Standards
and Expectations 
Student Edition
Lesson(s) 
Strand
A: Number Sense, Concepts, and Operations
Strand B: Measurement
Strand C: Geometry and Spatial Sense
Strand D: Algebraic Thinking
Strand E: Data Analysis and Probability 
Strand
A: Number Sense, Concepts, and Operations 
Standard 1: The student
understands the different ways numbers are represented and used in
the real world. 
Benchmark MA.A.1.3.1:
The student associates verbal names, written word names, and standard
numerals with integers, fractions, decimals; numbers expressed as
percents; numbers with exponents; numbers in scientific notation;
radicals; absolute value; and ratios. 
1. knows word names and
standard numerals for integers, fractions, decimals, numbers expressed
as percents, numbers with exponents, numbers expressed in scientific
notation, absolute value, radicals, and ratios. 
13,
28, 29,
31, 41,
51, 52,
53 
Benchmark MA.A.1.3.2:
The student understands the relative size of integers, fractions,
and decimals; numbers expressed as percents; numbers with exponents;
numbers in scientific notation; radicals; absolute value; and ratios. 
1. compares and orders fractions,
decimals, integers, and radicals using graphic models, number lines,
and symbols. 
13,
22, 32,
33, 52 
2. compares and orders numbers
expressed in absolute value, scientific notation, integers, percents,
numbers with exponents, fractions, decimals, radicals, and ratios. 
13,
22, 29,
32, 33,
41, 51,
52, 94,
95 
Benchmark MA.A.1.3.3:
The student understands concrete and symbolic representations of rational
numbers and irrational numbers in realworld situations. 
1. knows examples of rational
and irrational numbers in realworld situations. 
21,
33 
2. describes the meanings
of rational and irrational numbers using physical or graphical displays. 
33 
3. constructs models to
represent rational and irrational numbers. 
33 
Benchmark MA.A.1.3.4:
The student understands that numbers can be represented in a variety
of equivalent forms, including integers, fractions, decimals, percents,
scientific notation, exponents, radicals, and absolute value. 
1. knows the relationships
among fractions, decimals, and percents given a realworld context. 
21,
22, 51,
52, 53,
54, 55,
56, 57,
58, 81 
2. simplifies expressions
using integers, exponents, and radicals. 
12,
14, 15,
16, 28,
31, 32,
34, 35,
36 
3. knows equivalent
forms of large and small numbers in scientific and standard notation. 
29 
4. identifies and
explains the absolute value of a number. 
13 
Standard 2: The student
understands number systems. 
Benchmark MA.A.2.3.1:
The student understands and uses exponential and scientific notation. 
1. expresses rational
numbers in exponential notation including negative exponents (for
example, 2^{3} = _^{3} = 1/8). 
28 
2. expresses numbers
in scientific or standard notation including decimals between 0 and
1. 
29 
3. evaluates numerical
or algebraic expressions that contain exponential notation. 
28,
126 
Standard 3: The student
understands the effects of operations on numbers and the relationships
among these operations, selects appropriate operations, and computes
for problem solving. 
Benchmark MA.A.3.3.1:
The student understands and explains the effects of addition, subtraction,
multiplication, and division on whole numbers, fractions, including
mixed numbers, and decimals, including the inverse relationships of
positive and negative numbers. 
1. knows the effects
of the four basic operations on whole numbers, fractions, mixed numbers,
decimals, and integers. 
23,
24, 25,
26, 52,
53, 55,
56, 57,
58 
2. knows the inverse relationship
of positive and negative numbers. 
14,
15 
3. applies the properties
of real numbers to solve problems (commutative, associative, distributive,
identity, equality, inverse, and closure). 
12,
14, 15,
16, 22,
23, 24,
28, 101 
Benchmark MA.A.3.3.2:
The student selects the appropriate operation to solve problems involving
addition, subtraction, multiplication, and division of rational numbers,
ratios, proportions, and percents, including the appropriate application
of the algebraic order of operations. 
1. knows the appropriate
operations to solve realworld problems involving integers, ratios,
rates, proportions, numbers expressed as percents, decimals, and fractions. 
11,
14, 15,
18, 19,
21, 23,
24, 25,
26, 27,
41, 42,
43, 44,
46, 47,
51, 52,
53, 54,
55, 56,
57, 58,
85, 86 
2. solves realworld problems
involving integers, ratios, proportions, numbers expressed as percents,
decimals, and fractions in two or threestep problems. 
13,
14, 15,
16, 18,
19, 25,
41, 44,
46, 47,
56, 57,
58 
3. solves realworld
problems involving percents including percents greater than 100% (for
example percent of change, commission). 
51,
53, 54,
55, 56,
57, 58 
4. writes and simplifies
expressions from realworld situations using the order of operations. 
17 
Benchmark MA.A.3.3.3:
The student adds, subtracts, multiplies, and divides whole numbers,
decimals, and fractions, including mixed numbers, to solve realworld
problems, using appropriate methods of computing, such as mental mathematics,
paper and pencil, and calculator. 
1. solves multistep
realworld problems involving fractions, decimals, and integers using
appropriate methods of computation, such as mental computation, paper
and pencil, and calculator. 
12,
18, 25,
27, 41,
46, 55,
56, 57 
Standard 4: The
student uses estimation in problem solving and computation. 
Benchmark MA.A.4.3.1:
The student uses estimation strategies to predict results and to check
the reasonableness of results. 
1. knows appropriate
estimation techniques for a given situation using real numbers. 
11,
26, 32,
33, 55,
86 
2. estimates to predict
results and to check reasonableness of results. 
11,
26, 32,
33, 55,
56, 86 
Standard 5: The
student understands and applies theories related to numbers. 
Benchmark MA.A.5.3.1:
The student uses concepts about numbers, including primes, factors,
and multiples, to build number sequences. 
1. knows if numbers
are relatively prime. 
Prerequisite Skills,
p. 610 
2. applies number theory
concepts to determine the terms in a real number sequence. 
111 
3. applies number theory
concepts, including divisibility rules, to solve realworld or mathematical
problems. 
Prerequisite Skills,
p. 608 

Standard 1: The student measures
quantities in the real world and uses the measures to solve problems. 
Benchmark MA.B.1.3.1:
The student uses concrete and graphic models to derive formulas for
finding perimeter, area, surface area, circumference, and volume of
two and threedimensional shapes, including rectangular solids and
cylinders. 
1. uses concrete and graphic
models to explore and derive formulas for surface area and volume
of threedimensional regular shapes, including pyramids, prisms, and
cones. 
75,
76, 77,
78 
2. solves and explains realworld
problems involving surface area and volume of threedimensional shapes. 
75,
76, 77,
78 
Benchmark MA.B.1.3.2:
The student uses concrete and graphic models to derive formulas for
finding rates, distance, time, and angle measures. 
1. applies formulas
for finding rates, distance, time and angle measures. 
36,
41, 42,
43 
2. describes and uses
rates of change (for example, temperature as it changes throughout
the day, or speed as the rate of change in distance over time) and
other derived measures. 
42,
43, 114,
115 
Benchmark MA.B.1.3.3:
The student understands and describes how the change of a figure in
such dimensions as length, width, height, or radius affects its other
measurements such as perimeter, area, surface area, and volume. 
1. knows how a change
in a figure's dimensions affects its perimeter, area, circumference,
surface area, or volume. 
71,
72, 75,
76, 77,
78, 111 
2. knows how changes
in the volume, surface area, area, or perimeter of a figure affect
the dimensions of the figure. 
71,
72, 75,
76, 77,
78 
Benchmark MA.B.1.3.4:
The student constructs, interprets, and uses scale drawings such as
those based on number lines and maps to solve realworld problems. 
1. interprets and
applies various scales including those based on number lines, graphs,
models, and maps. (Scale may include rational numbers.) 
46 
2. constructs and
uses scale drawings to recreate a given situation. 
46 
Standard 2: The student
compares, contrasts, and converts within systems of measurement (both
standard/nonstandard and metric/customary). 
Benchmark MA.B.2.3.1:
The student uses direct (measured) and indirect (not measured) measures
to compare a given characteristic in either metric or customary units. 
1. finds measures
of length, weight or mass, and capacity or volume using proportional
relationships and properties of similar geometric figures. 
45,
46, 47 
Benchmark MA.B.2.3.2: The
student solves problems involving units of measure and converts answers
to a larger or smaller unit within either the metric or customary
system. 
1. solves problems
using mixed units within each system, such as feet and inches, hours
and minutes. 
Prerequisite Skills,pp.
604607 
2. solves problems using
the conversion of measurements within the customary system. 
Prerequisite Skills,pp.
604605 
3. solves problems
using the conversions of measurement within the metric system. 
Prerequisite Skills,pp.
606607 
Standard 3: The student
estimates measurements in realworld problem situations. 
Benchmark MA.B.3.3.1:
The student solves realworld and mathematical problems involving
estimates of measurements including length, time, weight/mass, temperature,
money, perimeter, area, and volume, in either customary or metric
units. 
1. knows a variety
of strategies to estimate, describe, make comparisons, and solve realworld
and mathematical problems involving measurements. 
34,
35, 36 
Standard 4: The student
selects and uses appropriate units and instruments for measurement
to achieve the degree of precision and accuracy required in realworld
situations. 
Benchmark MA.B.4.3.1:
The student selects appropriate units of measurement and determines
and applies significant digits in a realworld context. (Significant
digits should relate to both instrument precision and to the least
precise unit of measurement). 
1. knows an appropriate
scale needed to produce a proportional drawing or model. 
74 
2. knows proportional
relationships used in scale drawings. 
74 
3. produces a scale
drawing. 
74 
Standard 2: The student
compares, contrasts, and converts within systems of measurement (both
standard/nonstandard and metric/customary). 
Benchmark MA.B.2.3.1:
The student uses direct (measured) and indirect (not measured) measures
to compare a given characteristic in either metric or customary units. 
1. selects the appropriate
unit of measure for a given situation. 
Prerequisite Skills, p.
607 
2. knows the precision
of different measuring instruments. 
79 
3. determines the appropriate
precision unit for a given situation. 
79 
4. identifies the number
of significant digits as it relates to the least precise unit of measure. 
79 
5. determines the
greatest possible error of a given measurement and the possible actual
measurements of an object. 
79 
Benchmark MA.B.4.3.2:
The student selects and uses appropriate instruments, technology,
and techniques to measure quantities in order to achieve specified
degrees of accuracy in a problem situation. 
1. applies significant
digits in the realworld context. 
79 
2. selects and uses
appropriate instruments, technology, and techniques to measure quantities
and dimensions to a specified degree of accuracy. 
79,
Prerequisite Skills, p. 615 
Strand
C: Geometry and Spatial Sense 
Standard 1: The student
describes, draws, identifies, and analyzes two and threedimensional
shapes. 
Benchmark MA.C.1.3.1:
The student understands the basic properties of, and relationships
pertaining to, regular and irregular geometric shapes in two and
threedimensions. 
1. determines and
justifies the measures of various types of angles based upon geometric
relationships in two and threedimensional shapes. 
61,
62 
2. compares regular
and irregular polygons and two and threedimensional shapes. 
74 
3. draws and builds threedimensional
figures from various perspectives (for example, flat patterns, isometric
drawings, nets). 
74 
4. knows the properties
of two and threedimensional figures. 
34,
35, 45,
62, 64,
71, 72,
74, 75,
76 
Standard 2: The student
visualizes and illustrates ways in which shapes can be combined, subdivided,
and changed. 
Benchmark MA.C.2.3.1:
The student understands the geometric concepts of symmetry, reflections,
congruency, similarity, perpendicularity, parallelism, and transformations,
including flips, slides, turns, and enlargements. 
1. use the properties
of parallelism, perpendicularity, and symmetry in solving realworld
problems. 
61,
66 
2. identifies congruent
and similar figures in realworld situations and justifies the identification. 
45,
65 
3. identifies and
performs the various transformations (reflection, translation, rotation,
dilation) of a given figure on a coordinate plane. 
67,
68, 69 
Benchmark MA.C.2.3.2:
The student predicts and verifies patterns involving tessellations
(a covering of a plane with congruent copies of the same pattern with
no holes and no overlaps, like floor tiles). 
1. continues a tessellation
pattern using the needed transformations. 

2. creates an original tessellating
tile and tessellation pattern using a combination of transformations 

Standard 3: The student
uses coordinate geometry to locate objects in both two and three
dimensions and to describe objects algebraically. 
Benchmark MA.C.3.3.1:
The student represents and applies geometric properties and relationships
to solve realworld and mathematical problems. 
1. observes, explains,
makes and tests conjectures regarding geometric properties and relationships
(among regular and irregular shapes of two and three dimensions). 
34,
35, 45 
2. applies the Pythagorean
Theorem in realworld problems (for example, finds the relationship
among sides in 45^{o}  45^{o} and 30^{o}
 60^{o} right triangles). 
34,
35, 36,
63 
Benchmark MA.C.3.3.2:
The student identifies and plots ordered pairs in all four quadrants
of a rectangular coordinate system (graph) and applies simple properties
of lines. 
1. given an equation
or its graph, finds orderedpair solutions (for example, y = 2x). 
113 
2. given the graph
of a line, identifies the slope of the line (including the slope of
vertical and horizontal lines). 
43 
3. given the graph
of a linear relationship, applies and explains the simple properties
of lines on a graph, including parallelism, perpendicularity, and
identifying the x and y intercepts, themidpoint of a horizontal or
vertical line segment, and the intersection point of two lines. 
113,
114, 117 
Strand
D: Algebraic Thinking 
Standard 1: The student
describes, analyzes, and generalizes a wide variety of patterns, relations,
and functions 
Benchmark MA.D.1.3.1:
The student describes a wide variety of patterns, relationships, and
functions through models, such as manipulatives, tables, graphs, expressions,
equations, and inequalities. 
1. reads, analyzes,
and describes graphs of linear relationships. 
43,
113, 115,
117, 121 
2. uses variables
to represent unknown quantities in realworld problems. 
17,
18, 19,
27, 34,
35, 44,
102, 121 
3. uses the information
provided in a table, graph, or rule to determine if a function is
linear and justifies reasoning. 
121 
4. finds a function
rule to describe tables of related inputoutput variables. 
112 
5. predicts outcomes
based upon function rules. 
112,
113 
Benchmark MA.D.1.3.2:
The student creates and interprets tables, graphs, equations, and
verbal descriptions to explain causeandeffect relationships. 
1. interprets and
creates tables and graphs (function tables). 
112,
113 
2. writes equations
and inequalities to express relationships. 
17,
18, 19,
27, 34,
35, 53,
56, 102,
103, 105,
118 
3. graphs equations and
inequalities to explain causeandeffect relationships. 
113,
122 
4. interprets the meaning
of the slope of a line from a graph depicting a realworld situation. 
42,
43, 114,
115 
Standard 2: The student
uses expressions, equations, inequalities, graphs, and formulas to
represent and interpret situations. 
Benchmark MA.D.2.3.1:
The student represents and solves realworld problems graphically,
with algebraic expressions, equations, and inequalities. 
1. translates verbal
expressions and sentences into algebraic expressions, equations, and
inequalities. 
17,
18, 19,
27, 34, 35,
53, 56,
57, 58,
103, 105 
2. translates algebraic
expressions, equations, or inequalities representing realworld relationships
into verbal expressions or sentences. 
17,
58, 103,
105 
3. solves single
and multiplestep linear equations and inequalities in concrete or
abstract form. 
18,
19, 27,
102, 103,
104, 105,
106, 107 
4. graphs linear equations
on the coordinate plane using tables of values. 
43,
113, 115 
5. graphically displays
realworld situations represented by algebraic equations or inequalities. 
113,
115, 117 
6. evaluates algebraic expressions,
equations, and inequalities by substituting integral values for variables
and simplifying the results. 
12,
14, 15,
16, 23,
24, 25,
26, 28,
34, 35,
102, 103,
104, 105 
7. simplifies algebraic
expressions that represent realworld situations by combining like
terms and applying the properties of real numbers. 
23,
101, 123 
Benchmark MA.D.2.3.2:
The student uses algebraic problemsolving strategies to solve realworld
problems involving linear equations and inequalities. 
1. simplifies algebraic
expressions with a maximum of two variables. 
101,
123 
2. solves single
and multistep linear equations and inequalities that represent realworld
situations. 
18,
19, 27,
53, 56,
102, 103,
104, 105,
106, 107 
Strand
E: Data Analysis and Probability 
Standard 1: The student
understands and uses the tools of data analysis for managing information. 
Benchmark MA.E.1.3.1:
The student collects, organizes, and displays data in a variety of
forms, including tables, line graphs, charts, bar graphs, to determine
how different ways of presenting data can lead to different interpretations. 
1. reads and interprets
data displayed in a variety of forms including histograms. 
42,
91, 92,
97, 116 
2. constructs and
interprets displays of data, (including circle, line, bar, and boxandwhisker
graphs) and explains how different displays of data can lead to different
interpretations. 
91,
92, 93,
97, 116 
Benchmark MA.E.1.3.2:
The student understands and applies the concepts of range and central
tendency (mean, median, and mode). 
1. finds the mean,
median, and mode of a set of data using raw data, tables, charts,
or graphs. 
94 
2. interprets measures
of dispersion (range) and of central tendency. 
94,
95, 96 
3. determines appropriate
measures of central tendency for a given situation or set of data. 
94 
Benchmark MA.E.1.3.3:
The student analyzes realworld data by applying appropriate formulas
for measures of central tendency and organizing data in a quality
display, using appropriate technology, including calculators and computers. 
1. determines the
mean, median, mode, and range of a set of realworld data using appropriate
technology. 

2. organizes, graphs
and analyzes a set of realworld data using appropriate technology. 

Standard 2: The student
identifies patterns and makes predictions from an orderly display
of data using concepts of probability and statistics. 
Benchmark MA.E.2.3.1:
The student compares experimental results with mathematical expectations
of probabilities. 
1. compares and explains
the results of an experiment with the mathematically expected outcomes. 
86 
2. calculates simple
mathematical probabilities for independent and dependent events. 
85 
Benchmark
MA.E.2.3.2:
The student determines odds for and odds against a given situation 
1. predicts the mathematical odds
for and against a specified outcome in a given realworld situation. 
81 
Standard 3: The student uses
statistical methods to make inferences and valid arguments about realworld
situations. 
Benchmark MA.E.3.3.1:
The student formulates hypotheses, designs experiments, collects and
interprets data, and evaluates hypotheses by making inferences and
drawing conclusions based on statistics (range, mean, median, and
mode) and tables, graphs, and charts. 
1. formulates a hypothesis
and designs an experiment. 

2. performs the experiment
and collects, organizes, and displays the data. 
86 
3. evaluates the hypothesis
by making inferences and drawing conclusions based on statistical
results. 

Benchmark MA.E.3.3.2:
The student identifies the common uses and misuses of probability
or statistical analysis in the everyday world. 
1. knows appropriate uses
of statistics and probability in realworld situations. 
87 
2. knows when statistics
and probability are used in misleading ways. 
87 
3. identifies and uses different
types of sampling techniques (for example, random, systematic, stratified). 
87 
4. knows whether a sample
is biased. 
87 
