VIEWS: 12 PAGES: 55 POSTED ON: 8/19/2011
Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives The complex number system includes Number Sense, Properties, 1 real numbers and imaginary numbers and Operations Show that between any two rational High School numbers there are an infinite number of a rational numbers, and that between any 10th 1.2a; Specifies the density property two irrational numbers there are also an infinite number of irrational numbers Express the square root of a negative b number using imaginary numbers Formulate, represent, and use Number Sense, Properties, and Operations 2 algorithms with real numbers flexibly, accurately, and efficiently Use appropriate computation methods a that encompass estimation and 9th 1.3a, 6.2a; 10th 1.3a; 6.2a; 6.3a calculation Use technology to perform operations High School 9th 1.1b, 1.1c; 10th 1.1b, 1.1c; Now (addition, subtraction, multiplication, and b includes explicit use of technology and division) on numbers written in scientific operations of addition and subtraction notation Describe factors affecting take-home pay c and calculate the impact (PFL) Design and use a budget, including income (net take-home pay) and expenses (mortgage, car loans, and living d expenses) to demonstrate how living within your means is essential for a secure financial future (PFL) Page 1 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Properties, and Number Sense, Systematic counting techniques are 3 High School Operations used to describe and solve problems Use combinatorics (Fundamental Counting Principle, permutations and a 9th 3.6a; 10th 3.6a combinations) to solve problems in real world contexts Page 2 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Functions model situations where one quantity determines another and 1 can be represented algebraically, graphically, and using tables Patterns, Functions, and Algebraic Structures Determine* when a relation is a function 10th 2.4d; Specifies determination using a using a table, a graph or an equation table, graph, or equation. Demonstrate the relationship between all representations of linear functions using b point-slope, slope-intercept, and standard form of a line High School Represent* linear, quadratic, absolute value, power, exponential, logarithmic, rational, trigonometric (sine and cosine), 9th 2.2a, 2.2b; 10th 2.2a, 2.2b; Specifies c and step functions in a table, graph and functions to be represented equation and convert from one representation to another Determine the inverse (expressed d graphically or in tabular form) of a function from a graph or table Categorize sequences as arithmetic, geometric, or neither and develop e 9th 2.1a; 10th 2.1a formulas for the general terms related to arithmetic and geometric sequences *Using all tools including graphing technology Page 3 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Graphs and tables are used to 2 describe the qualitative behavior of Patterns, Functions, and Algebraic Structures common types of functions Evaluate* a function at a given point in a its domain given an equation (including function notation), a table, and a graph Identify* the domain and range of a b function given an equation (including High School function notation), a table, and a graph Identify* intercepts, zeros (or roots), maxima, minima, and intervals of 9th 2.4a; 2.4b; 10th 2.4a, 2.4b; Now c increase and decrease, and asymptotes of includes intervals of increase and a function given an equation (including decrease and asymptotes function notation), a table, and a graph Make qualitative statements about the 9th 5.1b; 10th 5.1b, 5.1c; Now d rate of change of a function, based on its emphasizes making qualitative graph or table statements *Using all tools including graphing technology Parameters influence the shape of Patterns, Functions, 3 the graphs of functions and Algebraic High School Structures Apply* transformations (translation, 9th 2.4c; 10th 2.4c; Apply translations, a reflection, dilation) to a parent function, reflections, and dilations to all functions f(x) Interpret the results of these b transformations verbally, graphically, and 9th 2.4c; 10th 2.4c symbolically Page 4 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Expessions , equations, and 4 inequalities can be expressed in multiple, equivalent forms Patterns, Functions, and Algebraic Structures Perform and justify steps in generating equivalent expressions by identifying High School a properties used including the commutative, associative, inverse, identity, and distributive properties Apply the properties of positive and 9th 1.2a; 10th 2.1b; Now includes negative rational exponents to generate b positive and negative rational exponents equivalent algebraic expressions including and nth roots those involving nth roots Solve equations for one variable in terms c 9th 2.3c; 10th 2.3c of the others Solutions to equations, inequalities 5 and systems of equations are found Patterns, Functions, and Algebraic using a variety of tools Find* solutions to quadratic and cubic equations and inequalities by using 9th 2.3a, 2.5a; 10th 2.3a, 2.5a; Now a appropriate algebraic methods such as High School Structures includes cubic equations factoring, completing the square, graphing or using the quadratic formula Find* solutions to equations involving b power, exponential, rational and radical functions Solve* systems of linear equations and 9th 2.3b, 2.5a; 10th 2.3b, 2.5a; Now c inequalities with two variables includes systems of linear inequalities *Using all tools including graphing technology Page 5 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Quantitative relationships in the real- Patterns, Functions, and Algebraic Structures 6 world can be modeled and solved using functions Represent, solve*, and interpret problems 9th 2.1a, 2.3a; 10th 2.1a, 2.3a; Now a in various contexts using linear, includes solving exponential functions quadratic, and exponential functions Represent, solve*, and interpret problems High School 9th 6.1c; 10th 6.1c; Now includes involving direct and inverse variations b inverse and combination of direct and and a combination of direct and inverse inverse variation variation Analyze* the impact of interest rates on a c personal financial plan (PFL) Evaluate* the costs and benefits of credit d (PFL) Analyze various lending sources, services e and financial institutions (PFL) *Using all tools including graphing technology Statistical methods take variability Data Analysis, Statistics, and into account, supporting informed decision-making through quantitative studies designed to answer specific questions High School 1 Probability Formulate appropriate research questions that can answered with statistical 9th 3.1b a analysis Determine appropriate data collection b methods to answer a research question Explain how data might be analyzed to c provide answers to a research question 9th 3.1b; 10th 3.1b Page 6 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives The design of an experiment or Data Analysis, Statistics, sample survey is of critical importance to analyzing the data and and Probability 2 drawing conclusions High School Identify the characteristics of a well- a designed and well-conducted survey 9th 3.1a; 10th 3.1a, 3.2d Identify the characteristics of a well- b designed and well-conducted experiment Differentiate between the inferences that can be drawn in experiments versus c observational studies Page 7 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Visual displays and summary statistics condense the information in data sets into usable knowledge 3 Data Analysis, Statistics, and Probability Identify and choose appropriate ways to summarize numerical or categorical data using tables, graphical displays, and numerical summary statistics (describing shape, center and spread) and accounting 9th 3.1c; 3.4a 10th 3.1c; 3.4a, 3.4b, for outliers, when appropriate a 3.4c; 3.4d High School Define and explain how sampling distributions (developed through simulation) are used to describe the sample-to-sample variability of sample b statistics Describe the relationship between two c categorical variables using percents When the relationship between two numerical variables is reasonably linear, apply* the least-squares criterion for line fitting, use Pearson’s correlation 9th 3.3a, 3.3b; 10th 3.3a, 3.3b; Now coefficient as a measure of strength, and requires use of least-squares criterion interpret the slope and y-intercept in the d and Pearson's correlation coefficient context of the problem *Using all tools including graphing technology Page 8 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Randomness is the foundation for using statistics to draw conclusions Data Analysis, Statistics, when testing a claim or estimating plausible values for a population and Probability 4 High School characteristic Define and explain the meaning of significance (both practical and a statistical) Explain the role of p-values in b determining statistical significance Determine the margin of error associated with an estimate of a population c characteristic Page 9 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Probability models outcomes for situations in which there is inherent randomness, quantifying the degree of certainty in terms of relative Data Analysis, Statistics, and Probability 5 frequency of occurrence Develop* simulations that demonstrate probability as a long-run relative 10th 3.5b; Now requires developing a frequency simulations Apply and solve problems using the concepts of independence and conditional b 10th 3.5c High School probability Apply and solve problems using the concept of mutually exclusive properties 10th 3.5d; Now specifies mutually when combining probabilities c exclusive properties Evaluate* and interpret probabilities 10th 3.4c; Now connects probability to d using a normal distribution normal curve Find* and interpret the expected value and standard deviation of a discrete 9th 3.4b; 10th 3.4c; Now specifies e random variable X finding the standard deviation Analyze* the cost of insurance as a method to offset the risk of a situation f (PFL) *Using all tools including graphing technology Page 10 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Attributes of two- and three- 1 dimensional objects are measurable Shape, Dimension, and Geometric and can be quanitified Calculate (or estimate when appropriate) a the perimeter and area of a two- 9th 4.2a; 10th 4.2b dimensional irregular shape Justify, interpret, and apply the use of Relationships High School 9th 4.2a; 10th 4.2c; Now specifies formulas for the surface area, and volume b cones, pyramids and spheres including of cones, pyramids, and spheres including real-world situations real-world situations Solve for unknown quantities in c relationships involving perimeter, area, 9th 2.5b; 10th 2.5b surface area, and volume Apply the effect of dimensional change, utilizing appropriate units and scales in d 9th 5.1c; 10th 5.1d problem solving situations involving perimeter, area, and volume Page 11 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Objects in the plane and their parts, 2 attributes, and measurements can be Shape, Dimension, and Geometric Relationships analyzed deductively Classify polygons according to their a similarities and/or differences Solve for unknown attributes of geometric b shapes based on their congruence, 9th 5.1a; 10th 4.1a, 4.1b, 5.1a similarity, or symmetry Know and apply properties of angles High School including corresponding, exterior, interior, vertical, complementary, and 9th 4.3a; 10th 4.3a; Now focus on c supplementary angles to solve problems. justification Justify the results using two-column proofs, paragraph proofs, flow charts, and/or illustrations Develop conjectures and solve problems about geometric figures including definitions and properties (congruence, 9th 4.3a; 10th 4.3a, 4.3b; Now focus is d similarity, and symmetry). Justify these on justification conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations Page 12 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Objects in the plane can be transformed and those 3 transformations can be described and Shape, Dimension, and Geometric Relationships analyzed mathematically Make conjectures involving two- dimensional objects represented with Cartesian coordinates. Justify these 9th 4.3b; 10th 4.1c; Now focus on a conjectures using two-column proofs, justification paragraph proofs, flow charts, and/or illustrations Represent transformations (reflection, b translation, rotation, and dilation) using 9th 4.1a; 10th 4.1b, 4.1c High School Cartesian coordinates Develop arguments to establish what remains invariant and what changes after a transformation (reflection, translation, c rotation, and dilations). Justify these conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations Using construction tools, including technology, make conjectures about relationships among properties of shapes in the plane including those formed 9th 4.3a; 10th 4.3a, 4.3b; Now specifies d through transformation. Justify these use of construction tools and justification conjectures using two-column proofs, paragraph proofs, flow charts, and/or illustrations Page 13 of 55 Math Standards Crosswalk High School Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Right triangles are central to 4 geometry and its applications Geometric Relationships Shape, Dimension, and Apply right triangle trigonometry (sine, a cosine, and tangent) to find indirect 10th 4.4a High School measures of lengths and angles Apply the Pythagorean theorem and its b 9th 4.2b; 10th 4.2a converse to solve real world problems Determine the midpoint of a line segment 10th 2.5c; Now specifies midpoint and c and the distance between two points in distance between two points the Cartesian coordinate plane Page 14 of 55 Math Standards Crosswalk Eighth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives In the real number system, rational and irrational numbers are in one to Number Sense, Properties, and 1 one correspondence to points on the number line Compare and order sets of integers and 1.2a Specifies fractions, decimals, or Eighth Grade a rational numbers that are expressed as Operations percents rather than variety of methods fractions, decimals, or percents Given a whole number from 0 - 100, determine whether it is a perfect square b or find the two consecutive whole 1.1a Focus is on square roots numbers between which its square root lies Approximate the location of square roots c between two whole numbers on a number 1.1a focus is on square roots line Number Sense, Properties, and Formulate, represent, and use 2 algorithms with rational numbers flexibly, accurately, and efficiently Eighth Grade Operations Add, subtract, multiply and divide rational 6.4a Now includes negative fractions and a numbers including integers, positive and decimals negative fractions and decimals Apply computational methods to solve b multi-step application problems involving 6.4a percents and rational numbers Analyze how credit and debt impact c personal financial goals (PFL) Page 15 of 55 Math Standards Crosswalk Eighth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Linear functions model situations with a constant rate of change and Patterns, Functions, and Algebraic Structures 1 can be represented algebraically, graphically, and using tables Convert from one representation of a linear function to another, including 2.1a, 2.1b; Specific to linear functions a situations, tables, equations (slope- and includes slope-intercept form intercept form), and graphs Use representations of linear functions to 2.1a, 2.5a; Now specifies situations Eighth Grade b analyze situations and solve problems instead of patterns Identify the dependent and independent 2.3a; Specific to dependent and c variable in real world situations independent variables Identify and interpret the slope(rate of change) and y-intercept in graphs, in d tables, and from equations in slope- intercept form Model and graph two linear equations in slope-intercept form on the same e coordinate plane and interpret the point of intersection as the solution to the system of equations Page 16 of 55 Math Standards Crosswalk Eighth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Properties of algebra, equality, and 2 inequality are used to solve linear Patterns, Functions, and Algebraic equations and inequalities Use the distributive, associative, and a commutative properties to simplify algebraic expressions Eighth Grade Solve one variable equations, including Structures those involving multiple steps, rational 2.5a; Now includes more complex b numbers, variables on both sides, and the equations distributive property Solve inequalities in one variable c (including negative coefficients) and 2.2a; Now includes solving and graphing graph the solution on a number line Represent the distributive property in a d variety of ways including numerically, geometrically, and algebraically Graphs and tables can be used to Functions, and Eighth Grade 2 distinguish between linear and Structures Algebraic Patterns, nonlinear functions Given a table or graph determine if the 2.4a; Now includes formal instead of a function is linear informal methods Explain the properties of linear functions b in tables and graphs Page 17 of 55 Math Standards Crosswalk Eighth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Visual displays and summary statistics of two-variable data Data Analysis, Statistics, and condense the information in data sets 1 into usable knowledge Given a scatterplot, calculate quadrant Eighth Grade count ratio to quantify the magnitude and Probability strength of the association between two variables for numeric data as positive, a negative, or no correlation Given a scatterplot suggesting a linear relationship, draw a line of fit to make b predictions Use time series plots (line graphs) to analyze the trend of a set of data over c time 3.4a; Specific to line graphs Objects in the plane and their parts Shape, Dimension, and 1 and attributes can be analyzed Classify quadrilaterals and apply angle Relationships Eighth Grade a and side properties, including the sum of 4.2a; Specific to quadrilaterals Geometric the interior angles Apply properties of complementary, b supplementary, and vertical angle relationships Apply properties of parallel lines including c corresponding angles and alternate interior angles Page 18 of 55 Math Standards Crosswalk Eighth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Direct and indirect measurements Geometric Relationships 2 can be used to describe and make Shape, Dimension, and comparisons Use properties of similar triangles to find a 4.2a, 4.3a; Specific to triangles Eighth Grade unknown lengths Use the Pythagorean Theorem to find b 4.5b unknown lengths in right triangles 5.1a, 5.2a; Explicit proportional Use proportional reasoning to estimate c reasoning specific to distance, weight, distance, weight, and capacity and capacity Use proportional reasoning to convert 5.2a; Explicit proportional reasoning d amoung measures including dimensional including dimensional analysis analysis Page 19 of 55 Math Standards Crosswalk Seventh Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives In the real number system, rational Number Sense, Properties, 1 numbers have a unique location on the number line and Operations Seventh Grade Read, write, locate on number line, a compare and order integers and positive 1.1a, 1.2a, 1.2b rational numbers Apply the definition of absolute value with b integers quantifying the distance from zero Express large and small numbers using c scientific notation Formulate, represent, and use Number Sense, Properties, and algorithms with integers and positive 2 rational numbers flexibly, accurately, and efficiently Seventh Grade Simplify numeric expressions using the a 6.2a Operations order of operations Add, subtract, multiply, and divide 6.2b, No longer includes positive rational b integers numbers Use mental math and estimation c strategies to solve problems involving 6.3b, Now specific to percent percents Solve problems involving percent of a number, discounts, taxes, simple interest, 1.4a, Now includes percent increase and d percent increase, and percent decrease decrease (PFL) Page 20 of 55 Math Standards Crosswalk Seventh Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Proportional reasoning involves 3 comparisons and multiplicative Number Sense, Properties, and relationships among ratios Use ratio relationships to solve for a a 1.4a missing value in a proportion Seventh Grade Model proportional relationships with bar 4.3a, 6.1a, Now includes bar models and Operations b models, ratio tables, and similar figures ratio tables Explain the difference between a ratio, c rate, and unit rate Estimate and compute unit cost of consumables (to include unit conversions d if necessary) sold in quantity to make purchase decisions based on cost and practicality (PFL) Relationships involving the constant Patterns, Functions, and 1 rate of change are modeled and Algebraic Structures solved using linear functions Seventh Grade Given a linear situation (including, direct a variation), identify variables and write an 2.5b equation in slope-intercept form Given a linear equation (including direct variation), substitute input values to b 2.5a, 2.5b create a table and graph coordinate points in all four quadrants Page 21 of 55 Math Standards Crosswalk Seventh Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Visual displays and summary statistics with one-variable data condense the information in data sets Data Analysis, Statistics, and Probability 1 into usable knowledge Distinguish between median as middle number and mean as balance point for an 3.3a, 3.2a, Now includes distinguishing a ordered set of data between median and mean Use Mean Absolute Deviation (MAD) to b analyze the spread of a set of data Seventh Grade Construct and interpret dot plots, histograms, stem-and-leaf plots, and 3.1a, 3.1b, Now includes constructing c circle graphs. circle graphs Construct and interpret a box plot using the five number summary and identify the interquartile range (IQR) for a set of d data Compare sets of data using shape (skewed, normal, uniform), with appropriate measures of central tendency (mean, median, mode), and appropriate e measures of spread (range, IQR, MAD) Given a frequency table, calculate relative f frequencies Page 22 of 55 Math Standards Crosswalk Seventh Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Objects in space and their parts and 1 attributes can be measured and Geometric Relationships Shape, Dimension, and analyzed Develop and apply formulas and Seventh Grade 4.5c; Now includes developing formulas; a procedures for the surface area and now includes cylinders volume of right cylinders and right prisms Develop and apply formulas and procedures for area of regular polygons, 5.4a, 4.5a. 4.5b; Now includes composite b circumference and area of circles, and igures area of composite figures Identify and construct two-dimensional c nets of prisms and cylinders Proportional reasoning is used to 2 Shape, Dimension, make indirect measurements Seventh Grade and Geometric Relationships Describe the relationship between the a 5.5a circumference and diameter of a circle b Read and interpret scales on maps 5.3a Use proportions to convert from one set of units to another within customary and c metric systems using standard units of measure for length, weight, capacity and time Page 23 of 55 Math Standards Crosswalk Sixth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives In the real number system, positive 1 rational numbers are represented in Number Sense, Properties, and Operations multiple equivalent forms Read, write, compare, convert between and order positive rational numbers in a 1.1b, 1.2a, 1.4a; Now includes a variety of forms including proper and converting; not limited to common improper fractions, mixed numbers, fractions and decimals decimals, and percents Sixth Grade Express whole numbers as products of prime factors with exponents and use b prime factorization to find the greatest common factor and least common multiple of two numbers Express the quotient and remainder of a whole number division problem (a/b or a c ÷ b) using fractions, terminating decimals, or repeating decimals Locate positive fractions and decimals on 1.1a; Not limited to common fractions d a number line and decimals Page 24 of 55 Math Standards Crosswalk Sixth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Formulate, represent, and use Number Sense, Properties, and Operations algorithms with positive rational 2 numbers flexibly, accurately, and efficiently Model and compute the addition, 6.2a, 6.2b, 6.4a; Now includes subtraction, multiplication and division of a combinations and multiplicationand positive fractions, decimals, and Sixth Grade division combinations of fractions and decimals Solve multi-step word problems involving 6.2b, 6.4a; Specifies multi-step; includes b fractions, decimals and whole numbers multiplication and divisionion Estimate sums, differences, products and 1.6a, 6.3a; Includes multiplication and quotients of rational numbers using c division but not necessarily in problem common fractions, common decimals, solving situations and whole numbers Compare and round positive numbers d from thousandths through millions Quantities can be expressed and 3 Number Sense, Properties, and compared using ratios and rates Apply the multiplicative identity to create a equivalent fractions and to reduce fractions to simplest form Sixth Grade Operations Express the comparison of two whole number quantities using differences, part b to part ratios, and part to whole ratios in real contexts, including investing and saving (PFL) Compute unit rates in real world situations involving mixtures, c concentrations, and distance-time relationships Page 25 of 55 Math Standards Crosswalk Sixth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Patterns can be described using 1 Patterns, Functions, and words, tables, and graphs Algebraic Structures Extend the pattern and describe the rule 2.1a, 2.2a; Now specifies extending; now a for arithmetic and geometric sequences includes describing the rule 6th Grade Model linear situations using tables and 2.3a, 2.5a; Now includes converting b graphs, and convert between these two between representations representations Given a linear equation, substitute non- negative input values to create a table c and graph coordinate points in the 1st quadrant Variables are used to represent Functions, and 2 unknown quantities Structures 6th Grade Algebraic Patterns, Describe patterns by using words and by 2.1a; Includes use of variables and a using variables with mathematical symbols symbols Evaluate expressions by substituting b whole number values for variables Questions can be answered by collecting and analyzing data and Data Analysis, Statistics, and 1 data displays Formulate questions for populations a larger than the classroom Recognize that a sample may not Sixth Grade Probability b represent a population accurately Recognize bias in surveys c Utilize appropriate techniques to design a d random sample Recognize the use of deceptive scales on a graph that make differences look much larger than they are, or the use of pictographs with areas that are e proportioned incorrectly Page 26 of 55 Math Standards Crosswalk Sixth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Mathematical models are used to Data Analysis, Statistics, and 2 determine probability Determine probabilities through a experiments or simulations Sixth Grade Express the probability of an event using Probability b fractions, decimals, and percents Make a table, tree diagram or an organized list to determine possible outcomes of two or more compound 3.7a; Now includes two or more c events compound events Predict outcomes of events using 3.6.b; Now includes theoretical d experimental and theoretical probabilities probabilities Polygons can be described, classified, 1 and analyzed by their attributes Geometric Relationships Shape, Dimension, and Develop and apply formulas and a procedures for finding area of triangles, 4.5b, 5.4b; Now includes trapezoids Sixth Grade parallelograms, and, trapezoids Describe properties of polygons up to ten 4.2a; “Identify” changed” to “describe”; b sides accurate vocabulary and notation now includes accurate notation Classify triangles and apply angle and c side properties, including the sum of the interior angles Use accurate geometric notation to d describe angles, lines, and segments Page 27 of 55 Math Standards Crosswalk Sixth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Standard units provide common 2 language for communicating Geometric Relationships Shape, Dimension, and measurements a Connect metric prefixes to place value Sixth Grade Measure to the nearest sixteenth of an b inch Select and use appropriate units to 5.1a, 5.1b; No longer includes accurately measure length, weight, temperature or estimation; “estimate” c changed to “accurately measure”; now capacity and time in problem solving situations includes time and use in problem solving situations Use a protractor to measure angles to the d nearest degree Page 28 of 55 Math Standards Crosswalk Fifth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives The characteristics of numbers can Number Sense, Properties, 1 be used to classify them in various ways and Operations Apply concepts of squares, primes, 1.1c, 1.3a, 1.3c; “Identify” changed to Fifth Grade a composites, factors, and multiples to “apply” solve problems Use the identity, associative, 1.5a, 1.5b, 2.1c b commutative, and distributive properties to solve problems Describe and use divisibility rules for 2, 3, c 4, 5, 6, 9, and 10 to solve problems In the real number system, commonly used rational numbers 2 have multiple equivalent Number Sense, Properties, and Operations representations Find equivalent forms of commonly used 1.1b, 1.4a; Now includes computational fractions, decimals, and percents using a strategies models, drawings, and computational strategies Fifth Grade Use common fractions and percents to calculate parts of whole numbers in 6.1a; Now includes fraction of a whole b problem situations, including comparisons and personal financial literacy of savings rates at different financial institutions (PFL) Model addition, subtraction, and 6.2d, 6.2e; Now includes c multiplication of fractions, decimals, and percents Compose and decompose multi-digit 1.3b; Now includes decimals d numbers based on place value; whole and decimal Represent numbers to 1,000,000 with e expanded notation and exponents Page 29 of 55 Math Standards Crosswalk Fifth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Formulate, represent, and use algorithms to mulitply and divide Number Sense, Properties, and Operations 3 multi-digit whole numbers with flexibilty, accuracy, and efficiency Use flexible methods of computing 6.2b, 6.2c, 6.4b; More specificity on including student-generated and computation; no longer includes addition a standard algorithms to multiply and and subtraction divide multi-digit numbers by two-digit Fifth Grade factors or divisors 6.2a; More specificity on models Model multiplication and division using expected; no longer includes addition and b area, linear, and grouping models subtraction Interpret remainders and select the most c useful form of the quotient in division problems Select and use appropriate methods to estimate products and quotients or 1.6b, 6.3a, 6.3b, 6.4d d calculate them mentally depending on the context and numbers involved Number patterns and relationships Patterns, Functions, 1 can be described using a variety of tools and Algebraic Fifth Grade Analyze and describe patterns and Structures 2.1a, 2.2a, 2.5a; Now includes a relationships using words, tables, graphs, technology symbols, and technology Explain, extend, and use patterns and relationships in solving problems, 2.1a, 2.2a; Now includes personal b including those involving saving and financial literacy checking accounts such as spending more means saving less (PFL) Page 30 of 55 Math Standards Crosswalk Fifth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives When a relationship exists between 2 two quantities, a change in one Patterns, Functions, and results in a change in the other Algebraic Structures Express change relationships involving 2.1a, 2.2a, 2.3a, 2.5a; Now change whole numbers with if/then statements, Fifth Grade a relationships and if/then statements are input/output boxes, function tables, and new rule statements Select, describe and use symbols to b 2.1b; “Variables” changed to “symbols” express unknown quantities Use patterns to solve problems including those involving saving and checking 2.1a, 2.2a; Now includes personal c accounts such as the pattern created financial literacy when saving $10 a month (PFL) Visual displays and summary statistics are used to describe and Data Analysis, Statistics, and 1 interpret data Formulate a question and hypothesis to design appropriate data collection and Implied in 3.4a a display methods Fifth Grade Probability Select and create appropriate displays of data including double bar graphs, time 3.1b, 3.1d; Now includes double bar b plots, and line graphs. graphs and time plots Interpret data using the concepts of shape of distribution, range, mode, 3.2a, 3.2b; Now includes mean and shape c median and mean of distribution Draw conclusions, and make convincing arguments based on categorical and d numerical data analysis 3.1a, 3.1c, 3.3a, 3.4b Page 31 of 55 Math Standards Crosswalk Fifth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Mathematical models are used to Data Analysis, Statistics, and determine probability analyze and 2 describe the outcomes of events Organize all possible outcomes of events a in a list or chart 3.7a; “Solve” changed to “organize” Fifth Grade Probability Use fractions, decimals, and percents to b quantify the likelihood of events 3.5c; Now includes decimals and percents Explain why a game involving a chance devices such as number cubes or spinners c is fair or unfair 3.6a; No longer includes designing Compare individual data to class data collected from chance devices to describe the differences in outcomes based on 3.6b; No longer includes prediction; d sample size emphasis on sample size Geometric figures in the plane and in 1 space are described and analyzed by Geometric Relationships Shape, Dimension, and their attributes Relate two-dimensional shapes to three- 4.1a, 4.2a; Now includes faces, edges a dimensional shapes using faces, edges, Fifth Grade and vertices and vertices Predict and describe the results of 4.6a; Now includes formal mathematical b transformations: translations, reflections, language for transformations rotations 5.1d, 5.1e; Now includes comparison of c Classify and compare angles angles Apply concepts of parallel, perpendicular, d 4.2a, 4.6b; Now includes congruence congruence and line symmetry Page 32 of 55 Math Standards Crosswalk Fifth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Linear measure, area, and volume are 2 fundamentally different and require Geometric Relationships Shape, Dimension, and different units of measure Accurately measure length to the nearest a 5.6b; Now includes nearest 1/8" and mm 1/8 inch or millimeter Fifth Grade Determine the perimeter of polygons and b 4.5a, 4.5b, 5.4a area of rectangles Distinguish between appropriate units for c 5.1a, 5.6a area and linear measures d Model volume using cubic units Use, apply, and select appropriate scales e 5.3a, 5.3b on number lines, graphs, and maps Page 33 of 55 Math Standards Crosswalk Fourth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives The decimal number system describes place value patterns and Number Sense, Properties, and relationships that are repeated in 1 large and small numbers and forms the foundation for efficient algorithms Fourth Grade Operations Read and write numbers from 1 to 1.2a, 1.2b; Includes numbers to 100,000; a 100,000 and explain place value for five- ordering removed; “identify” changed to digit numbers “explain” Compose and decompose multi-digit b 1.2b (embedded), 1.2c numbers based on place value Read and write numbers to the c hundredths place Identify the value of any given digit in a d number with decimals to the hundredths place Page 34 of 55 Math Standards Crosswalk Fourth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Formulate, represent, and use algorithms Number Sense, Properties, and Operations 2 to mulitply and divide with flexibilty, accuracy, and efficiency Use flexible and efficient methods of computing including standard algorithms 6.4b; No longer includes addition and a to solve three or four digit by one-digit subtraction multiplication or division problems Fourth Grade Estimate using strategies such as front 1.5a, 6.4a; No longer includes addition b end or rounding to justify the and subtraction reasonableness of solutions to problems Demonstrate fluency with multiplication 6.3a; “Understanding” changed to c facts and their related division facts 0 to “fluency” 12 Explain why multi-digit multiplication and division procedures work based on place 6.1a; Explain based on place value d value properties and use them to solve properties problems Different models and representations Number Sense, Properties, and 3 can be used to compare fractional parts Solve comparison problems using models 1.1a; Now includes all denominators Fourth Grade a of fractions with like and unlike Operations through 10 denominators through 10 Estimate and justify the reasonableness b of solutions to problems involving comparison of fractions Demonstrate equivalent fractions, c decimals, and percents using drawings and models Page 35 of 55 Math Standards Crosswalk Fourth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Number patterns and relationships 1 Patterns, Functions, can be represented by symbols and Algebraic Use number relationships to find the Fourth Grade a 2.1b Structures missing number in a sequence Use a symbol to represent and find an b unknown quantity in a problem situation c Complete input/output tables 2.2a; 2.3a; 2.4a d Find the unknown in simple equations Number properties and relationships 2 can be used to solve problems Patterns, Functions, and Algebraic Structures Use and describe number patterns for 1.3a; Includes description of number Fourth Grade a counting by 2, 5, 9, 10, and 11 from a patterns; no longer includes 3 and 100; given starting number now includes 9 and 11 Communicate the inverse relationship between multiplication and division, and b use this relationship to efficiently solve and check problems Use the commutative and associative 1.4b; Only multiplication; excludes c properties of multiplication to solve properties of 0 and 1 problems Data Analysis, Statistics, Visual displays of classroom data can be used to summarize information and Probability 1 across the content areas Fourth Grade Compose questions to generate data a related to grade level areas of study Collect data from class experiments or b multi-classroom surveys Create data displays appropriate to data 3.1a; Addresses appropriate displays for c collected data Describe data using the concept of shape d of the distribution Page 36 of 55 Math Standards Crosswalk Fourth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Mathematical models are used to test predictions about the likehood of Data Analysis, Statistics, and 2 events Formulate a question to test a prediction, 3.3a; Contains an element in this conduct an experiment using chance objective with a greater depth of Fourth Grade devices, such as coins, spinners, and Probability knowledge a number cubes, to test predictions Represent the outcomes of experiments with fractions, and describe using the concepts of impossible, unlikely, likely, 3.3b; Includes impossible and certain; b and certain represents outcomes with fractions Describe the likelihood of real life situaton using the likelihood of real life situations using the concepts of impossible, 3.3b; Includes impossible and certain and c unlikely, likely and certain (PFL) real life situations Geometric figures are described by 1 their attributes and specific location Geometric Relationships in the plane Shape, Dimension, and Identify parallel, perpendicular, and a intersecting line segments in the plane 4.2a; 4.2b; Includes perpendicular Fourth Grade and within geometric shapes Create geometric designs using b transformations (reflections, translations, and rotations) Compare geometric figures according to 4.1a, 4.1b, 4.2a; “Identify” changed to c the attributes of congruence, symmetry, “compare” and angle size. Name and locate points specified by d ordered number pairs on a coordinate 4.4a; Now specifies all quadrants grid Page 37 of 55 Math Standards Crosswalk Fourth Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Appropriate measurement tools, units, and systems are used to 2 measure different attributes of Shape, Dimension, and Geometric objects and time a Model area using square units 5.3b b Distinguish between area and perimeter 4.3a; “Solve” changed to “distinguish” Relationships Convert using unit equivalencies within Fourth Grade the standard measurement system (yards c to feet and feet to inches, pounds to ounces, gallons to quarts) Convert using unit equivalencies within the metric measuring system (meters to d centimeters, kilometers to meter, and liters to milliliters) Estimate and measure elapsed time to e the nearest quarter hour. Select an appropriate tool and unit for 5.1b; Now excludes area, volume, f measuring length, weight and capacity. temperature, time 5.5a; Now excludes area Page 38 of 55 Math Standards Crosswalk Third Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Number Sense, Properties, and The whole number system describes place value relationships from ones 1 to 10,000 and forms the foundation for efficient algorithms Third Grade Operations Read and write numbers from 1 to 10,000 1.2a,1.2b,1.2c; Ordering no longer a and explain place value for four-digit included; “identify” changed to “explain” numbers Generalize the change represented when b moving from one place to another place in a number Compose and decompose multi-digit 1.2c,1.2d; “Equivalent representations” c numbers based on place value changed to “compose and decompose” Parts of a whole can be modeled and 2 represented in different ways Number Sense, Properties, and Use drawings, models, and numerals to represent fractions (halves, thirds, 1.1b,1.3b; “Identify” changed to a fourths, sixths, eighths) based on a whole “represent”; added sixths and eighths Third Grade Operations shape, number set, or number line Estimate and justify the reasonableness 1.5a; Justification added; now includes b of solutions to problems involving fractions representations of fractions Describe why equivalent fractions are two c ways of modeling the same quantity using a model or drawing Page 39 of 55 Math Standards Crosswalk Third Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Formulate, represent, and use Number Sense, Properties, and algorithms to add and subtract multi- 3 digit whole numbers with flexibilty, accuracy, and efficiency Third Grade Operations Use number sense to estimate and justify a the reasonableness of solutions to 1.5a; Justification added problems Use flexible methods of computing, 6.5a; “Student generated strategies” b including student-generated strategies included; eliminated multiplication and standard algorithms Estimate using strategies such as front c 1.5a, 6.4a end estimation or landmark numbers Multiplying and dividing are inverse 4 operations modeled in a variety of Number Sense, Properties, and ways 6.3a; “Understanding” changed to Demonstrate fluency with multiplication a “fluency”; includes all single digit facts; and division facts with single digit factors now includes division Third Grade Operations Describe relationships between related b facts and between multiplication and division. Represent multiplication and division An add on from 6.1a of addition and c problems with drawings, models, number subtraction sentences, and stories. Model strategies to achieve a personal d financial goal using arithmetic operations (PFL) Page 40 of 55 Math Standards Crosswalk Third Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Number patterns are based on 1 Patterns, Functions, Patterns, Functions, operations and relationships and Algebraic Extend simple arithmetic and geometric 2.1a, 2.1b; Now includes simple Third Grade a Structures sequences arithmetic sequences Count by and analyze patterns in b multiples of 2, 3, 5, 9, 10, 11, 25, 50 and 2.1b; Now includes 9,11, 25, 50,and 100 100 Use known multiplication facts to solve c unknown multiplication problems Number properties can be used to 2 solve problems and Algebraic Use the commutative property to solve Third Grade Structures a 1.4b; Now includes multiplication addition and multiplication problems Use the associative property to solve b 1.4b addition problems. Use the relationship between addition and c multiplication to solve problems. Data Analysis, Statistics, Visual displays of data can be used to answer questions of interest 1 and Probability Third Grade Compose questions to generate data a Collect and organize data from simple b experiments or surveys in class 3.1a; Data collection added Create picture graphs, bar graphs, dot plots, and frequency tables from a data 3.1a; Dot plots and frequency tables c set added Describe data using the concepts of 3.2a; Now includes description of clusters d mode, clusters and gaps and gaps Page 41 of 55 Math Standards Crosswalk Third Grade Referent: Grade Level Expectations Standard Grade CSAP Assessment Framework District Curriculum Notes Implications Evidence Outcomes Objectives Mathematical models are used to Data Analysis, Statistics, and 2 explore and describe fairness Third Grade Probability Investigate chance devices such as coins, a spinners, and number cubes 3.3a Apply the concepts of impossible, unlikely b and likely 3.3a Determine if a chance device is fair or c unfair Geometric figures are described by Geometric Relationships 1 their attributes and position in the Shape, Dimension, and plane Construct and describe two-dimensional Third Grade 4.2a; Now includes “construct” and a shapes by attributes and properties such “describe” as sides, angles, and symmetry Recognize and demonstrate transformations - reflections, b translations, and rotations - of basic shapes or designs Use geometric properties of points and c 4.2b line segments to describe figures Objects have distinct attributes that Shape, Dimension, 2 can be measured with appropriate and Geometric Relationships Third Grade tools Use standard units to measure to the 5.3a; Degree of precision now indicated a nearest 1/2 or whole inch or centimeter as nearest 1/2” Estimate and measure distance and 4.3a, 5.1c,5.3a, 5.4a; Includes b perimeter estimation and measurement of distance Page 42 of 55 Math Standards Crosswalk Second Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Number Sense, Properties, The whole number system describes place value relationships from ones 1 to 1,000 and forms the foundation for and Operations Second Grade efficient algorithms Read and write numbers to 1,000 and a identify place value for three-digit numbers Describe relationships between ones, b tens, and hundreds Explain the value of a digit in a three- c digit number d Order a collection of whole numbers Formulate, represent, and use Number Sense, Properties, and Operations algorithms to add and subtract two- 2 digit whole numbers with flexibilty, accuracy, and efficiency Demonstrate fluency with basic addition a and subtraction facts to sums of twenty Second Grade Find value of a collection of coins and b choose coins to have a given value Create stories and models, including c linear and difference, to illustrate addition and subtraction Select and use appropriate methods to estimate sums and differences or d calculate them mentally depending on the context and numbers involved Apply addition and subtraction concepts e to financial decision making (PFL) Page 43 of 55 Math Standards Crosswalk Second Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Fractions represent parts of a whole Properties, and Number Sense, Second Grade 3 object or set Operations Partition basic shapes, using common a fractions such as 1/2, 1/3, and 1/4 Partition sets using common fractions b such as 1/2, 1/3, 1/4 1 Patterns are based on rules Patterns, Functions, Count objects by groups using 2, 5, and a Second Grade and Algebraic 10 Structures Identify a missing number in a sequence, b and describe a rule Create and extend repeating patterns of 3- 5 elements using a variety of materials c such as numbers, letters, shapes, and manipulatives Number relationships can be used to Patterns, Functions, and 2 Algebraic Structures develop computation strategies Use ten based strategies to solve addition Second Grade a and subtraction facts to 20 Demonstrate the structure of numbers as b tens and ones in addition and subtraction Communicate the inverse relationship c between addition and subtraction, and use this relationship to efficiently solve and check problems Page 44 of 55 Math Standards Crosswalk Second Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Visual displays of data can be Data Analysis, Statistics, and Second Grade 1 constructed in a variety of formats Probability Construct picture graphs and bar graphs a from a data set Read and explain information in picture b graphs and bar graphs. Describe data using concepts of median c and range Mathematical models are used to Data Analysis, Statistics, and Second Grade describe the likelihood of an outcome Probability 2 or event Collect data using chance devices, such as spinners and describe outcomes as a likely or unlikely. Apply the concepts of likely or not likely b to decisions from daily life (PFL) Shape, Dimension, and Shapes can be created and described 1 by quantifiable attributes Second Grade Relationships Recognize, describe, and create Geometric geometric figures according to given a quantifiable attributes (e.g., number of sides and size) Identify symmetry in two-dimensional b figures Use quantifiable attributes to describe c and estimate size of objects Page 45 of 55 Math Standards Crosswalk Second Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Some attributes of objects are Geometric Relationships 2 measurable and can be quantified Shape, Dimension, and using different tools Second Grade Identify the measurable attribute and a appropriate unit of measure for an object Use common objects as non-standard b units Use standard linear measuring tools to c measure to the nearest whole unit Identify common units of time, weight, d and temperature and their appropriate use Page 46 of 55 Math Standards Crosswalk First Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes The whole number system describes place value relationships from ones Number Sense, Properties, and 1 to one-hundred and forms the foundation for efficient algorithms First Grade a Count, read, and write numbers to 100 Operations b Estimate quantities less than 100 Represent quantities using tens units and c ones units Locate numbers up to 100 on a number d display Compare two sets of objects, including e pennies, up to at least 25 using language such as "three more or three fewer" (PFL) Page 47 of 55 Math Standards Crosswalk First Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Adding and subtracting involves 2 composing and decomposing using a variety of strategies Number Sense, Properties, and Use addition when putting sets together a and subtraction for breaking sets apart or describing the difference between sets First Grade Operations Use number relationships such as doubles, one more or one less, and the b relationship between composing and decomposing to solve addition and subtraction problems Identify coins and find the value of a c collection of two coins(PFL) Demonstrate fluency with basic addition d and related subtraction facts through sums to 10 Parts of objects can be shown as 3 Properties, and Number Sense, fractions First Grade Operations Identify unit fractions 1/2, 1/3, and 1/4 a as parts of wholes or parts of groups Understand fractions as equal shares or b parts Page 48 of 55 Math Standards Crosswalk First Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes First Grade 1 Patterns can grow Structures Functions, Algebraic Patterns, and a Count objects by groups of 2 or 5. Extend a repeating pattern based on a b rule. Number relationships can be used to 2 Functions, and solve problems First Grade Structures Algebraic Patterns, Use number relationships such as a doubles, or plus or minus one to solve problems Use the inverse relationship between b adding and subtracting to solve problems Visual displays of data can be created 1 using individual student data Data Analysis, Statistics, and First Grade Probability Contribute individual data to classroom a data display Read information from picture graphs, b bar graphs, and tally charts Describe data by applying the concepts of c largest, smallest and most often Page 49 of 55 Math Standards Crosswalk First Grade Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Shapes can be created and described Geometric Relationships Shape, Dimension, and 1 by composing and decomposing Recognize, describe, and make shapes First Grade a according to given relationships, attributes, or properties. Sort geometric figures and describe how b they are alike and different Combine and take apart shapes tocreate c new shapes and describe results Measurement is used to compare and 2 Geometric Relationships order objects and events Shape, Dimension, and Measure the length of common objects a using nonstandard units such as created First Grade units, popsicle sticks, or paper clips Compare and order objects by length and b weight Distinguish units of time (day, night, c morning, afternoon, hours) and connect them to common events d Compare and order units of time Page 50 of 55 Math Standards Crosswalk Kindergarten Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Whole numbers can be used to name, Number Sense, Properties, and 1 count, represent, and order quantity a Count and represent objects to 20 Identify, read, and write corresponding b Kindergarten numerals Operations Compare sets up to 10 objects and use c language to describe more, less, or same Compare two sets of objects to at least d 25 using language such as “more”, “less”, or “the same” Identify small groups of objects fewer e than 5 without counting, including zero as “no objects” f Estimate quantities less than 20 Adding and subtracting to ten Number Sense, Properties, involves composing and decomposing 2 using a variety of strategies and representations and Operations Kindergarten Use objects, including coins,and drawings a to model addition and subtraction problems to 10 (PFL) Identify numbers one more or one less b than a given number up to 10 Determine if more than or less than is c needed to change one quantity to another Page 51 of 55 Math Standards Crosswalk Kindergarten Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Functions, and Kindergarten 1 Patterns can repeat Structures Algebraic Patterns, a Duplicate a simple pattern Extend a repeating two element pattern using a variety of materials such as b numbers, letters, shapes, and manipulatives 2 Relationships exist between numbers Functions, and Kindergarten Structures Generalize the counting sequence pattern Algebraic Patterns, a from counting all to knowing “one more” and “one less” Communicate the relationship between b composing and decomposing numbers Visual displays of classroom information can used to answer Data Analysis, Statistics, and 1 Kindergarten questions Probability Collect classroom data a Identify and compare own data to group's b data Describe bar graphs to answer questions c such as more or less and simple trends. Page 52 of 55 Math Standards Crosswalk Kindergarten Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Shapes are described by their Dimension, and 1 Relationships Kindergarten characteristics and position Geometric Shape, Recognize and informally describe two a dimensional shapes with varying orientation, sizes, and shapes. Use relational vocabulary to describe b spatial relationships (e.g., above, below, next to) Measurement is used to compare and 2 Shape, Dimension, order objects and Geometric Relationships Kindergarten Recognize and compare attributes of a length, height, weight, capacity of objects Use estimates of measurements from b everyday experiences Order several objects by length, height, c weight, capacity, or price (PFL) Page 53 of 55 Math Standards Crosswalk Preschool Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Quantities can be represented and 1 Properties, Operations Preschool counted Number Sense, Count and represent objects, including and a coins, to 10 (PFL) b Match a quantity with a numeral Counting is a means for solving 2 Properties, and Number Sense, problems Operations Preschool Use vocabulary of same, different, more, a and less to express number relationships Solve problems answering the question b “how many” to ten Objects can be sorted based on Structures Functions, 1 Preschool Algebraic Patterns, patterns and relationships and a Sort by a single attribute Match, place in a series, and group b objects according to one attribute Information and objects can be Data Analysis, Statistics, and 1 sorted Probability Preschool Use words to describe attributes of a objects Sort and group similar objects into b simple categories Contribute to class display of information c (charts, graphs) Shapes can be observed in the world Dimension, and Relationships 1 and described in relation to one Geometric Preschool another Shape, Match, sort, group and name basic a shapes found in the natural environment Follow directions to arrange, order, or b position objects Page 54 of 55 Math Standards Crosswalk Preschool Grade Level Expectations Standard Grade District Curriculum Notes Implications Evidence Outcomes Measurement is used to compare Shape, Dimension, 2 objects and Geometric Relationships a Describe the order of common events. Preschool Group objects according to their size using standard and non-standard forms b (height, weight, length, or color brightness) of measurement Sort coins by physical attributes such as c color or size (PFL) Page 55 of 55