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 whole numbers, fractions, decimals (through
hundredthousandths), and percents. 
31,
33, 55,
104, 105 
2. reads and writes whole
numbers and decimals in expanded form. 
31 
Benchmark MA.A.1.3.2:
The student understands the relative size of integers, fractions,
an decimals; numbers expressed as percents; numbers with exponents;
numbers in scientific notation; radicals; absolute value; and ratios. 
1. compares and orders fractions
and decimals using graphic models, number lines, and symbols. 
32 
2. compares and orders fractions,
decimals, and common percents. 
32,
55 
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 positive
rational numbers in realworld situations. 
81 
2. describes the meanings
of positive rational numbers using part/whole relationships and relative
size comparisons in realworld situations. 
101,
104 
3. constructs models to
represent positive rational numbers. 
32,
52a, 53,
104, 
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 
52,
53, 56,
57, 105,
106, 107,
108 
2. expresses a given
quantity in a variety of ways, such as fractions, decimals, or numbers
expressed as percents. 
31,
53, 56,
57, 105,
106, 107,
108 
3. knows whether numbers
expressed in different forms are equal. 
14,
52, 53,
55, 56,
57, 105,
106, 107,
108 
4. converts a number
expressed in one form to its equivalent in another form. 
14,
31, 32,
52, 53,
56, 57,
101, 105,
106, 107,
108 
Standard 2: The student
understands number systems. 
Benchmark MA.A.2.3.1:
The student understands and uses exponential and scientific notation. 
1. knows the meaning
and use of exponential notation (for example 23=2X2X2=8). 
14,
15, 41,
143 
2. expresses whole
numbers in exponential notation or in factored form. 
14 
3. evaluates numerical
expressions that contain exponential notation. 
14,
15, 143 
Benchmark MA.A.2.3.2:
The student understands the structure of number systems other than
the decimal number system. 
1. compares the decimal number system
to systems that do not use place value (for example, Roman numeral,
ancient Egyptian). 

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,
and decimals. 
15,
16, 34,
35, 41,
42, 43,
44, 63,
64, 65,
66, 71,
72, 73,
74, 75,
108 
2. uses models or pictures
to show the effects of addition, subtraction, multiplication, and
division, on whole numbers, decimals, fractions, and mixed numbers. 
43,
63, 71,
72, 73,
106, 107 
3. knows and applies the
commutative, associative, and distributive properties in the addition
and multiplication of rational numbers. 
91 
4. uses concrete models
and realworld examples to explore the inverse relationship of positive
and negative numbers. 
81,
82, 83,
84, 85,
92, 93,
94, 95 
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 whole numbers, decimals,
and fractions. 
11,
15, 16,
34, 35,
41, 42,
43, 44,
46, 56,
57, 63,
64, 65,
66, 71,
72, 73,
74, 75,
107, 108 
2. solves realworld problems
involving whole numbers, fractions, decimals, and common percents
using one or twostep problems. 
11,
15, 16,
32, 34,
35, 41,
42, 43,
44, 46,
56, 57,
63, 72,
73, 74,
75, 92,
93, 94,
95, 107,
108 
3. applies order of
operations when solving problems (parentheses, multiplication, division,
addition, and subtraction). 
16,
91 
4. knows proportional
relationships and describes such relationships in words, tables, or
graphs. 
102,
103 
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 one or twostep
realworld problems involving whole numbers and decimals using appropriate
methods of computation (for example, mental computation, paper and
pencil, and calculator). 
11,
15, 34,
35, 41,
42, 43,
44, 46,
56, 57,
95 
2. justifies the choice
of method for calculations, such as mental computation, concrete materials,
algorithms, or calculators. 
91 
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 an appropriate
estimation technique for a given situation using whole numbers (for
example, clustering, compatible number, frontend). 
34,
108 
2. estimates to predict
results and to check reasonableness of results. 
11,
34 
3. determines whether an
exact answer is needed or an estimate would be sufficient. 
11,
34 
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
(less than or equal to 100) are prime or composite. 
13 
2. finds the greatest common
factor and least common multiple of two or more numbers. 
51,
52, 54,
55, 64,
65, 66,
72, 73,
74, 75 
3. determines the prime
factorization of a number less than or equal to 100. 
13 
4. uses divisibility rules. 
12 

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 create formulas for finding the perimeter and area of plane
figures and the volume of rectangular solids. 
18,
45, 141,
142, 143,
145, 146 
2. uses concrete and graphic
models to discover an approximation for "pi" and creates a formula
for finding circumference. 
46 
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. identifies a protractor
as a tool for measuring angles and measures angles using a protractor. 
131,
132 
2. identifies and
names angles according to their measure (including acute, right, obtuse,
straight). 
131 
3. classifies triangles
according to the measurement of their angles and according to the
length of their sides. 
134 
4. determines the measure
of a missing angle using angle relationships. 
131,
134, 141 
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. given a twodimensional
figure, creates a new figure by increasing or decreasing the original
dimensions. 
18,
45, 143 
2. knows the relationship
between the area or perimeter of an original figure and that of a
newly created figure. 
18,
141, 143 
3. solves realworld or
mathematical problems involving perimeter or area and how these are
affected by changes in the dimensions of the figure. 
18,
45, 141,
142, 143 
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. knows proportional
relationships in scale drawings. 
103 
2. uses scale drawings to
solve realworld problems including distance (as in map reading). 
103 
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. compares objects according
to their length, weight or mass, and capacity using customary or metric
units. 
121,
122, 123,
124 
2. measures length,
weight or mass, and capacity using appropriate measuring instruments. 
121,
122, 123,
124 
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. changes one customary
or metric unit of measurement to another within the same system. 
121,
122, 125 
2. uses concrete manipulatives
or constructs models of square units (such as square inch and square
meter) for measuring area and cubic units (such as cubic centimeter
or cubic yard) for measuring volume. 
18,
141, 142,
145, 146 
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. estimates the measure
(length, weight or mass, and capacity) of an object or figure and
then compares the estimate with the actual measurement of the object
or figure. 
121,
122, 123,
124 
2. knows whether an
exact answer is needed or an estimate is sufficient. 
11,
122 
3. estimates solutions
to realworld problems by estimating the length, volume or capacity,
weight or mass, perimeter, or area of objects or shapes in either
customary or metric units. 
45,
121, 123,
124 
4. estimates solutions
to realworld problems involving measurement, including estimates
of time, temperature and money. 
11,
34, 121 
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. selects the appropriate
unit of measure for a given realworld situation. 

2. knows the approximate
nature of measurement and measures to the specified degree of accuracy
(for example, nearest centimeter or sixteenth of an inch). 
121 
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. selects an appropriate
measurement tool (for example, scales, rulers, thermometers, measuring
cups, protractors, gauges). 
121,
123, 132 
2. determines the
interval of a scale and reads the scales on a variety of measuring
instruments. 
121,
123, 131 
3. measures accurately with
the measurement tools. 
121,
123, 131 
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. 
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. identifies, draws,
and uses symbolic notation to denote the attributes of twodimensional
geometric figures (including points, parallel and perpendicular lines,
planes, rays, and parts of a circle). 
134, 144 
2. knows and draws
angles (including acute, obtuse, right, and straight). 
131, 134b 
3. analyzes relationships
among twodimensional geometric figures (for example, the diagonal
of a rectangle divides the rectangle into two congruent triangles
each having one half the area of the rectangle). 
18, 134 
4. uses appropriate
measuring devices (including ruler and protractor) as needed in analysis
of figures. 
45,
46, 134 
5. knows the attributes
of and draws threedimensional figures (including rectangular solids
and cylinders). 
144,
145, 146 
6. knows the properties
of two and threedimensional figures. 
18,
41, 46,
134, 144,
145, 146 
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. uses manipulatives
and drawings to solve problems requiring spatial visualization. 
145 
2. describes and applies
the property of symmetry in figures. 
135 
3. recognizes and
draws congruent and similar figures. 
136 
4. identifies and
performs the various transformations (reflection, translation, rotation)
of a given figure on a coordinate plane. 

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. constructs tiling
patterns to cover a plane. 

2. identifies a tessellation. 

3. identifies geometric
shapes that can be tessellated. 

4. tessellates using translation
and other desired 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,
and makes conjectures regarding geometric properties and relationships
(among angles, triangles, squares, rectangles, parallelograms). 
45,
133, 141,
142, 143,
145, 146 
2. applies known geometric
properties (for example, symmetry, congruence) to solve realworld
and mathematical problems. 
18,
45, 46,
135, 136 
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. identifies the
x and y axes in a coordinate plane and identifies
the coordinates of a given point in the first quadrant. 
86 
2. plots specific
points in the first quadrant of the Cartesian coordinate system. 
86 
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. describes, predicts,
and creates numerical and geometric patterns through models (for example,
manipulatives, tables, graphs). 
76 
2. states in words
a rule for a pattern. 
11,
76, 96,
97 
3. predicts outcomes
based on patterns. 
11,
76 
4. finds patterns
in realworld situations. 
11,
76, 96,
97 
5. describes relationships
and patterns using words, tables, symbols, variables, expressions,
or equations. 
76,
96, 97 
6. given initial terms
in a pattern, supplies a specific missing term in the pattern (for
example, given first four terms, supplies sixth term). 
11,
76 
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 function tables and graphs (first quadrant). 
96,
97 
2. substitutes values
for variables in expressions and describes the results or patterns
observed. 
17,
96, 97 
3. graphs (first quadrant)
functions from function tables to explain causeandeffect relationships. 
97 
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. uses variables
to represent numbers and relationships. 
16,
92, 93,
94, 95,
96, 97 
2. translates verbal
expressions into algebraic expressions. 
15,
16, 18,
92, 93,
94, 95,
96, 97,
141 
3. translates simple
algebraic expressions, equations or formulas representing realworld
relationships into verbal expressions or sentences. 
45,
92, 94,
95, 96 
4. uses pictures, models,
manipulatives or other strategies to solve simple onestep linear
equations with rational solutions. 
92,
93, 94,
95 
Benchmark MA.D.2.3.2:
The student uses algebraic problemsolving strategies to solve realworld
problems involving linear equations and inequalities. 
1. knows how to solve
simple equations representing realworld situations, using pictures,
models, manipulatives (such as algebra tiles), or other strategies. 
18,
92, 93,
94, 95 
2. uses concrete materials
to solve equations and inequalities and explains reasoning orally
or in writing. 
92,
93, 94,
95 
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 analyzes
data displayed in a variety of forms (charts, pictographs, stemandleaf
plots). 
21,
22, 23,
24, 25,
28 
2. generates and collects
data for analysis. 
21,
22, 25,
113 
3. chooses appropriate
titles, scales, labels, keys, and intervals for displaying data in
graphs. 
21,
22, 25 
4. constructs, interprets,
and explains displays of data, such as tables and graphs (single
and multiplebar graphs and single and multiple line graphs). 
21,
22, 23,
24, 25,
28 
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. organizes items
in a set of data. 

2. finds the range, mean,
median, and mode of a set of data. 
26,
27 
3. describes realworld
data by applying and explaining appropriate procedures for finding
measures of central tendency. 
26,
27 
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. describes a set
of data by using the measures of central tendency. 
26,
27 
2. uses technology,
such as graphing calculators and computer spreadsheets, to create
graphs. 

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. determines all possible outcomes
of an event using a tree diagram or organized list. 
112,
115 
2. calculates simpe mathematical
probabilities. 
111,
112, 113,
114, 115 
3. uses manipulatives to obtain
experimental results, compares results to mathematical expectations,
and discusses the validity of the experiment. 
113 
Benchmark MA.E.2.3.2:
The student determines odds for and odds against a given situation. 
1. examines and describes situations
that include finding the odds for and against a specified outcome. 
111 
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. with classmates, formulates
hypotheses based on research and prior data, designs an appropriate
experiment, collects and analyses data using appropriate statistics,
and displays and interprets results in appropriate tables or graphs. 
113 
Benchmark MA.E.3.3.2:
The student identifies the common uses and misuses of probability
or statistical analysis in the everyday world. 
1. explores uses and misuses of statistics in realworld situations such as advertisements and polls. 
28 
