Unit 1: The Number System

GO-MATH Pacing Guide Grade 7

Unit 1: The Number System Module 1: Adding and Subtracting Integers---estimated 12 days

Module 2: Multiplying and Dividing Integers---estimated 8 days

Module 3: Rational Numbers---estimated 18 days

Unit 1 Assessment: 2 days

Unit 1

Estimated 40 Days

Standards

The Number System

Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and

divide rational numbers.

M.7.4---Apply and extend previous understandings of addition and subtraction to add and subtract rational

numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

• 7.4a---Describe situations in which opposite quantities combine to make 0. (e.g., A hydrogen atom has 0

charge because its two constituents are oppositely charged.)

• 7.4b---Understand p + q as the number located a distance |q| from p, in the positive or negative direction,

depending on whether q is positive or negative. (i.e., To add “p + q” on the number line, start at “0” and

move to “p” then move |q| in the positive or negative direction depending on whether “q” is positive or

negative.) Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of

rational numbers by describing real-world contexts.

• 7.4c---Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show

that the distance between two rational numbers on the number line is the absolute value of their difference

and apply this principle in real-world contexts.

• 7.4d---Apply properties of operations as strategies to add and subtract rational numbers.

M.7.5---Apply and extend previous understandings of multiplication and division and of fractions to multiply and

divide rational numbers.

• 7.5a--- Understand that multiplication is extended from fractions to rational numbers by requiring that

operations continue to satisfy the properties of operations, particularly the distributive property, leading to

products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational

numbers by describing real-world contexts.

• 7.5b---Understand that integers can be divided, provided that the divisor is not zero, and every quotient of

integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/ (–q).

Interpret quotients of rational numbers by describing real world contexts.

• 7.5c---Apply properties of operations as strategies to multiply and divide rational numbers.

• 7.5d---Convert a rational number to a decimal using long division; know that the decimal form of a rational

number terminates in 0s or eventually repeats.

M.7.6---Solve real-world and mathematical problems involving the four operations with rational numbers.

Instructional Note: Computations with rational numbers extend the rules for manipulating fractions to complex

fractions.

Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

M.7.9---Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in

any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to

calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of

answers using mental computation and estimation strategies. (e.g., If a woman making $25 an hour gets a 10%

raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to

place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the

bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.)

Days Module/Lesson/ and EQ (Essential Question) Standard Mathematical Habits of Mind (MHM)

Vocabulary

1 Module 1: Adding and Subtracting Integers

Module 1: Essential Question:

How can you use addition and subtraction of integers to solve real-world

problems?

P. 2 -Vocabulary

preview, p.2

Visualize vocab. P.4

Are You Ready? p. 5-6

2 Lesson 1.1----- Adding Integers with the Same Sign

EQ:---How do you add integers with the same sign? M.7.4

M.7.4b

M.7.4d

MHM5

3 Lesson 1.2-----Adding Integers with Different Signs

EQ:---How do you add integers with different signs? M.7.4

M.7.4b

MHM5 additive inverse

3 Lesson 1.3-----Subtracting Integers

EQ:---How do you subtract integers? M.7.4

M.7.4c

MHM2

2 Lesson 1.4-----Applying Addition and Subtraction of

Integers

EQ:---How do you solve multistep problems involving

addition and subtraction of integers?

M.7.4

M.7.4d

M.7.6

M.7.9

MHM1

1

**Module 1 Quiz-Ready to Go On? p.31;

Module 1-Mixed Review: Assessment Readiness p.32

1 Module 2: Multiplying and Dividing Integers


How can you use multiplication and division of integers to solve real-world

problems?

Visualize vocabulary p.

33-34;

Are You Ready? P. 35-36

2 Lesson 2.1-----Multiplying Integers

EQ:---How do you multiply integers? M.7.5

M.7.5a

MHM2

2 Lesson 2.2-----Dividing Integers

EQ:---How do you divide integers? M.7.5

M.7.5b

M.7.6

MHM7

2 Lesson 2.3-----Applying Integer Operations

EQ:---How can you use integer operations to solve

real-world problems?

M.7.5a

M.7.5c

M.7.6

M.7.9

MHM4

1

**Module 2 Quiz-Ready to Go On? p. 55;


1 Module 3: Rational Numbers


How can you use rational numbers to solve real-world problems?

p. 57-58 visualize

vocabulary,

Are You Ready? P. 59-60

2

Lesson 3.1-----Rational Numbers and Decimals

EQ:---How can you convert a rational number to a

decimal?

M.7.5b

M.7.5d

MHM3 rational number,

repeating decimals,

terminating decimals

2 Lesson 3.2----- Adding Rational Numbers

EQ:---How can you add rational numbers? M.7.4a-b

M.7.4d

M.7.6

MHM2

3

Lesson 3.3-----Subtracting Rational Numbers

EQ:---How do you subtract rational numbers?

Going Further-3.3-Identifying Operations

M.7.4

M.7.4c

MHM2

2 Lesson 3.4-----Multiplying Rational Numbers

EQ:---How do you multiply rational numbers?

M.7.5

M.7.5a-b

MHM2

3

Lesson 3.5-----Dividing Rational Numbers

EQ:---How do you divide rational numbers?

Going Further: 3.5-Applying Properties to Numerical

Expressions

M.7.5

M.7.5b-c

M.7.6

M.7.4d

MHM4 complex fraction

4

Getting Ready :3.6—Estimation Strategies

Lesson 3.6-----Applying Rational Number Operations

EQ:---How do you use different forms of rational

numbers and strategically choose tools to solve

problems?

Game 3.6—Fraction Challenge

M.7.9

M.7.6

M.7.9

M.7.5

MHM1

1



2

Unit 1 Study Guide Review: (1 Day)

Unit 1 -Mixed Review: Assessment Readiness: (1 Day)

Notes:

Unit 2: Ratios and Proportional Relationships

Module 4: Ratios and Proportionality---estimated 10 days

Module 5: Proportions and Percents----estimated 10 days


Unit 2 Estimated 22 Days

Standards

Ratios and Proportional Relationships

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.

M.7.1---Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other

quantities measured in like or different units. (e.g., If a person walks 1/2 mile in each 1/4 hour, compute the unit

rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.)

M.7.2--- Recognize and represent proportional relationships between quantities.

• 7.2a.--- Decide whether two quantities are in a proportional relationship (e.g., by testing for equivalent

ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line

through the origin).

M.7.3---Use proportional relationships to solve multistep ratio and percent problems

M.7.6---Solve real-world and mathematical problems involving the four operations with rational numbers.

Instructional Note: Computations with rational numbers extend the rules for manipulating fractions to complex

fractions.

Expressions and Equations

Cluster: Use properties of operations to generate equivalent expressions.

M.7.8---Understand that rewriting an expression in different forms in a problem context can shed light on the

problem and how the quantities in it are related. (e.g., a + 0.05a = 1.05a means that “increase by 5%” is the same

as “multiply by 1.05.”)

Days Module/Lesson/ and EQ (Essential Question) Standard Mathematical Habits of Mind (MHM)

Vocabulary

1

Module 4: Rates and Proportionality

Module Essential Question:

How can you use rates and proportionality to solve real-world problems?

p.112-Unit 2 Vocabulary

Preview, Visualize

vocabulary p. 114,

Are You Ready? P. 115-

116

2 Lesson 4.1---Unit Rates

EQ:---How do you find and use unit rates?

M.7.1

M.7.6

MHM4 complex fraction,

unit rates

2

Lesson 4.2---Constant Rates of Change

EQ:---How can you identify and represent

proportional relationships?

M.7.2

M.7.2a-c

MHM2 constant of

proportionality,

proportion, proportional

relationship, rate of

change

4

Lesson 4.3---Proportional Relationships and

Graphs

EQ:---How can you use graphs to represent and

analyze proportional relationships?

Going Further 4.3 ---Assessing Proportionality

Activity 4.3--- Proportional or Not Proportional?

Game 4.3 ----Match the Proportional

Relationships

M.7.2

M.7.2a-d

M.7.3

MHM4

1

**Module 4 Quiz-Ready to Go On? p.135;


1

Module 5: Proportions and Percents Module Essential Question:

How can you use proportional relationships and percent to solve real-

world problems?

Visualize vocabulary p. 138, Are You Ready? P. 139-140

3

Game 5.1 --Percento!

Lesson 5.1--Percent Increase and Decrease

M.7.3

M.7.3

MHM2 percent decrease,

percent increase

EQ:---How do you use percents to describe change?

2

Lesson 5.2 ---Rewriting Percent Expressions

EQ:---How can you rewrite expressions to help you

solve markup and markdown problems?

M.7.3

M.7.8

M.7.9

MHM5

3 Lesson 5.3--- Applications of Percent

EQ:---How do you use percents to solve problems

M.7.3

M.7.9

MHM4 principal, simple interest

1



2

Unit 2 Study Guide Review: (1 Day)

Unit 2-Mixed Review: Assessment Readiness: (1 Day)

Notes:

Unit 3: Expressions, Equations, and Inequalities Module 6: Expressions and Equations---estimated 16 days

Module 7: Inequalities---estimated 10 days


Unit 3

Estimated 28 Days

Standards



M.7.7--- Apply properties of operations as strategies to add, subtract, factor and expand linear expressions with

rational coefficients.




Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

M.7.10---Use variables to represent quantities in a real-world or mathematical problem and construct simple

equations and inequalities to solve problems by reasoning about the quantities.

• M.7.10a ---Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and

r, are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to

an arithmetic solution, identifying the sequence of the operations used in each approach. (e.g., The

perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? An arithmetic solution similar to “54 – 6

– 6 divided by 2” may be compared with the reasoning involved in solving the equation 2w – 12 = 54. An

arithmetic solution similar to “54/2 – 6” may be compared with the reasoning involved in solving the

equation 2(w – 6) = 54.)

• M.7.10b---Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r,

are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the

problem. (e.g., As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to

be at least $100. Write an inequality for the number of sales you need to make and describe the solutions.)

1

Module 6--Expressions and Equations


How can you use algebraic expressions and equations to solve real-world

Visualize Vocabulary p.

169-170,

Are You Ready? P. 171-

problems? 172

4

Lesson 6.1–Algebraic Expression

EQ:---How do you add, subtract, factor and

multiply algebraic expressions?

Going Further 6.1 ---Applying Properties to

Algebraic Expressions

M.7.7

M.7.8

M.7.7

MHM4 factor

4

Lesson 6.2 -One-Step Equations with Rational

Coefficients

EQ:---How do you use one-step equations with

rational coefficients to solve problems?

M.7.10 MHM7

2 Lesson 6.3--- Writing Two-Step Equations

EQ:---How do you write a two-step equation?

M.7.10 MHM1

4

Lesson 6.4 ---Solving Two-Step Equations

EQ:---How do you solve a two-step equation?

Going Further 6.4-- Arithmetic and Algebraic

Solutions

Activity 6.4-- Equality Property Sort---(Optional)

M.7.10

M.7.10a

MHM4

1



1 Module 7: Inequalities


How can you use inequalities to solve real-world problems?


200,

Are You Ready? p. 201-

202

3

Lesson 7.1---Writing and Solving One-Step

Inequalities

EQ:---How do you write and solve one-step

inequalities?

Activity 7.1 ---A Shared Solution (optional)

M.7.10b

M.7.10b

MHM1

2

Lesson 7.2---Writing Two-Step Inequalities

EQ:---How do you write a two-step inequality?

M.7.10 MHM2

3

Lesson 7.3 --- Solving Two-Step Inequalities

EQ:---How do you solve a two-step inequality?

Activity 7.3 ---Inequalitrio (optional)

M.7.10b

M.7.10b

MHM5

1



2

* Unit 3 Study Guide Review: (1 Day)

Unit 3 -Mixed Review: Assessment Readiness: (1 Day)

Notes:

Unit 4: Geometry Module 8: Modeling Geometric Figures---estimated 14 days

Module 9: Circumference, Area, and Volume---estimated 12 days



Standards






Geometry

Cluster: Draw, construct and describe geometrical figures and describe the relationships between them.

M.7.11---Solve problems involving scale drawings of geometric figures, including computing actual lengths and

areas from a scale drawing and reproducing a scale drawing at a different scale.

M.7.12---Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.

Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a

unique triangle, more than one triangle, or no triangle.

M.7.13---Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections

of right rectangular prisms and right rectangular pyramids.

Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

M.7,14---Know the formulas for the area and circumference of a circle and use them to solve problems; give an

informal derivation of the relationship between the circumference and area of a circle.

M.7.15---Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem

to write and solve simple equations for an unknown angle in a figure.

M.7.16---Solve real-world and mathematical problems involving area, volume and surface area of two- and

three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

1 Module 8: Modeling Geometric Figures Module Essential Question:

How can you use proportions to solve real-world geometric problems?


233-234,

Are You Ready p. 235-236

4

Lesson 8.1---Similar Shapes and Scale Drawings

EQ:---How can you use scale drawings to solve

problems?

Going Further 8.1 ---Scale Drawings and Area

Activity 8.1 ---Scale a Comic (optional)

M.7.11

M.7.11

M.7.11

MHM4 scale

scale drawing

3 Lesson 8.2---Geometric Drawings

EQ:---How can you draw shapes that satisfy given

conditions?

Activity 8.2 ---Draw a Triangle

M.7.12

M.7.12

MHM5

2 Lesson 8.3 --- Cross Sections

EQ:---How can you identify cross sections of three-

dimensional figures?

M.7.13

MHM4 cross section

intersection

3 Lesson 8.4 ---Angle Relationships

EQ:---How can you use angle relationships to solve

problems?

M.7.15

MHM2 adjacent angles,

complementary angles,

congruent angles,

supplementary angles,

vertex, vertical angles

1



1 Module 9: Circumference, Area, andVolume


How can you apply geometry concepts to solve real-world problems?

Visualize Vocabulary p. 261-262; Are You Ready? p. 263-264

2

Lesson 9.1---Circumference

EQ:---How do you find and use the circumference of a

circle?

M.7.14

MHM7 circumference,

diameter,

radius

2

Lesson 9.2 ---Area of Circles

EQ:---How do you find the area of a circle?

M.7.14

M.7.8

MHM4

2 Lesson 9.3---Area of Composite Figures

EQ:---How do you find the area of composite figures?

M.7.16 MHM5

2

Lesson 9.4---Solving Surface Area Problem

EQ:---How can you find the surface area of a figure

made up of cubes and prisms?

M.7.16

M.7.8

MHM4

2

Lesson 9.5---Solving Volume Problems

EQ:---How do you find the volume of a figure made of

cubes and prisms?

M.7.16 MHM7

1


Module 9-Mixed Review: Assessment Readiness p. 296

2



Notes:

Unit 5: Statistics Module 10: Random Samples and Populations---estimated 10 days

Module 11: Analyzing and Comparing Data---estimated 10 days



Standards

Ratios and Proportional Relationships

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems. M.7.3---Use proportional relationships to solve multistep ratio and percent problems (e.g., simple interest, tax, markups and

markdowns, gratuities and commissions, fees, percent increase and decrease, and/or percent error).

Statistics and Probability

Cluster: Use random sampling to draw inferences about a population.

M.7.17---Understand that statistics can be used to gain information about a population by examining a sample of the

population; generalizations about a population from a sample are valid only if the sample is representative of that

population. Understand that random sampling tends to produce representative samples and support valid inferences.

M.7.18---Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. (e.g.,

Estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school

election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.)

Cluster: Draw informal comparative inferences about two populations.

M.7.21---Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring

the difference between the centers by expressing it as a multiple of a measure of variability. (e.g., The mean height of

players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice

thevariability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of

heights is noticeable.)

M.7.22---Use measures of center and measures of variability for numerical data from random samples to draw informal

comparative inferences about two populations. (e.g., Decide whether the words in a chapter of a seventh-grade science

book are generally longer than the words in a chapter of a fourth-grade science book.)

1

Module 10: Random Samples and Populations


How can you use random samples and populations to solvereal-world


307-308;


problems? 310

2

Lesson 10.1 ---Populations and Samples

EQ:---How can you use a sample to gain information

about a population?

M.7.17 MHM6 biased sample,

population,

random sample,

sample

3

Getting Ready 10.2 --- Applying Proportional

Lesson 10.2---Making Inferences from a Random

Sample

EQ:---How can you use a random sample to make

inferences about a population?

M.7.3

M.7.17

M.7.18

M.7.2c

MHM4

3 Lesson 10.3---Generating Random Samples

EQ:---How can you generate and use random

samples to represent a population?

M.7.18 MHM5

1



1 Module 11: Analyzing and Comparing Data


How can you solve real-worldproblems by analyzing and comparing

data?

Visualize Vocabulary p. 331-332; Are You Ready? p. 333-334

2

Lesson 11.1-----Comparing Data Displayed in Dot Plots

EQ:---How do you compare two sets of data displayed

in dot plots?

M.7.21

M.7.22

MHM7

3 Lesson 11.2-----Comparing Data Displayed in Box Plots

EQ:---How do you compare two sets of data displayed

in box plots?

M.7.21

M.7.22

MHM2

3 Lesson 11.3-----Using Statistical Measures to Compare M.7.21 MHM6

Populations

EQ:---How do you solve equations that contain

multiplication or division?

M.7.22

1



2



Notes:

Unit 6: Probability Module 12: Experimental Probability---estimated 12 days)

Module 13: Theoretical Probability and Simulations---estimated 12 days



Standards

Statistics and Probability

Cluster: Investigate chance processes and develop, use, and evaluate probability models.

M.7.23---Understand that the probability of a chance event is a number between 0 and 1 that expresses the

likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an

unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely and a probability near 1

indicates a likely event.

M.7.24---Approximate the probability of a chance event by collecting data on the chance process that

produces it and observing its long-run relative frequency, and predict the approximate relative frequency given

the probability. (e.g., When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200

times, but probably not exactly 200 times.)

M.7.26---Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

• 7.26c---Design and use a simulation to generate frequencies for compound events. (e.g., Use random digits

as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is

the probability that it will take at least 4 donors to find one with type A blood?)

1

Module 12: Experimental Probability


How can you use experimental probability to solve real-world problems?


363-364; Are You Ready?

p. 365-366

3

Lesson 12.1-----Probability

EQ:---How can you describe the likelihood of an

event?

M.7.23

M.7.25a

MHM6 complement,

event,

experiment,

outcome,

probability,

sample space, trial

2 Lesson 12.2-----Experimental Probability of Simple

Events

EQ:---How do you find the experimental probability of

a simple event?

M.7.24

M.7.25b

MHM4 experimental probability,

simple event,

simulation

3 Lesson 12.3----Experimental Probability of Compound

Events

EQ:---How do you find the experimental probability of

a compound event?

M.7.26

M.7.26a-c

MHM2 compound event

2 Lesson 12.4-----Making Predictions with Experimental

Probability

EQ:---How do you make predictions using

experimental probability?

M.7.24

M.7.2c

M.7.3

M.7.6

MHM4

1



1

Module 13: Theoretical Probability and Simulations


How can you use theoretical probability to solve real-world problems?


395-396;


398

3

Lesson 13.1 -- Theoretical Probability of Simple Events

EQ:---How can you find the theoretical probability of a

simple event?

M.7.24

M.7.25

M.7.25a

MHM7 Theoretical probability

2 Lesson 13.2 --Theoretical Probability of Compound

Events

EQ:---How do you find the probability of a compound

event?

M.7.26

M.7.26a-b

MHM2

2

Lesson 13.3 --Making Predictions with Theoretical

Probability

EQ:---How do you make predictions using theoretical

M.7.24

M.7.25a

M.7.3

MHM4

probability?

3

Lesson 13.4 --Using Technology to Conduct a

Simulation

EQ:---How can you use technology simulations to

estimate probabilities?

M.7.26

M.7.26c

MHM5

1


Module 13 -Mixed Review: Assessment Readiness p. 424

2



Notes:

Unit 7: Getting Ready for Grade 8 Module GR1: Real Numbers and Equations

Lesson GR1.1: Integer Exponents Lesson GR1.2: Square Roots Lesson GR1.3: Cube Roots Lesson GR1.4: Equations with Variables on Both Sides Lesson GR1.5: Using the Distributive Property to Solve Equations Lesson GR1.6: Equations in Two Variables

Module GR2: Proportional Relationships

Lesson GR2.1: Rate of Change Lesson GR2.2: Rate of Change and Slope Lesson GR2.3: The Equation of a Proportional Relationship Lesson GR2.4: Understanding Functions Lesson GR2.5: Proportional Relationships and Functions

Module GR3: Functions Lesson GR3.1: Graphs of Functions Lesson GR3.2: Comparing Functions Lesson GR3.3: Rate of Change for Real-World Linear Functions Lesson GR3.4: Initial Value for Real-World Linear Functions Lesson GR3.5: Equations of Linear Functions

Module GR4: Geometry Lesson GR4.1: Translations Lesson GR4.2: Congruence Lesson GR4.3: The Pythagorean Theorem Lesson GR4.4: The Converse of the Pythagorean Theorem

Documents

Unit 1: The Number System