can you join        DE.1.3.2 Classification: Identify the new shape formed by combining two shapes
these two triangles with full sides touching to make a rectangle?" CC.K.G.6

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