# Geometry

Document Sample

```					                                                        Geometry
Standard                                              Objective                                                   Taught
Kansas Standards, 2004
Standard 1       use numerical and computational concepts and procedures in a variety of situations.
demonstrate number sense for real numbers and algebraic expressions in a variety
S1.B1        R/M of situations.
know, explain, and use equivalent representations for rational numbers and simple
algebraic expressions including integers, fractions, decimals, percents, and ratios;
rational number bases with integer exponents; rational numbers written in scientific
1.1.K1        R notation with integer exponents; time; and money (\$).
generate and/or solve real-world problems using equivalent representations of real
numbers and algebraic expressions (\$), e.g., a math classroom needs 30 books and
15 calculators. If B represents the cost of a book and C represents the cost of a
calculator, generate two different expressions to represent the cost of books and
1.1.A1        R calculators for 9 math classrooms.

determine whether or not solutions to real-world problems using real numbers and
algebraic expressions are reasonable (\$), e.g., in January, a business gave its
employees a 10% raise. The following year, due to the sluggish economy, the
employees decided to take a 10% reduction in their salary. Is it reasonable to say
1.1.A2        R    they are now making the same wage they made prior to the 10% raise.
demonstrate an understanding of the real number system; recognizes, applies, and
S1.B2              explain their properties; and extend these properties to algebraic expressions.
explain and illustrate the relationship between the subsets of the real number system
[natural (counting) numbers, whole numbers, integers, rational numbers, irrational
1.2.K1        R    numbers] using mathematical models, e.g., number lines or Venn diagrams.
identify all the subsets of the real number system [natural (counting) numbers, whole
numbers, integers, rational numbers, irrational numbers] to which a given number
1.2.K2        R    belongs.
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: commutative (a +
b = b + a and ab = ba), associative [a + (b + c) = (a + b) + c and a(bc) = (ab)c],
distributive [a (b + c) = ab + ac], and substitution properties (if a = 2, then 3a = 3 x 2
*1.2.K3a     R/M   = 6) (\$).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: identity properties
(additive identity: a + 0 = a, multiplicative identity: a o 1 = a, additive inverse: +5 + -5
*1.2.K3b     R/M   = 0, multiplicative inverse: 8 x 1/8 = 1) (\$).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: symmetric
*1.2.K3c     R/M   property of equality (if a = b, then b = a) (\$).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: addition and
multiplication properties of equality (if a = b, then a + c = b + c and if a = b, then ac =
bc) and inequalities (if a > b, then a + c > b + c and if a > b, and c > 0 then ac > bc)
*1.2.K3d     R/M   (\$).
name, use, and describe the following property with the real number system and
demonstrate their meaning including the use of concrete objects: zero product
*1.2.K3e     R/M   property (if ab = 0, then a = 0 and/or b = 0) (\$).
use and describe the following property with the real number system: transitive
1.2.K4a      R/M   property (if a = b and b = c, then a = c) (\$).
use and describe the following property with the real number system: reflexive
1.2.K4b      R/M   property (a = a) (\$).

1
Geometry
generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: commutative, associative, distributive,
and substitution properties, e.g., the chorus is sponsoring a trip to an amusement
park. They need to purchase 15 adult tickets at \$6 each and 15 student tickets at \$4
each. How much money will the chorus need for tickets? Solve this problem two
1.2.A1a   R   ways (\$).

generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: identity and inverse properties of
addition and multiplication, e.g., the purchase price (P) of a series EE Savings Bond
is found by the formula ½ F = P where F is the face value of the bond. Use the
1.2.A1b   R   formula to find the face value of a savings bond purchased for \$500 (\$).
generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: symmetric property of equality, e.g.,
Sam took a \$15 check to the bank and received a \$10 bill and a \$5 bill. Later Sam
took a \$10 bill and a \$5 bill to the bank and received a check for \$15. \$ addition and
multiplication properties of equality, e.g., the total price for the purchase of three
shirts in \$62.54 including tax. If the tax is \$3.89, what is the cost of one shirt, if all
1.2.A1c   R   shirts cost the same? (\$).

generate and/or solve real-world problems with real numbers using the concepts of
the following property to explain reasoning: addition and multiplication properties of
equality, e.g., the total price for the purchase of three shirts is \$62.54 including tax.
1.2.A1d   R   If the tax is \$3.89, what is the cost of one shirt? (\$).

generate and/or solve real-world problems with real numbers using the concepts of
these properties to explain reasoning:zero product property, e.g., Jenny was thinking
of two numbers. Jenny said that the product of the two numbers was 0. What could
1.2.A1e   R   you deduct from this statement? Explain your reasoning (\$).
numbers, fractions (including mixed numbers), decimals or irrational numbers and
their rational approximations in solving a given real-world problem (\$), e.g., a store
sells CDs for \$12.99 each. Knowing that the sales tax is 7%, Marie estimates the
cost of a CD plus tax to be \$14.30. She selects nine CDs. The clerk tells Marie her
1.2.A2    R   bill is \$157.18. How can Marie explain to the clerk she has been overcharged?
S1.B3         use computational estimation with real numbers in a variety of situations.
estimate real number quantities using various computational methods including
1.3.K1    R   mental math, paper and pencil, concrete objects, and/or appropriate technology (\$).
use various estimation strategies and explain how they were used to estimate real
1.3.K2    R   number quantities and algebraic expressions (\$).
know and explain why a decimal representation of an irrational number is an
1.3.K3    R   approximate value.
1.3.K4    R   know and explain between which two consecutive integers an irrational number lies.
adjust original rational number estimate of a real-world problem based on additional
information (a frame of reference) (\$), e.g., estimate how long it takes to walk from
*1.3.A1   R   here to there; time how long it takes to take five steps and adjust your estimate.
estimate to check whether or not the result of a real-world problem using real
numbers and/or algebraic expressions is reasonable and make predictions based on
the information (\$), e.g., if you have a \$4,000 debt on a credit card and the minimum
1.3.A2    R   of \$30 is paid per month, is it reasonable to pay off the debt in 10 years?
determine if a real-world problem calls for an exact or approximate answer and
perform the appropriate computation using various computational methods including
mental mathematics, paper and pencil, concrete objects, and/or appropriate
technology (\$), e.g., do you need an exact or an approximate answer in calculating
the area of the walls to determine the number of rolls of wallpaper needed to paper a
1.3.A3    R   room? What would you do if you were wallpapering 2 rooms?

2
Geometry
explain the impact of estimation on the result of a real-world problem
(underestimate, overestimate, range of estimates) (\$), e.g., if the weight of 25 pieces
of paper was measured as 530.6 grams, what would the weight of 2,000 pieces of
paper equal to the nearest gram? If the student were to estimate the weight of one
piece of paper as about 20 grams and then multiply this by 2,000 rather than multiply
the weight of 25 pieces of paper by 80; the answer would differ by about 2,400
grams. In general, multiplying or dividing by a rounded number will cause greater
1.3.A4        R discrepancies than rounding after multiplying or dividing.
model, perform, and explain computation with real numbers and polynomials in a
S1.B4            variety of situations.
compute with efficiency and accuracy using various computational methods
1.4.K1        R including mental math, paper and pencil, concrete objects, and appropriate
perform and explain the following computational procedure: addition, subtraction,
1.4.K2a      R/M multiplication, and division using the order of operations (N).
perform and explain the following computational procedure: multiplication or division
1.4.K2bi      R to find a percent of a number, e.g., what is 0.5% of 10? (\$).
perform and explain the following computational procedure: multiplication or division
to find percent of increase and decrease, e.g., a college raises its tuition form \$1,320
1.4.K2bii     R per year to \$1,425 per year. What percent is the change in tuition? (\$).
perform and explain the following computational procedure: multiplication or division
1.4.K2biii    R to find percent one number is of another number, e.g., 89 is what percent of 82? (\$).
perform and explain the following computational procedure: multiplication or division
to find a number when a percent of the number is given, e.g., 80 is 32% of what
1.4.K2biv     R number? (\$).
perform and explain the following computational procedure: manipulation of variable
quantities within an equation or inequality (2.4.K1d), e.g., 5x - 3y = 20 could be
1.4.K2c       R written as 5x - 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3.
perform and explain the following computational procedure: simplification of radical
expressions (without rationalizing denominators) including square roots of perfect
1.4.K2d       R square monomials and cube roots of perfect cubic monomials.
perform and explain the following computational procedure: simplification or
evaluation of real numbers and algebraic monomial expressions raised to a whole
1.4.K2e       R number power and algebraic binomial expressions squared or cubed.
perform and explain the following computational procedure: simplification of
products and quotients of real number and algebraic monomial expressions using
1.4.K2f       R the properties of exponents.
find prime factors, greatest common factor, multiples, and the least common multiple
1.4.K3        R of algebraic expressions.
generate and/or solve multi-step real-world problems with real numbers and
algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with applications from business, chemistry, and physics that involve
addition, subtraction, multiplication, division, squares, and square roots when the
formulae are given as part of the problem and variables are defined, e.g., given F =
ma, where F = force in newtons, m = mass in kilograms, a = acceleration in meters
*1.4.A1a      R per second squared. Find the acceleration if a force of 20 newtons is applied to a
generate and/or solve multi-step real-world problems with real numbers and
algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with volume and surface area given the measurement formulas of
rectangular solids and cylinders, e.g., a silo has a diameter of 8 feet and a height of
*1.4.A1b      R 20 feet. How many cubic feet of grain can it store? (\$).
generate and/or solve multi-step real-world problems with real numbers and
algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with probabilities, e.g., if the probability of getting a defective light bulb is
1.4.A1c       R 2%, and you buy 150 light bulbs, how many would you expect to be defective? (\$).

3
Geometry
generate and/or solve multi-step real-world problems with real numbers and
algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
*1.4.A1d      R      concepts with application of percents (\$) (O).
generate and/or solve multi-step real-world problems with real numbers and
algebraic expressions using computational procedures (addition, subtraction,
multiplication, division, roots, and powers excluding logarithms), and mathematical
concepts with simple exponential growth and decay (excluding logarithms) and
economics, e.g., a population of cells doubles every 20 years. If there are 20 cells to
start with, how long will it take for there to be more than 150 cells? or If the radiation
level is now 400 and it decays by ½ or its half-life is 8 hours, how long will it take for
1.4.A1e       R      the radiation level to be below an acceptable level of 5? (\$).
Standard 2           use algebraic concepts and procedures in a variety of situations.
recognize, describe, extend, develop, and explain the general rule of a pattern in
S2.B1        R/M     variety of situations.
identify, state, and continue the following patterns using various formats including
numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph),
verbal (oral description), kinesthetic (action), and written: arithmetic and geometric
2.1.K1a      R/M     sequences using real numbers and/or exponents; e.g., radioactive half-lives.
identify, state, and continue the following patterns using various formats including
numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph),
verbal (oral description), kinesthetic (action), and written: patterns using geometric
2.1.K1b      I/R/M   figures.
identify, state, and continue the following patterns using various formats including
numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph),
verbal (oral description), kinesthetic (action), and written: algebraic patterns
including consecutive number patterns or equations of functions, e.g., n, n + 1, n + 2,
2.1.K1c      I/R/M   ... or f(n) = 2n - 1.
identify, state, and continue the following patterns using various formats including
numeric (list or table), algebraic (symbolic notation), visual (picture, table, or graph),
verbal (oral description), kinesthetic (action), and written: special patterns, e.g.,
2.1.K1d      I/R     Pascal's triangle and the Fibonacci sequence.
2.1.K2       R/M     generate and explain a pattern.
recognize the same general pattern presented in different representations [numeric
2.1.A1       I/R/M   (list or table), visual (picture, table, or graph), and written] (\$).
use variables, symbols, real numbers, and algebraic expressions to solve equations
S2.B2         R      and inequalities in variety of situations.
know and explain the use of variables as parameters for a specific variable situation,
2.2.K1       R/M     e.g., the m and b in y = mx + b.
manipulate variable quantities within an equation or inequality, e.g., 5x - 3y = 20
2.2.K2        R      could be written as 5x - 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3.
2.2.K3a       R      solve linear equations and inequalities both analytically and graphically (\$) (N).
represent real-world problems using variables, symbols, expressions, equations,
2.2.A1        R      inequalities, and simple systems of linear equations (\$).

represent and/or solve real-world problems with linear equations and inequalities
both analytically and graphically, e.g., tickets for a school play are \$5 for adults and
\$3 for students. You need to sell at least \$65 in tickets. Give an inequality and a
*2.2.A2a      R graph that represents this situation and three possible solutions (\$) (N).
S2.B3         R analyze functions in a variety of situations.
evaluate and analyze functions using various methods including mental math, paper
2.3.K1        R and pencil, concrete objects, and graphing utilities or other appropriate technology.
determine whether a graph, list of ordered pairs, table of values, or rule represents a
2.3.K3        R function.
recognize how changes in the constant and/or slope within a linear function changes
*2.3.K6      R/M the appearance of a graph (\$).
2.3.K7        R use function notation.
4
Geometry
2.3.K8     R  evaluate function(s) given a specific domain (\$).
interpret the meaning of the x- and y- intercepts, slope, and/or points on and off the
*2.3.A2    R line on a graph in the context of a real-world situation (\$) (O).
analyze the effects of parameter changes (scale changes or restricted domains) on
2.3.A3a    R the appearance of a function's graph.
analyze how changes in the constants and/or slope within a linear function affects
2.3.A3b    R the appearance of a graph.
develop and use mathematical models to represent and justify mathematical
relationships found in a variety of situations involving tenth grade knowledge and
S2.B4      R skills.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: factor trees
2.4.K1b    R to model least common multiple, greatest common factor, and prime factorization.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: algebraic
expressions to model relationships between two successive numbers in a sequence
2.4.K1c    R or other numerical patterns.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: coordinate
planes to model relationships between ordered pairs and equations and inequalities
2.4.K1f    R and linear and quadratic functions (\$).
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include:
2.4.K1g    R constructions to model geometric theorems and properties.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: two- and
three-dimensional geometric models (geoboards, dot paper, coordinate plane, nets,
or solids) and real-world objects to model perimeter, area, volume, and surface
area, properties of two- and three-dimensional figures, and isometric views of three-
2.4.K1h   R/M dimensional figures.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: scale
2.4.K1i   R/M drawings to model large and small real-world objects.
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: frequency
tables, bar graphs, line graphs, circle graphs, Venn diagrams, charts, tables, single
and double stem-and-leaf plots, scatter plots, box-and-whisker plots, histograms,
2.4.K1l    R and matrices to organize and display data (\$).
know, explain, and use mathematical models to represent and explain mathematical
concepts, procedures, and relationships. Mathematical models include: Venn
2.4.K1m    R diagrams to sort data and show relationships.
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: process models (concrete objects,
pictures, diagrams, flowcharts, number lines, hundred charts, measurement tools,
multiplication arrays, division sets, or coordinate grids) to model computational
procedures, algebraic relationships, mathematical relationships, and problem
2.4.A1a    R situations and to solve equations (\$).
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: equations and inequalities to
2.4.A1c    R model numerical and geometric relationships (\$).
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: function tables to model numerical
2.4.A1d    R and algebraic relationships (\$).
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: coordinate planes to model
relationships between ordered pairs and equations and inequalities and linear and
5
Geometry
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: two- and three-dimensional
geometric models (geoboards, dot paper, coordinate plane, nets, or solids) and real-
world objects to model perimeter, area, volume, and surface area, properties of two-
2.4.A1f      R/M     and three-dimensional figures and isometric views of three-dimensional figures.
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: scale drawings to model large and
2.4.A1g      R/M     small real-world objects.
recognize that various mathematical models can be used to represent the same
problem situation. Mathematical models include: frequency tables, bar graphs, line
graphs, circle graphs, Venn diagrams, charts, tables, single and double stem-and-
leaf plots, scatter plots, box-and-whisker plots, histograms, and matrices to describe,
2.4.A1i       R      interpret, and analyze data (\$).
use the mathematical modeling process to analyze and make inferences about real-
2.4.A2        R      world situations (\$).
Standard 3           use geometric concepts and procedures in a variety of situations.
recognize geometric figures and compare and justify their properties of geometric
S3.B1        I/R/M   figures in a variety of situations.
recognize and compare properties of two-and three-dimensional figures using
concrete objects, constructions, drawings, appropriate terminology, and appropriate
3.1.K1       I/R/M   technology.
3.1.K2a      I/R/M   discuss properties of regular polygons related to angle measures.
3.1.K2b      I/R/M   discuss properties of regular polygons related to diagonals.
recognize and describe the symmetries (point, line, plane) that exist in three-
3.1.K3       I/R/M   dimensional figures.
recognize that similar figures have congruent angles, and their corresponding sides
3.1.K4       I/R/M   are proportional.
3.1.K5a      I/R/M   use the Pythagorean Theorem to determine if a triangle is a right triangle.
3.1.K5b      I/R/M   use the Pythagorean Theorem to find a missing side of a right triangle.
recognize and describe congruence of triangles using: Side-Side-Side (SSS), Angle-
3.1.K6a      I/R/M   Side-Angle (ASA), Side-Angle-Side (SAS), and Angle-Angle-Side (AAS).
recognize and describe the ratios of the sides in special right triangles: 30°-60°-90°
3.1.K6b      I/R/M   and 45°-45°-90°.
recognize, describe, and compare the relationships of the angles formed when
3.1.K7       I/R/M   parallel lines are cut by a transversal.
recognize and identify parts of a circle: arcs, chords, sectors of circles, secant and
3.1.K8       I/R/M   tangent lines, central and inscribed angles.
solve real-world problems by using the properties of corresponding parts of similar
3.1.A1a      I/R/M   and congruent figures, e.g., scale drawings, map reading, or proportions.
solve real-world problems by applying the Pythagorean Theorem, e.g., when
checking for square corners on concrete forms for a foundation, determine if a right
*3.1.A1b     I/R/M   angle is formed by using the Pythagorean Theorem (O).
solve real-world problems by using properties of parallel lines, e.g., street
3.1.A1c      I/R/M   intersections.
use deductive reasoning to justify the relationships between the sides of 30°-60°-90°
3.1.A2       I/R/M   and 45°-45°-90° triangles using the ratios of sides of similar triangles.
understand the concepts of and develop a formal or informal proof through
understanding of the difference between a statement verified by proof (theorem) and
3.1.A3        I/R    a statement supported by examples.
S3.B2                estimate, measure, and use geometric formulas in a variety of situations.
determine and use real number approximations (estimations) for length, width,
weight, volume, temperature, time, distance, perimeter, area, surface area, and
3.2.K1       R,M     angle measurement using standard and nonstandard units of measure (\$).
select and use measurement tools, units of measure, and level of precision
appropriate for a given situation to find accurate real number representations for
length, weight, volume, temperature, time, distance, area, surface area, mass,
3.2.K2       R,M     midpoint, and angle measurements (\$).
6
Geometry
approximate conversions between customary and metric systems given the
3.2.K3     R      conversion unit or formula.
state, recognize, and apply formulas for perimeter and area of squares, rectangle,
3.2.K4a   R,M     and triangles (\$).
state, recognize, and apply formulas for circumference and area of circles; volume of
3.2.K4b   I,R,M   rectangular solids (\$).
use given measurement formulas to find perimeter, area, volume, and surface area
3.2.K5    I,R,M   of two- and three-dimensional figures (regular and irregular).
recognize and apply properties of corresponding parts of similar and congruent
3.2.K6    I,R,M   figures to find measurements of missing sides.
know, explain, and use ratios and proportions to describe rates of change (\$), e.g.,
3.2.K7    R,M     miles per gallon, meters per second, calories per ounce, or rise over run.
solve real-world problems by converting within the customary and the metric
systems, e.g., Marti and Ginger are making a huge batch of cookies and so they are
multiplying their favorite recipe quite a few times. They find that they need 45
3.2.A1a    R      tablespoons of liquid. To the nearest ¼ of a cup, how many cups would be needed?
solve real-world problems by finding the perimeter and the area of circles, squares,
rectangles, triangles, parallelograms, and trapezoids, e.g., a track is made up of a
rectangle with dimensions 100 meters by 50 meters with semicircles at each end
(having a diameter of 50 meters). What is the distance of one lap around the inside
3.2.A1b   R,M     lane of the track? (\$).
solve real-world problems by finding the volume and the surface area of rectangular
solids and cylinders, e.g., a car engine has 6 cylinders. Each cylinder has a height of
3.2.A1c   I,R,M   8.4 cm and a diameter of 8.8 cm. What is the total volume of the cylinders? (\$).
solve real-world problems by using the Pythagorean theorem, e.g., a baseball
diamond is a square with 90 feet between each base. What is the approximate
3.2.A1d   I,R,M   distance from home plate to second base? (\$).
solve real-world problems by using rates of change, e.g., the equation w = -52 + 1.6t
can be used to approximate the wind chill temperatures for a wind speed of 40 mph.
Find the wind chill temperature (w) when the actual temperature (t) is 32 degrees.
3.2.A1e   R,M     What part of the equation represents the rate of change? (\$).
estimate to check whether or not measurements or calculations for length, weight,
volume, temperature, time, distance, perimeter, area, surface area, and angle
measurement in real-world problems are reasonable and adjust original
measurement or estimation based on additional information (a frame of reference)
3.2.A2     R      (\$).
use indirect measurements to measure inaccessible objects, e.g., you are standing
next to the railroad tracks and a train passes. The number of cars in the train can be
determined if you know how long it takes for one car to pass and the length of time
3.2.A3     R      the whole train takes to pass you.
recognize and apply transformations on two- and three-dimensional figures in a
S3.B3             variety of situations.
describe and perform single and multiple transformations [refection, rotation,
translation, reduction (contraction/shrinking), enlargement (magnification/growing)]
3.3.K1    I,R,M   on two- and three-dimensional figures.
recognize a three-dimensional figure created by rotating a simple two-dimensional
figure around a fixed line, e.g., a rectangle rotated about one of its edges generates
a cylinder; an isosceles triangle rotated about a fixed line that runs from the vertex to
3.3.K2      I     the midpoint of its base generates a cone.
3.3.K3      I     generate a two-dimensional representation of a three-dimensional figure.
determine where and how an object or a shape can be tessellated using single or
3.3.K4      i     multiple transformations and create a tessellation.
analyze the impact of transformations on the perimeter and area of circles,
rectangles, and triangles and volume of rectangular prisms and cylinders, e.g.,
reducing by a factor of ½ multiplies an area by a factor of ¼ and multiplies the
volume by a factor of 1/8, whereas, rotating a geometric figure does not change
*3.3.A1   I,R,M   perimeter or area.

7
Geometry
describe and draw a simple three-dimensional shape after undergoing one specified
3.3.A2        I,R    transformation without using concrete objects to perform the transformation.
3.3.A3          I    use a variety of scales to view and analyze two- and three-dimensional figures.
analyze and explain transformations using such things as sketches and coordinate
3.3.A4        I,R    systems.
use an algebraic perspective to analyze the geometry of two- and three-dimensional
S3.B4                figures in a variety of situations.
recognize and examine two- and three-dimensional figures and their attributes
including the graphs of functions on a coordinate plane using various methods
including mental math, paper and pencil, concrete objects, and graphing utilities or
3.4.K1         I     other appropriate technology.
determine if a given point lies on the graph of a given line or parabola without
3.4.K2        R      graphing and justify the answer.
calculate the slope of a line from a list of ordered pairs on the line and explain how
3.4.K3       R,M     the graph of the line is related to its slope.
find and explain the relationship between the slopes of parallel and perpendicular
lines, e.g., the equation of a line 2x + 3y = 12. The slope of this line is -2/3. What is
*3.4.K4       R,M    the slope of a line perpendicular to this line.
3.4.K5       I,R,M   use the Pythagorean Theorem to find distance (may use the distance formula).
recognize the equation of a line and transform the equation into slope-intercept form
*3.4.K6      R,M     in order to identify the slope and y-intercept and use this information to graph the line.
translate between the written, numeric, algebraic, and geometric representations of a
real-world problem (\$), e.g., given a situation, write a function rule, make a T-table of
3.4.A2        R      the algebraic relationship, and graph the order pairs.
recognize and explain the effects of scale changes on the appearance of the graph
3.4.A3        R      of an equation involving a line or parabola.
analyze how changes in the constants and/or leading coefficients within the equation
3.4.A4        R      of a line or parabola affects the appearance of the graph of the equation.
Standard 4           use concepts and procedures of data analysis in a variety of situations.
collect, organize, display, explain, and interpret numerical (rational) and non-
S4.B2                numerical data sets in a variety of situations.
organize, display, and read quantitative (numerical) and qualitative (non-numerical)
data in a clear, organized, and accurate manner including a title, labels, categories,
and rational number intervals using the following data display: frequency tables and
4.2.K1a       R      line plots (\$).
organize, display, and read quantitative (numerical) and qualitative (non-numerical)
data in a clear, organized, and accurate manner including a title, labels, categories,
and rational number intervals using the following data display: bar, line, and circle
4.2.K1b       R      graphs (\$).
organize, display, and read quantitative (numerical) and qualitative (non-numerical)
data in a clear, organized, and accurate manner including a title, labels, categories,
and rational number intervals using the following data display: Venn diagrams or
4.2.K1c       R      other pictorial displays (\$).
organize, display, and read quantitative (numerical) and qualitative (non-numerical)
data in a clear, organized, and accurate manner including a title, labels, categories,
4.2.K1d       R      and rational number intervals using the following data display: charts and tables (\$).
explain how the reader's bias, measurement errors, and display distortions can
4.2.K2        R      affect the interpretation of data.
approximate a line of best fit given a scatter plot, make predictions, and analyze
4.2.A6        R      decisions using the equation of that line.
REVISED 5/4/11

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