| 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. |
1-2,
2-1, 4-2,
4-5, 4-7,
4-8 |
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 and decimals, integers, and radicals
using graphic models, number lines, and symbols. |
2-1,
5-1, 5-6,
6-1, 6-4,
9-2 |
| 2. compares and
orders numbers expressed in absolute value, scientific
notation, integers, percents, numbers with exponents,
fractions, decimals, radicals, and ratios. |
2-1,
4-2, 4-7,
4-8, 5-1,
5-6, 6-1,
6-4, 9-1,
9-2 |
Benchmark MA.A.1.3.3:
The student understands concrete and symbolic representations
of rational numbers and irrational numbers in real-world
situations |
| 1. knows examples
of rational and irrational numbers in real-world situations. |
5-2 |
| 2. describes
the meanings of rational and irrational numbers using
physical or graphical displays. |
5-1,
5-2, 5-3,
5-4, 5-6,
5-7, 9-1,
9-2 |
| 3. constructs
models to represent rational and irrational numbers. |
4-3 |
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 real-world context. |
5-1,
5-2, 6-1,
6-4, 6-5,
9-2 |
| 2. simplifies
expressions using integers, exponents, and radicals. |
2-4,
2-5, 4-2,
4-6, 4-7,
9-1, 9-2 |
| 3. knows
equivalent forms of large and small numbers in scientific
and standard notation. |
4-8 |
| 4. identifies
and explains the absolute value of a number. |
2-1 |
| 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). |
4-2,
4-7 |
| 2. expresses
numbers in scientific or standard notation including decimals
between 0 and 1. |
4-8,
10-2 |
| 3. evaluates
numerical or algebraic expressions that contain exponential
notation. |
4-2,
4-7 |
Benchmark MA.A.2.3.2:
The student understands the structure of number systems
other than the decimal number system. |
| 1. expresses base ten numbers
as equivalent numbers in different bases, such as base
two, base five, and base eight. |
4-2 |
| 2. discusses the application
of the binary (base two) number system in computer technology. |
4-2 |
| 3. expresses non-base ten
numbers as equivalent numbers in base ten. |
4-2 |
| 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. |
2-2,
2-3, 2-4,
2-5, 5-3,
5-4, 5-5 |
| 2. knows the
inverse relationship of positive and negative numbers. |
2-2,
2-3, 3-3 |
| 3. applies the
properties of real numbers to solve problems (commutative,
associative, distributive, identity, equality, inverse,
and closure). |
1-4,
2-2, 2-3,
2-4, 2-5,
4-6, 5-4,
5-5, 5-7,
13-2, 13-3 |
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 real-world problems
involving integers, ratios, rates, proportions, numbers
expressed as percents, decimals, and fractions. |
1-1,
2-2, 2-3,
2-4, 2-5,
5-9, 6-1,
6-2, 6-4,
6-5, 6-7,
6-8 |
| 2. solves real-world
problems involving integers, ratios, proportions, numbers
expressed as percents, decimals, and fractions in two-
or three-step problems. |
1-1,
2-2, 2-3,
2-4, 2-5,
6-1, 6-2,
6-4, 6-5,
6-7, 6-8,
7-1, 7-2 |
| 3. solves
real-world problems involving percents including percents
greater than 100% (for example percent of change, commission). |
1-2,
6-2, 6-4,
6-8 |
| 4. writes
and simplifies expressions from real-world situations
using the order of operations. |
1-3,
4-2, 6-2,
6-4, 6-8 |
Benchmark MA.A.3.3.3:
The student adds, subtracts, multiplies, and divides whole
numbers, decimals, and fractions, including mixed numbers,
to solve real-world problems, using appropriate methods
of computing, such as mental mathematics, paper and pencil,
and calculator. |
| 1. solves multi-step
real-world problems involving fractions, decimals, and
integers using appropriate methods of computation, such
as mental computation, paper and pencil, and calculator. |
1-1,
2-5, 3-6,
3-7, 7-1,
7-2, 7-3,
7-4, 7-5,
7-6 |
| 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. |
6-2,
6-7 |
| 2. estimates
to predict results and to check reasonableness of results. |
1-2,
3-5, 5-4,
5-5, 5-7,
6-2, 6-7,
8-2 |
| 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. |
4-4 |
| 2. applies number
theory concepts to determine the terms in a real number
sequence. |
5-10 |
| 3. applies number
theory concepts, including divisibility rules, to solve
real-world or mathematical problems. |
4-1,
4-3, 4-4,
4-5 |
|
| 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 three-dimensional shapes, including
rectangular solids and cylinders. |
| 1. uses concrete
and graphic models to explore and derive formulas for
surface area and volume of three-dimensional regular shapes,
including pyramids, prisms, and cones. |
10-5,
10-7, 11-2,
11-3, 11-4,
11-5, 11-6 |
| 2. solves and
explains real-world problems involving surface area and
volume of three-dimensional shapes |
11-2,
11-3, 11-4,
11-5 |
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. |
3-7,
5-3, 5-4,
8-2, 9-3,
9-4, 10-1,
10-4, 10-6 |
| 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. |
8-2,
8-5 |
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. gknows how
a change in a figure's dimensions affects its perimeter,
area, circumference, surface area, or volume. |
4-2,
11-2, 11-3,
11-4, 11-6 |
| 2. knows how
changes in the volume, surface area, area, or perimeter
of a figure affect the dimensions of the figure. |
11-6 |
| 3. solves real-world
or mathematical problems involving the effects of changes
either to the dimensions of a figure or to the volume,
surface area, area, perimeter, or circumference of figures. |
4-2,
11-6 |
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
real-world problems. |
| 1. interprets
and applies various scales including those based on number
lines, graphs, models, and maps. (Scale may include rational
numbers.) |
6-3 |
| 2. constructs
and uses scale drawings to recreate a given situation. |
6-3 |
| 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. |
6-2,
6-3, 9-7 |
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. |
5-3,
5-4, 5-5,
6-1 |
| 2. solves problems
using the conversion of measurements within the customary
system. |
3-4,
4-5, 5-4,
6-1 |
| 3. solves problems
using the conversions of measurement within the metric
system. |
4-5,
6-1 |
| Standard 3:
The student estimates measurements in real-world problem
situations. |
Benchmark MA.B.3.3.1:
The student solves real-world 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 real-world and mathematical problems involving
measurements. |
3-4,
5-7 |
| Standard 4: The
student selects and uses appropriate units and instruments
for measurement to achieve the degree of precision and
accuracy required in real-world situations. |
Benchmark MA.B.4.3.1:
The student selects appropriate units of measurement and
determines and applies significant digits in a real-world
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 situation. |
6-6,
11-7 |
| 2. knows
the precision of different measuring instruments. |
6-6,
11-7 |
| 3. determines
the appropriate precision unit for a given situation. |
11-7 |
| 4. identifies
the number of significant digits as it relates to the
least precise unit of measure. |
11-7 |
| 5. determines
the greatest possible error of a given measurement and
the possible actual measurements of an object. |
11-7 |
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 real-world context. |
11-7 |
| 2. selects
and uses appropriate instruments, technology, and techniques
to measure quantities and dimensions to a specified degree
of accuracy. |
11-7 |
Strand
C: Geometry and Spatial Sense |
| Standard 1: The
student describes, draws, identifies, and analyzes two-
and three-dimensional 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 three-dimensions. |
| 1. determines
and justifies the measures of various types of angles
based upon geometric relationships in two- and three-dimensional
shapes. |
9-7,
10-2, 10-4,
10-6, 10-8 |
| 2. compares
regular and irregular polygons and two- and three-dimensional
shapes. |
9-7,
10-5, 10-8,
11-1, 11-2,
11-4, 11-6 |
| 3. draws and
builds three-dimensional figures from various perspectives
(for example, flat patterns, isometric drawings, nets). |
10-3,
10-6, 11-1 |
| 4. knows
the properties of two- and three-dimensional figures. |
9-7,
10-3, 10-5,
10-7, 10-8,
11-1, 11-2,
11-3, 11-4,
11-5, 11-6 |
| 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 real-world problems. |
9-7,
10-1, 10-3 |
| 2. identifies
congruent and similar figures in real-world situations
and justifies the identification. |
9-7,
10-2, 11-6 |
| 3. identifies
and performs the various transformations (reflection,
translation, rotation, dilation) of a given figure on
a coordinate plane. |
10-3 |
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. |
10-6 |
| 2. creates an
original tessellating tile and tessellation pattern using
a combination of transformations. |
10-6 |
| 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 real-world 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). |
9-4,
9-7, 11-6 |
| 2. applies
the Pythagorean Theorem in real-world problems (for example,
finds the relationship among sides in 45° - 45°
and 30° - 60° right triangles). |
9-5 |
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 ordered-pair solutions
(for example, y = 2x). |
1-6,
2-6, 8-2 |
| 2. given
the graph of a line, identifies the slope of the line
(including the slope of vertical and horizontal lines). |
8-4,
8-5, 8-6,
8-7 |
| 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,
the midpoint of a horizontal or vertical line segment,
and the intersection point of two lines. |
8-3,
8-6, 8-9,
10-1 |
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. |
1-2,
8-1, 8-2,
8-4, 8-5,
8-10, 13-5 |
| 2. uses
variables to represent unknown quantities in real-world
problems. |
1-2,
1-3, 1-5,
3-3, 3-4,
3-5, 3-6,
3-7, 8-2,
8-6, 8-9,
8-10 |
| 3. uses
the information provided in a table, graph, or rule to
determine if a function is linear and justifies reasoning. |
8-2,
13-5 |
| 4. finds
a function rule to describe tables of related input-output
variables. |
3-7,
8-1, 8-7 |
| 5. predicts
outcomes based upon function rules. |
1-2,
3-7, 8-1,
8-2 |
Benchmark MA.D.1.3.2:
The student creates and interprets tables, graphs, equations,
and verbal descriptions to explain cause-and-effect relationships. |
| 1. interprets
and creates tables and graphs (function tables). |
1-6,
4-6, 8-1,
8-2, 8-4,
8-5, 8-9,
8-10, 13-5 |
| 2. writes
equations and inequalities to express relationships. |
1-5,
3-6, 3-7,
7-1, 7-2,
7-3, 7-4,
7-5, 7-6,
8-6, 8-7,
8-8, 8-9,
8-10 |
| 3. graphs equations
and inequalities to explain cause-and-effect relationships. |
8-10 |
| 4. interprets
the meaning of the slope of a line from a graph depicting
a real-world situation. |
8-4,
8-5, 8-6,
8-7 |
| 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 real-world problems
graphically, with algebraic expressions, equations, and
inequalities. |
| 1. translates
verbal expressions and sentences into algebraic expressions,
equations, and inequalities. |
1-3,
1-5, 1-6,
3-2, 3-6,
3-7, 4-2,
5-3, 7-3,
7-4, 7-5,
7-6, 8-9,
8-10 |
| 2. translates
algebraic expressions, equations, or inequalities representing
real-world relationships into verbal expressions or sentences. |
1-3,
4-5 |
| 3. solves
single- and multiple-step linear equations and inequalities
in concrete or abstract form. |
3-3,
3-4, 3-5,
3-6, 3-7,
7-1, 7-2,
7-3, 7-4,
7-5, 7-6 |
| 4. graphs linear
equations on the coordinate plane using tables of values. |
2-6,
8-2, 8-5 |
| 5. graphically
displays real-world situations represented by algebraic
equations or inequalities. |
8-2,
8-6, 8-9,
8-10 |
| 6. evaluates
algebraic expressions, equations, and inequalities by
substituting integral values for variables and simplifying
the results. |
1-3,
2-3, 4-2,
4-6, 4-7,
13-2 |
| 7. simplifies
algebraic expressions that represent real-world situations
by combining like terms and applying the properties of
real numbers. |
2-4,
3-2, 13-2,
13-3 |
Benchmark MA.D.2.3.2:
The student uses algebraic problem-solving strategies
to solve real-world problems involving linear equations
and inequalities. |
| 1. simplifies
algebraic expressions with a maximum of two variables. |
2-4,
3-2, 3-3,
4-5, 7-1,
7-2, 7-3,
13-2, 13-3,
13-4 |
| 2. solves single-
and multi-step linear equations and inequalities that
represent real-world situations. |
3-3,
3-4, 3-5,
3-6, 3-7,
7-1, 13-4 |
| 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. |
1-7,
12-1, 12-3,
12-4, 12-5 |
| 2. constructs
and interprets displays of data, (including circle, line,
bar, and box-and-whisker graphs) and explains how different
displays of data can lead to different interpretations. |
1-7,
4-6, 12-1,
12-3, 12-4,
12-5 |
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. |
2-5,
5-8 |
| 2. interprets
measures of dispersion (range) and of central tendency. |
5-8,
12-2 |
| 3. determines
appropriate measures of central tendency for a given situation
or set of data. |
5-8,
12-2 |
Benchmark MA.E.1.3.3:
The student analyzes real-world 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 real-world
data using appropriate technology. |
5-8 |
| 2. organizes,
graphs and analyzes a set of real-world data using appropriate
technology. |
5-8,
12-3, 12-4 |
| 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. |
6-9,
12-9 |
| 2. calculates simple
mathematical probabilities for independent and dependent
events. |
6-9,
12-6, 12-9 |
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 real-world
situation. |
12-8 |
| Standard 3: The student uses statistical
methods to make inferences and valid arguments about real-world
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. |
5-8,
12-9 |
| 2. performs the
experiment and collects, organizes, and displays the data. |
5-8,
12-9 |
| 3. evaluates
the hypothesis by making inferences and drawing conclusions
based on statistical results. |
1-7,
6-9, 12-1,
12-2, 12-3,
12-9 |
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 real-world situations. |
2-8,
12-5, 12-9 |
| 2. knows when
statistics and probability are used in misleading ways. |
2-8,
12-5 |
| 3. identifies
and uses different types of sampling techniques (for example,
random, systematic, stratified). |
2-8,
12-5 |
| 4. knows whether
a sample is biased. |
2-8,
12-5 |
|
Extra Examples—
Answer Sheet