pearson connected mathematics 2 - common core additional

ARKANSAS DEPARTMENT OF EDUCATION MATHEMATICS ADOPTION

Pearson Connected Mathematics 2 - Common Core Additional Investigations

Common Core State Standards Correlation

and

Common Core State Standards Comparison with Arkansas Student Learning Expectations for Mathematics

Correlation

Grade 7

ARKANSAS DEPARTMENT OF EDUCATION

MATHEMATICS ADOPTION

Two Pearson Connected Mathematics 2 (CMP2) with Common Core Additional Investigations Grade 7 correlations have been provided within this document. • Part 1: A correlation of Connected Mathematics 2 with Common Core Additional

Investigations Grade 7 to the Common Core State Standards for Mathematics. Part 1 pages 1-8

• Part 2: A correlation of Connected Mathematics 2 with Common Core Additional

Investigations Grade 7 to the Common Core State Standards Comparison with Arkansas Student Learning Expectations for Mathematics. Part 2 pages 9-49

The correlation in Part 2 is included at the request of the Arkansas Department of Education and shows how both sets of criteria intersect and align to common content. Please note the CCSS introduces some content at different grade levels, as a result, several grade levels of the Arkansas Curriculum Framework were aligned to and were included at a single grade level. Consequently, the correlation reflects this shift to other levels. Thank you in advance for your time and consideration of CMP2 for Arkansas middle school students.

Part 1 Pearson Connected Mathematics 2 Common Core Additional Investigations

Correlated to the Common Core State Standards for Mathematics

1

Grade 7 Connected Mathematics 2 Units

• Common Core: Additional Investigations • Variables and Patterns: Introducing Algebra • Stretching and Shrinking: Understanding Similarity • Comparing and Scaling: Ratio, Proportion, and Percent • Accentuate the Negative: Integers and Rational Numbers • Moving Straight Ahead: Linear Relationships • Filling and Wrapping: Three-Dimensional Measurement • What Do You Expect?: Probability and Expected Value • Data Distributions: Describing Variability and Comparing Groups

Table of Contents

Ratios and Proportional Relationships 7.RP ............................................................2 The Number System 7.NS........................................................................................2 Expressions and Equations 7.EE ..............................................................................4 Geometry 7.G ..........................................................................................................5 Statistics and Probability 7.SP ................................................................................6

Part 1 A Correlation of Connected Mathematics 2 with Common Core Investigations

to the Common Core State Standards for Mathematics

2

Key: Inv. = Investigation; ACE = Applications Connections Extensions

Common Core State Standards for Mathematics

Grade 7

Pearson Connected Mathematics 2 with Common Core Additional

Investigations (CMP2) Grade 7

Ratios and Proportional Relationships 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

CCSS Investigation 1: Graphing Proportions

2. Recognize and represent proportional relationships between quantities.

Comparing and Scaling (Inv. 1, 2, 3, 4) Stretching and Shrinking (Inv. 2)

a. 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.

Comparing and Scaling (Inv. 4) CCSS Investigation 1: Graphing Proportions

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Comparing and Scaling (Inv. 3, 4) Moving Straight Ahead (Inv. 1, 2, 3, 4)

c. Represent proportional relationships by equations.

Variables and Patterns (Inv. 1, 2, 3, Inv. 4 ACE 13) Comparing and Scaling (Inv. 4) Stretching and Shrinking (Inv. 4, 5) Moving Straight Ahead (Inv. 1, 2, 3, 4)

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Variables and Patterns (Inv. 2) Comparing and Scaling (Inv. 3 ACE 9, 10) Moving Straight Ahead (Inv. 1, 2, 3, 4) CCSS Investigation 1: Graphing Proportions

3. Use proportional relationships to solve multistep ratio and percent problems.

Variables and Patterns (Inv. 4 ACE 12) Comparing and Scaling (Inv. 1, 2, 3, 4) Stretching and Shrinking (Inv. 4, 5)

The Number System 7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 1. 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.

Accentuate The Negative (Inv. 2, 4)



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Grade 7



a. Describe situations in which opposite quantities combine to make 0.

Accentuate The Negative (Inv. 2)

b. 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. 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.


c. 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.


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


2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.


a. 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.


b. 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.




4



Grade 7



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


d. 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.

Comparing and Scaling (Inv. 3) Accentuate The Negative (Inv. 3)

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

Accentuate The Negative (Inv. 2, 3, 4)

Expressions and Equations 7.EE Use properties of operations to generate equivalent expressions. 1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Moving Straight Ahead (Inv. 3, 4) CCSS Investigation 2: Equivalent Expressions

2. 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.

CCSS Investigation 2: Equivalent Expressions

Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 3. 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.

Variables and Patterns (Inv. 2, 3, 4) Accentuate the Negative (Inv. 1, 2, 3, 4) Moving Straight Ahead (Inv. 1, 2, 3, 4)

4. 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.

Variables and Patterns (Inv. 1, 2, 3) Moving Straight Ahead (Inv. 1, 2, 3, 4)



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Grade 7



a. 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.

Variables and Patterns (Inv. 3) Moving Straight Ahead (Inv. 1, 2, 3, 4)

b. 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.

Moving Straight Ahead (Inv. 2 ACE 44) CCSS Investigation 3: Inequalities

Geometry 7.G Draw, construct, and describe geometrical figures and describe the relationships between them. 1. 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.

Stretching and Shrinking (Inv. 1, 2, 3, 4, 5) Comparing and Scaling (Inv. 4)

2. 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.

Filling and Wrapping (Inv. 1, 2, 3, 4) CCSS Investigation 4: Geometry Topics

3. Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

CCSS Investigation 4: Geometry Topics

4. 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.

CCSS Investigation 4: Geometry Topics



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Grade 7



5. 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.

Stretching and Shrinking (Inv. 3 ACE 22–24) CCSS Investigation 4: Geometry Topics

6. 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.

Stretching and Shrinking (Inv. 2, 3) Filling and Wrapping (Inv. 1, 2, 3, 4, 5)

Statistics and Probability 7.SP Use random sampling to draw inferences about a population. 1. 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.

CCSS Investigation 5: Variability

2. 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. For example, 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. Draw informal comparative inferences about two populations.

Investigation 5: Variability



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Grade 7



3. 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. For example, 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 the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

Data Distributions (Inv. 2) CCSS Investigation 5: Variability

4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, 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.

Data Distributions (Inv. 3, 4)

Investigate chance processes and develop, use, and evaluate probability models. 5. 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.

What Do You Expect? (Inv. 1 ACE 14)

6. 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. For example, 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.

What Do You Expect? (Inv. 1, 2, 3, 4)

7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.




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Grade 7



a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.


b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?


8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.


a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.


b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.


c. Design and use a simulation to generate frequencies for compound events. For example, 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?



to the Common Core State Standards Comparison with Arkansas Student Learning Expectations for Mathematics

9 Key: SE = Student Edition; TE = Teacher’s Edition; Inv. = Investigation

Grade 7 Connected Mathematics 2 Units

• Common Core: Additional Investigations • Variables and Patterns: Introducing Algebra • Stretching and Shrinking: Understanding Similarity • Comparing and Scaling: Ratio, Proportion, and Percent • Accentuate the Negative: Integers and Rational Numbers • Moving Straight Ahead: Linear Relationships • Filling and Wrapping: Three-Dimensional Measurement • What Do You Expect?: Probability and Expected Value • Data Distributions: Describing Variability and Comparing Groups

Table of Contents

Ratio and Proportional Relationships ..........................................................10

The Number System....................................................................................16

Expressions and Equations..........................................................................23

Geometry ....................................................................................................29

Statistics and Probability ............................................................................36





Arkansas Student Learning Expectations

for Mathematics

Connected Mathematics 2 with Common Core

Investigations Grade 7

Ratio and Proportional Relationships AR.7.NO.1.1 (NO.1.7.1) Rational Numbers: Relate, with and without models and pictures, concepts of ratio, proportion, and percent, including percents less than 1 and greater than 100

Comparing and Scaling Inv. 1: SE: 5-16, TE: 15-26 Inv. 2: SE: 19-26, TE: 32-46 Inv. 3: SE: 34-46, TE: 52-68 Inv. 4: SE: 49-61, TE: 73-88

CC.7.RP.1 Analyze proportional relationships and use them to solve real-world and mathematical problems. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, 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.

AR.6.NO.3.6 (NO.3.6.6) Application of Computation: Use proportional reasoning and ratios to represent problem situations and determine the reasonableness of solutions with and without appropriate technology

Comparing and Scaling Inv. 1: SE: 5-17, TE: 15-26






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AR.6.A.6.1 (A.6.6.1) Algebraic Models and Relationships: Complete, with and without appropriate technology, and interpret tables and line graphs that represent the relationship between two variables in quadrant I

Moving Straight Ahead Inv. 1: SE: 5-23, TE: 34 Inv. 4: SE: 70-74, TE: 96-100

AR.7.A.6.1 (A.6.7.1) Algebraic Models and Relationships: Use tables and graphs to represent linear equations by plotting, with and without appropriate technology, points in a coordinate plane

Moving Straight Ahead Inv. 1: SE: 7-8, TE: 23-36 Inv. 2: SE: 24-25, TE: 43-48

AR.8.A.6.1 (A.6.8.1) Algebraic Models and Relationships: Describe, with and without appropriate technology, the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change (rise/run) and y-intercept in real world problems

Moving Straight Ahead Inv. 4: SE: 70-74, TE: 96-100

CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships between quantities.

AR.7.A.7.1 (A.7.7.1) Analyze Change: Use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of change

Moving Straight Ahead Inv. 1: SE: 5-23, TE: 34 Inv. 4: SE: 70-74, TE: 96-100






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AR.8.A.6.2 (A.6.8.2) Algebraic Models and Relationships: Represent, with and without appropriate technology, linear relationships concretely, using tables, graphs and equations.


AR.8.A.6.3 (A.6.8.3) Algebraic Models and Relationships: Differentiate between independent/dependent variables given a linear relationship in context


CC.7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships between quantities.

AR.8.A.7.1 (A.7.8.1) Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost)







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AR.6.A.6.1 (A.6.6.1) Algebraic Models and Relationships: Complete, with and without appropriate technology, and interpret tables and line graphs that represent the relationship between two variables in quadrant I


AR.7.A.6.1 (A.6.7.1) Algebraic Models and Relationships: Use tables and graphs to represent linear equations by plotting, with and without appropriate technology, points in a coordinate plane


CC.7.RP.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.

AR.7.NO.1.1 (NO.1.7.1) Rational Numbers: Relate, with and without models and pictures, concepts of ratio, proportion, and percent, including percents less than 1 and greater than 100

Comparing and Scaling Inv. 1: SE: 5-16, TE: 15-26 Inv. 2: SE: 19-26, TE: 32-46 Inv. 3: SE: 34-46, TE: 52-68 Inv. 4: SE: 49-61, TE: 73-88






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AR.8.A.6.1 (A.6.8.1) Algebraic Models and Relationships: Describe, with and without appropriate technology, the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change (rise/run) and y-intercept in real world problems


CC.7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

AR.7.A.7.1 (A.7.7.1) Analyze Change: Use, with and without appropriate technology, tables and graphs to compare and identify situations with constant or varying rates of change


CC.7.RP.2c Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

AR.8.A.6.2 (A.6.8.2) Algebraic Models and Relationships: Represent, with and without appropriate technology, linear relationships concretely, using tables, graphs and equations.







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AR.8.A.6.3 (A.6.8.3) Algebraic Models and Relationships: Differentiate between independent/dependent variables given a linear relationship in context


CC.7.RP.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

AR.8.A.7.1 (A.7.8.1) Analyze Change: Use, with and without technology, graphs of real life situations to describe the relationships and analyze change including graphs of change (cost per minute) and graphs of accumulation (total cost)


AR.8.NO.3.6 (NO.3.8.6) Application of Computation: Solve, with and without technology, real world percent problems including percent of increase or decrease

Common Core Investigations Inv. 2: SE: 15, TE: 18

CC.7.RP.3 Analyze proportional relationships and use them to solve real-world and mathematical problems. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

AR.8.NO.3.3 (NO.3.8.3) Estimation: Use estimation to solve problems involving rational numbers; including ratio, proportion, percent (increase or decrease) then judge the reasonableness of solutions

Comparing and Scaling Inv. 1: SE: 15-17, TE: 26 Inv. 2: SE: 31-32, TE: 46 Inv. 3: SE: 51-67, TE: 74-98






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The Number System AR.8.NO.2.2 (NO.2.8.2) Number theory: Understand and apply the inverse and identity properties

Accentuate the Negative Inv. 2: SE: 28-29, TE: 45-48

CC.7.NS.1 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 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.

AR.8.NO.2.3 (NO.2.8.3) Number theory: Use inverse relationships (addition and subtraction, multiplication and division, squaring and square roots) in problem solving situations

Filling and Wrapping Inv. 5: SE: 65-66, TE: 105-108

AR.8.NO.2.2 (NO.2.8.2) Number theory: Understand and apply the inverse and identity properties


CC.7.NS.1a Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.








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AR.6.M.13.5 (M.13.6.5) Applications: Find the distance between two points on a number line


AR.7.NO.3.5 (NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology

Accentuate the Negative Inv. 2: SE: 24-29, TE: 41-48 Filling and Wrapping Inv. 3: SE: 32-35, TE: 57-64

CC.7.NS.1b 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. 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.

AR.8.NO.2.5 (NO.2.8.5) Understand Operations: Model and develop addition, subtraction, multiplication and division of rational numbers

Accentuate the Negative Inv. 3: SE: 51-56, TE: 80






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AR.8.NO.2.2 (NO.2.8.2) Number theory: Understand and apply the inverse and identity properties




AR.7.NO.3.5 (NO.3.7.5) Application of Computation: Represent and solve problem situations that can be modeled by and solved using concepts of absolute value, exponents and square roots (for perfect squares) with and without appropriate technology


AR.6.M.13.5 (M.13.6.5) Applications: Find the distance between two points on a number line


CC.7.NS.1c 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.

AR.7.M.13.6 (M.13.7.6) Applications: Find the distance between two points on a number line and locate the midpoint







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AR.8.NO.2.4 (NO.2.8.4) Number theory: Apply rules (conventions) for order of operations to rational numbers


AR.7.NO.2.3 (NO.2.7.3) Number theory: Apply rules (conventions) for order of operations to integers and positive rational numbers including parentheses, brackets or exponents


CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.

AR.6.NO.2.4 (NO.2.6.4) Number theory: Apply rules (conventions) for order of operations to whole numbers with and without parentheses







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AR.6.NO.2.5 (NO.2.6.5) Understand Operations: Model multiplication and division of fractions (including mixed numbers) and decimals using pictures and physical objects

Covered in Grade 6: Bits and Pieces II Inv. 2: SE: 38-39, TE: 81-84

AR.7.NO.2.4 (NO.2.7.4) Understand Operations: Model and develop addition, subtraction, multiplication and division of integers

Accentuate the Negative Inv. 2: SE: 22-29, TE: 37-48 Inv. 3: SE: 44-49, TE: 63-80



CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

AR.7.NO.2.1 (NO.2.7.1) Number theory: Apply the distributive property of multiplication over addition or subtraction to simplify computations with integers, fractions and decimals







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AR.8.NO.3.1 (NO.3.8.1) Computational Fluency: Compute, with and without appropriate technology, with rational numbers in multi-step problems

Moving Straight Ahead Inv. 4: SE: 87, TE: 114

(Continued) CC.7.NS.2 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.





CC.7.NS.2b 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.

AR.7.NO.2.4 (NO.2.7.4) Understand Operations: Model and develop addition, subtraction, multiplication and division of integers

Accentuate the Negative Inv. 2: SE: 22-29, TE: 37-48 Inv. 3: SE: 44-49, TE: 63-80



CC.7.NS.2c Apply properties of operations as strategies to multiply and divide rational numbers.








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CC.7.NS.2d 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.

AR.8.NO.1.4 (NO.1.8.4) Rational Numbers: Understand and justify classifications of numbers in the real number system




CC.7.NS.3 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)








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Expressions and Equations CC.7.EE.1 Use properties of operations to generate equivalent expressions. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

AR.7.A.5.3 (A.5.7.3) Expressions, Equations and Inequalities: Translate phrases and sentences into algebraic expressions and equations including parentheses and positive and rational numbers and simplify algebraic expressions by combining like terms

Variables and Patterns Inv. 3: SE: 49-62, TE: 69-80

CC.7.EE.2 Use properties of operations to generate equivalent expressions. 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. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”








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AR.7.NO.3.2 (NO.3.7.2) Computational Fluency: Solve with and without appropriate technology, multi-step problems using a variety of methods and tools (i.e., objects, mental computation, paper and pencil)

Moving Straight Ahead Inv. 3: SE: 50-53, TE: 88 Inv. 4: SE: 87, TE: 114

AR.7.A.5.4 (A.5.7.4) Expressions, Equations and Inequalities: Write and evaluate algebraic expressions using positive rational numbers

Variables and Patterns Inv. 3: SE: 49-62, TE: 69-80 Common Core Investigations Inv. 3: SE: 11-17, TE: 26



AR.7.NO.3.1 (NO.3.7.1) Computational Fluency: Compute, with and without appropriate technology, with integers and positive rational numbers using real world situations to solve problems

Accentuate the Negative Inv. 1: SE: 16-19, TE: 32 Inv. 2: SE: 32-40, TE: 56 Inv. 3: SE: 50-58, TE: 80

CC.7.EE.3 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 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 as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: 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. AR.7.NO.3.3 (NO.3.7.3)

Estimation: Determine when an estimate is sufficient and use estimation to decide whether answers are reasonable in problems including fractions and decimals

See related content: Comparing and Scaling Inv. 1: SE: 15-17, TE: 26 Inv. 2: SE: 31-32, TE: 46 Inv. 3: SE: 51-67, TE: 74-98






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AR.8.NO.3.3 (NO.3.8.3) Estimation: Use estimation to solve problems involving rational numbers; including ratio, proportion, percent (increase or decrease) then judge the reasonableness of solutions

Comparing and Scaling Inv. 1: SE: 15-17, TE: 26 Inv. 2: SE: 31-32, TE: 46 Inv. 3: SE: 51-67, TE: 74-98

(Continued) CC.7.EE.3 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 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 as strategies to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: 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.

AR.8.NO.3.2 (NO.3.8.2) Computational Fluency: Solve, with and without appropriate technology, multi-step problems using a variety of methods and tools (i.e. objects, mental computation, paper and pencil)

Moving Straight Ahead Inv. 3: SE: 50-53, TE: 88 Inv. 4: SE: 87, TE: 114






for Mathematics



AR.8.A.5.1 (A.5.8.1) Expressions, Equations and Inequalities: Solve and graph two-step equations and inequalities with one variable and verify the reasonableness of the result with real world application with and without technology

Moving Straight Ahead Inv. 3: SE: 53-54, 57-68; TE: 81-88

AR.8.A.5.3 (A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials


AR.7.A.5.1 (A.5.7.1) Expressions, Equations and Inequalities: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology

Moving Straight Ahead Inv. 3: SE: 47-48, 53-54; TE: 67-70, 81-84 Common Core Investigations Inv. 3: SE: 11-17, TE: 26

CC.7.EE.4 Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 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.








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AR.6.NO.2.4 (NO.2.6.4) Number theory: Apply rules (conventions) for order of operations to whole numbers with and without parentheses




AR.5.NO.2.4 (NO.2.5.4) Number theory: Apply rules (conventions) for order of operations to whole numbers where the left to right computations are modified only by the use of parentheses


CC.7.EE.4a 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. For example, The perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?








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CC.7.EE.4b 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. For example, 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.

AR.7.A.5.1 (A.5.7.1) Expressions, Equations and Inequalities: Solve and graph one-step linear equations and inequalities using a variety of methods (i.e., hands-on, inverse operations, symbolic) with real world application with and without technology

Moving Straight Ahead Inv. 3: SE: 47-48, 53-54; TE: 67-70, 81-84 Common Core Investigations Inv. 3: SE: 11-17, TE: 26

AR.8.A.5.3 (A.5.8.3) Expressions, Equations and Inequalities: Translate sentences into algebraic equations and inequalities and combine like terms within polynomials

Variables and Patterns Inv. 3: SE: 49-62, TE: 69-80 Common Core Investigations Inv. 3: SE: 11-17, TE: 26

CC.7.EE.4b 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. For example, 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.

AR.9-12.SEI.AI.2.4 (SEI.2.AI.4) Solve and graph simple absolute value equations and inequalities

See related content: Accentuate the Negative Inv. 2: SE: 24-27, TE: 41-44






for Mathematics



Geometry AR.7.M.13.5 (M.13.7.5) Applications: Apply properties (scale factors, ratio, and proportion) of congruent or similar triangles to solve problems involving missing lengths and angle measures

Stretching and Shrinking Inv. 5: SE: 78-102, TE: 90-102

AR.8.M.13.3 (M.13.8.3) Applications: Apply proportional reasoning to solve problems involving indirect measurements, scale drawings or rates


AR.7.G.8.1 (G.8.7.1) Characteristics of Geometric Shapes: Identify, draw, classify and compare geometric figures using models and real world examples

Common Core Investigations Inv. 4: SE: 19-26, TE: 36

AR.7.G.8.6 (G.8.7.6) Characteristics of Geometric Shapes: Develop the properties of similar figures (ratio of sides and congruent angles)


CC.7.G.1 Draw, construct, and describe geometrical figures and describe the relationships between them. 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.

AR.9-12.M.G.3.4 (M.3.G.4) Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)







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AR.6.G.8.3 (G.8.6.3) Characteristics of Geometric Shapes: Identify, describe, draw, and classify triangles as equilateral, isosceles, scalene, right, acute, obtuse, and equiangular

Common Core Investigations Inv. 4: SE: 21, 25; TE: 36

AR.9-12.T.G.2.2 (T.2.G.2) Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

Common Core Investigations Inv. 4: SE: 25, 33, TE: 36

CC.7.G.2 Draw, construct, and describe geometrical figures and describe the relationships between them. 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.

AR.6.M.13.6 (M.13.6.6) Applications: Use estimation to check the reasonableness of measurements obtained from use of various instruments (including angle measures)

See related content: Stretching and Shrinking Inv. 5: SE: 78-83, 84, TE: 90-102, 103






for Mathematics



AR.7.G.11.1 (G.11.7.1) Spatial Visualization and Models: Build three-dimensional solids from two-dimensional patterns (nets)


AR.8.G.8.2 (G.8.8.2) Characteristics of Geometric Shapes: Make, with and without appropriate technology, and test conjectures about characteristics and properties between two-dimensional figures and three-dimensional objects


AR.8.G.8.1 (G.8.8.1) Characteristics of Geometric Shapes: Form generalizations and validate conclusions about properties of geometric shapes


CC.7.G.3 Draw, construct, and describe geometrical figures and describe the relationships between them. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

AR.7.G.8.2 (G.8.7.2) Characteristics of Geometric Shapes: Investigate geometric properties and their relationships in one-, two-, and three-dimensional models, including convex and concave polygons







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AR.7.G.8.5 (G.8.7.5) Characteristics of Geometric Shapes: Model and develop the concept that pi (π) is the ratio of the circumference to the diameter of any circle

See related content: Common Core Investigations Inv. 4: SE: 19, TE: 36

AR.8.M.12.1 (M.12.8.1) Attributes and Tools: Understand, select and use, with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area and volume to solve real world problems


AR.7.M.13.3 (M.13.7.3) Attributes and Tools: Develop and use strategies to solve problems involving area of a trapezoid and circumference and area of a circle


AR.8.M.13.2 (M.13.8.2) Applications: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology


CC.7.G.4 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 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.

AR.7.M.13.4 (M.13.7.4) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials







for Mathematics



AR.7.G.8.3 (G.8.7.3) Characteristics of Geometric Shapes: Recognize the pairs of angles formed and the relationship between the angles including two intersecting lines and parallel lines cut by a transversal (vertical, supplementary, complementary, corresponding, alternate interior, alternate exterior angles and linear pair)

See Connected Mathematics 2 Grade 8: Common Core Investigations Inv. 4: SE: 23-26, TE: 39-40

AR.7.G.8.4 (G.8.7.4) Characteristics of Geometric Shapes: Use paper or physical models to determine the sum of the measures of interior angles of triangles and quadrilaterals

See related content: Common Core Investigations Inv. 4: TE: 36 Check-Up

AR.7.M.13.5 (M.13.7.5) Applications: Apply properties (scale factors, ratio, and proportion) of congruent or similar triangles to solve problems involving missing lengths and angle measures


CC.7.G.5 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 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.

AR.9-12.R.G.4.2 (R.4.G.2) Solve problems using properties of polygons: -- sum of the measures of the interior angles of a polygon, -- interior and exterior angle measure of a regular polygon or irregular polygon, -- number of sides or angles of a polygon

See related content: Common Core Investigations Inv. 4: TE: 36 Check-Up






for Mathematics



AR.7.M.12.3 (M.12.7.3) Attributes and Tools: Find different areas for a given perimeter and find a different perimeter for a given area

Variables and Patterns Inv. 2: SE: 42, TE: 63

AR.8.M.12.1 (M.12.8.1) Attributes and Tools: Understand, select and use, with and without appropriate technology, the appropriate units and tools to measure angles, perimeter, area, surface area and volume to solve real world problems


AR.7.M.12.1 (M.12.7.1) Attributes and Tools: Understand, select and use the appropriate units and tools (metric and customary) to measure length, weight, mass and volume to the required degree of accuracy for real world problems


CC.7.G.6 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 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.

AR.8.M.13.2 (M.13.8.2) Applications: Solve problems involving volume and surface area of pyramids, cones and composite figures, with and without appropriate technology







for Mathematics



AR.7.M.13.4 (M.13.7.4) Applications: Derive and use formulas for surface area and volume of prisms and cylinders and justify them using geometric models and common materials


AR.7.M.13.7 (M.13.7.7) Applications: Estimate and compute the area of more complex or irregular two-dimensional shapes by dividing them into more basic shapes


AR.8.M.13.5 (M.13.8.5) Applications: Estimate and compute the area of irregular two-dimensional shapes


AR.8.G.8.1 (G.8.8.1) Characteristics of Geometric Shapes: Form generalizations and validate conclusions about properties of geometric shapes


(Continued) CC.7.G.6 Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 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.

AR.7.M.12.2 (M.12.7.2) Attributes and Tools: Understand relationships among units within the same system

Filling and Wrapping Inv. 5: 63-74, TE: 101-108






for Mathematics



Statistics and Probability AR.7.DAP.14.1 (DAP.14.7.1) Collect, organize and display data: Identify different ways of selecting samples and compose appropriate questions

Data Distributions Inv. 4: SE: 74-77, TE: 99-114

AR.8.DAP.15.1 (DAP.15.8.1) Data Analysis: Compare and contrast the reliability of data sets with different size populations


CC.7.SP.1 Use random sampling to draw inferences about a population. 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.

AR.8.DAP.16.1 (DAP.16.8.1) Inferences and Predictions: Use observations about differences between sets of data to make conjectures about the populations from which the data was taken







for Mathematics







CC.7.SP.2 Use random sampling to draw inferences about a population. 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. For example, 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.

AR.5.DAP.16.1 (DAP.16.5.1) Inferences and Predictions: Make predictions and justify conclusions based on data

What Do You Expect? Inv. 3: SE: 40-48 TE: 65-72






for Mathematics







AR.7.DAP.16.1 (DAP.16.7.1) Inferences and Predictions: Make, with and without appropriate technology, conjectures of possible relationships in a scatter plot and approximate the line of best fit (trend line)

Data Distributions Inv. 1: SE: 26, TE: 36 Inv. 4: SE: 84, TE: 114

CC.7.SP.3 Draw informal comparative inferences about two populations. 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. For example, 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 the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

AR.8.DAP.14.2 (DAP.14.8.2) Collect, organize and display data: Explain which types of display are appropriate for various data sets (scatter plot for relationship between two variants and line of best fit)

Data Distributions Inv. 1: SE: 26, TE: 36 Inv. 4: SE: 88, TE: 114






for Mathematics



AR.5.DAP.15.2 (DAP.15.5.2) Data Analysis: Determine, with and without appropriate technology, the range, mean, median and mode (whole number data sets) and explain what each indicates about the set of data

Data Distributions Inv. 2: SE: 29-43, TE: 46-66 Inv. 4: SE: 76-77, TE: 103-104

AR.8.DAP.14.3 (DAP.14.8.3) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, double-bar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs


AR.8.DAP.15.2 (DAP.15.8.2) Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread


(Continued) CC.7.SP.3 Draw informal comparative inferences about two populations. 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. For example, 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 the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

AR.7.DAP.15.2 (DAP.15.7.2) Data Analysis: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)







for Mathematics



AR.7.DAP.15.2 (DAP.15.7.2) Data Analysis: Analyze, with and without appropriate technology, a set of data by using and comparing measures of central tendencies (mean, median, mode) and measures of spread (range, quartile, interquartile range)


CC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, 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.

AR.7.DAP.14.3 (DAP.14.7.3) Collect, organize and display data: Construct and interpret circle graphs, box-and-whisker plots, histograms, scatter plots and double line graphs with and without appropriate technology







for Mathematics



AR.8.DAP.14.3 (DAP.14.8.3) Collect, organize and display data: Interpret or solve real world problems using data from charts, line plots, stem-and leaf plots, double-bar graphs, line graphs, box-and whisker plots, scatter plots, frequency tables or double line graphs






AR.8.DAP.15.3 (DAP.15.8.3) Data Analysis: Given at least one of the measures of central tendency create a data set

Covered in Grade 6: Data About Us Inv. 2: SE: 34-35, TE: 53-56

(Continued) CC.7.SP.4 Draw informal comparative inferences about two populations. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, 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.

AR.8.DAP.15.2 (DAP.15.8.2) Data Analysis: Analyze, with and without appropriate technology, graphs by comparing measures of central tendencies and measures of spread







for Mathematics



AR.7.DAP.17.1 (DAP.17.7.1) Probability: Understand that probability can take any value between 0 and 1 (events that are not going to occur have probability 0, events certain to occur have probability 1)

What Do You Expect? Inv. 1: SE: 7-9, TE: 23-32

AR.3.DAP.17.1 (DAP.17.3.1) Probability: Use fractions to predict probability of an event


AR.2.DAP.17.1 (DAP.17.2.1) Probability: Describe the probability of an event as being more, less, and equally likely to occur


CC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. 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.

AR.1.DAP.17.1 (DAP.17.1.1) Probability: Describe the probability of an event as being more, less, or equally likely to occur







for Mathematics



AR.K.DAP.17.1 (DAP.17.K.1) Probability: Describe the probability of an event as being possible or not possible

What Do You Expect? Inv. 1: SE: 14, TE: 68

AR.9-12.DIP.AI.5.8 (DIP.5.AI.8) Compute simple probability with and without replacement

What Do You Expect? Inv. 1: SE: 10-18, TE: 32

AR.9-12.DIP.AI.5.10 (DIP.5.AI.10) Communicate real world problems graphically, algebraically, numerically and verbally

What Do You Expect? Inv. 1: SE: 10-18, TE: 32 Inv. 3: SE: 43-48, TE: 72

(Continued) CC.7.SP.5 Investigate chance processes and develop, use, and evaluate probability models. 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. AR.4.DAP.17.1 (DAP.17.4.2)

Probability: Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcome (roll number cubes, pull tiles from a bag, spin spinner, or determine the fairness of the game)

What Do You Expect Inv. 1: SE: 9, TE: 27-32 Unit Project: SE: 61-62, TE: 96-104






for Mathematics



AR.8.DAP.17.2 (DAP.17.8.2) Probability: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predict results, and explain differences

See related content: What Do You Expect Unit Project: SE: 61-62, TE: 96-104

AR.73.DAP.17.2 (DAP.17.7.2) Probability: Design, with and without appropriate technology, an experiment to test a theoretical probability and explain how the results may vary


AR.3.DAP.17.2 (DAP.17.3.2) Probability: Conduct simple probability experiments, record the data and draw conclusions about the likelihood of possible outcomes (roll number cubes, pull tiles from a bag, spin a spinner, or determine the fairness of games)


CC.7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. 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. For example, 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.








for Mathematics




What Do You Expect? Inv. 3: SE: 39, 43-48 TE: 72

AR.4.DAP.17.1 (DAP.17.4.1) Probability: Use fractions to predict probability of an event


AR.4.DAP.16.1 (DAP.16.4.1) Inferences and Predictions: Make predictions for a given set of data


(Continued) CC.7.SP.6 Investigate chance processes and develop, use, and evaluate probability models. 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. For example, 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.

AR.3.DAP.16.1 (DAP.16.3.1) Inferences and Predictions: Make predictions for a given set of data





What Do You Expect? Inv. 3: SE: 39, 43-48 TE: 72

AR.9-12.M.G.3.1 (M.3.G.1) Calculate probabilities arising in geometric contexts


CC.7.SP.7 Investigate chance processes and develop, use, and evaluate probability models. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

AR.4.DAP.15.2 (DAP.15.4.2) Data Analysis: Match a set of data with a graphical representation of the data







for Mathematics



AR.73.DAP.17.2 (DAP.17.7.2) Probability: Design, with and without appropriate technology, an experiment to test a theoretical probability and explain how the results may vary

What Do You Expect? Unit Project: SE: 61-62, TE: 96-104

CC.7.SP.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. AR.8.DAP.17.2 (DAP.17.8.2)

Probability: Make predictions based on theoretical probabilities, design and conduct an experiment to test the predictions, compare actual results to predict results, and explain differences




AR.8.DAP.14.1 (DAP.14.8.1) Collect, organize and display data: Design and conduct investigations which include: -- adequate number of trials, -- unbiased sampling, -- accurate measurement, -- record-keeping


CC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

AR.6.DAP.17.1 (DAP.17.6.1) Probability: Distinguish between theoretical and experimental probability







for Mathematics



AR.5.DAP.17.1 (DAP.17.5.1) Probability: Identify and predict the probability of events within a simple experiment


AR.5.DAP.17.2 (DAP.17.5.2) Probability: List and explain all possible outcomes in a given situation


AR.1.DAP.17.1 (DAP.17.1.1) Probability: Describe the probability of an event as being more, less, or equally likely to occur


(Continued) CC.7.SP.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

AR.2.DAP.17.1 (DAP.17.2.1) Probability: Describe the probability of an event as being more, less, and equally likely to occur


AR.3.DAP.17.3 (DAP.17.3.3) Probability: Use physical models, pictures, and organized lists to find combinations of two sets of objects


CC.7.SP.8 Investigate chance processes and develop, use, and evaluate probability models. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

AR.4.DAP.17.1 (DAP.17.4.3) Probability: Find all possible combinations of two or three sets of objects

See related content: What Do You Expect? Inv. 2: SE: 26, TE: 49-54






for Mathematics



AR.8.DAP.17.1 (DAP.17.8.1) Probability: Compute, with and without appropriate technology, probabilities of compound events, using organized lists, tree diagrams and logic grid








CC.7.SP.8a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.


What Do You Expect? Inv. 1: SE: 10-18, TE: 32 Inv. 3: SE: 43-48, TE: 72






for Mathematics







CC.7.SP.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.





CC.7.SP.8c Design and use a simulation to generate frequencies for compound events. For example, 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?



pearson connected mathematics 2 - common core additional

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