Accelerated Grade 7 Textbook - Carnegie Learning

[Pages:23]Accelerated Grade 7 Textbook

Table of Contents

1 Thinking Proportionally

Course 2, Module 1, Topic 1: Circles and Ratio

Students learn formulas for the circumference and area of circles and use those formulas to solve mathematical and real-world problems. Students also learn that the irrational number pi ()

is the ratio of a circle's circumference to its diameter.

Standard: 7.G.4

Lesson Title / Subtitle

Standards Lesson Summary

Pi: The Ultimate Ratio

1

Exploring the Ratio of Circle Circumference to

Diameter

7.G.4

Students explore the relationship between the distance around and the distance across various circles. They notice that for every circle the ratio of the circumference to diameter is pi.

That's a Spicy Pizza! 2

Area of Circles

7.G.4

Students explore the area of a circle in terms of its circumference. They derive the area for a circle and then solve problems using the formulas for the circumference and area for circles

Circular Reasoning 3

Solving Area and Circumference Problems

7.G.4

Students use the area of a circle formula and the circumference formula to solve for unknown measurements in real-world and mathematical problem.

Learning Individually with MATHia or Skills Practice

7.G.4 Students practice solving problems involving area and circumference of circles.

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Course 2, Module 1, Topic 2: Fractional Rates

Students calculate and use unit rates from ratios of fractions. They review strategies for solving proportions and then use means and extremes to solve real-world proportion problems.

Standards: 7.RP.1, 7.RP.2.c, 7.RP.3

Lesson Title / Subtitle

Standards Lesson Summary

Eggzactly! 2

Solving Problems with Ratios of Fractions

7.RP.1

Students determine ratios and write rates, including complex ratios and rates. Students will write proportions and use rates to determine miles per hour. They will scale up and scale down to determine unknown quantities.

3

Tagging Sharks Solving Proportions Using Means and Extremes

7.RP.2.c 7.RP.3

Students solve several proportions embedded in real world contexts. Several proportions that contain one variable are solved using one of three methods: the scaling method, the unit rate method, and the means and extremes method. Students learn to isolate a variable in an equation by using inverse operations.

Learning Individually with MATHia or Skills Practice

7.RP.1 Students determine and compare unit rates. They solve proportions using equivalent ratios and means and 7.RP.2.c extremes.

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Course 2, Module 1, Topic 3: Proportionality

Students differentiate between proportional and non-proportional relationships, including linear relationships that are not proportional. They identify and use the constant of proportionality

from tables, graphs, equations, and real-world situations; represent proportional relationships with equations; and explain the meaning of points on the graph of a proportional relationship.

Standard: 7.RP.2

Lesson Title / Subtitle

Standards Lesson Summary

How Does Your Garden Grow? 1

Proportional Relationships

7.RP.2.a

Students explore graphs and tables of proportional and non-proportional relationships. They determine that the graphs of proportional relationships are straight lines that pass through the origin. They also learn that tables of proportional relationships have a constant ratio of corresponding values of the quantities. Students learn the term direct variation and relate it to proportional relationships.

Complying with Title IX 2

Constant of Proportionality

7.RP.2.b 7.RP.2.c

Students explore equations of proportional relationships. They determine the constant of proportionality, the constant ratio of the outputs to the inputs in a proportional relationship. Students explore the reciprocal relationship of constants of proportionality in equations. They use the constant of proportionality to write and solve equations.

Fish-Inches

3

Identifying the Constant of Proportionality in

Graphs

7.RP.2.b 7.RP.2.d

Students analyze real world and mathematical situations, both proportional and non-proportional, represented on graphs and then identify the constant of proportionality when appropriate. Throughout the lesson, students interpret the meaning of points on graphs in terms of a proportional relationship, including the meaning of (1, y) and (0, 0).

Minding Your Ps and Qs

4

Constant of Proportionality in Multiple

Representations

7.RP.2

Students use proportional relationships to create equivalent multiple representations, such as diagrams, equations, tables, and graphs of the situation. A proportional relationship may initially be expressed using only words, or a table of values, or an equation, or a graph.

Learning Individually with MATHia or Skills Practice

7.RP.2.a 7.RP.2.b 7.RP.2.c

Students write ratios and determine the constant of proportionality in real-world problems. They practice determining the constant of proportionality, writing equations, and drawing a line to represent the direct variation equation to solve problems. Students are given graphs to determine if it represents a direct variation.

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Course 2, Module 1, Topic 4: Proportional Relationships

Students use proportions and percent equations to solve real-world problems about money and scale drawings. They use multiple representations to solve and compare percents. Then

students use proportionality to solve problems with scale drawings and scale factors.

Standards: 7.RP.3, 7.G.6 , 7.G.1

Lesson Title / Subtitle

Standards Lesson Summary

Markups and Markdowns

1

Introducing Proportions to Solve Percent

Problems

7.RP.3

Students analyze strategies for determining the unknown value in a percent problem. Students use proportions to solve percent problems. They connect percent problems with direct variation and proportional relationships.

Perks of Work

2

Calculating Tips, Commission, and Simple

Interest

7.RP.3

Students solve proportions and percent equations in the context of tipping and commissions. They analyze both strategies as they determine the amount of a tip or commission, the percent tip or commission, and the total sale when given the percent and the tip or commission amount.

No Taxation Without Calculation 3

Sales Tax, Income Tax, and Fees

7.RP.3

Students use percents to solve sales tax, income tax, and fee problems. They identify the percent relationship between two amounts as a proportional relationship, with a unit rate and constant of proportionality.

More Ups and Downs 4

Percent Increase and Percent Decrease

7.RP.3 7.G.6

Students compute percent increase and percent decrease in several situations. They apply percent increase and decrease to solving problems involving geometric measurement.

Pound for Pound, Inch for Inch 5

Scale and Scale Drawings

7.G.1

Students use scale models to calculate measurements and enlarge and reduce the size of models. They enlarge or reduce the size of objects and calculate relevant measurements, explore scale drawings, and describe the meaning of several different scales. Students then determine which scale will produce the largest and smallest drawing of an object when different units of measure are given.

Learning Individually with MATHia or Skills Practice

7.RP.3 7.G.1

Students practice converting between fractions, decimals, and percents. They solve percent problems for the part, the percent, or the whole, and solve percent change problems. Students use scale factors to determine unknown measures given real-life situations.

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2 Operating with Signed Numbers

Course 2, Module 2, Topic 1: Adding and Subtracting Rational Numbers

Students use physical motion, number lines, and two-color counters to develop conceptual understanding of adding and subtracting integers. They develop rules for these operations and

apply the rules to the set of rational numbers.

Standards: 7.NS.1, 7.NS.3

Lesson Title / Subtitle

Standards Lesson Summary

Walk the Line 2

Adding Integers, Part 1

7.NS.1.b

Students explore patterns for adding two integers using a number line. They focus on the absolute values of the numbers being added and develop informal rules for adding integers.

Two-Color Counters 3

Adding Integers, Part 2

7.NS.1.a 7.NS.1.b

Students use two-color counters to develop rules for adding integers. They model adding positive and negative integers with the two-color counters. Students use a graphic organizer to represent how to add additive inverses using a variety of representations.

What's the Difference? 4

Subtracting Integers

7.NS.1.c

Students use number lines and two-color counters to model subtraction of signed numbers. They develop and apply rules for subtracting integers.

All Mixed Up 5

Adding and Subtracting Rational Numbers

7.NS.3

Students apply their knowledge of adding and subtracting positive and negative integers to the set of rational numbers.

Learning Individually with MATHia or Skills Practice

7.NS.1 Students practice adding and subtracting integers using a number line.

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Course 2, Module 2, Topic 2: Multiplying and Dividing Rational Numbers

Students use number lines and two-color counters to model and develop rules for the signs of the products and quotients of signed numbers. They convert rational numbers from fractional

to decimal form. Then students apply rules and properties to the set of rational numbers.

Standards: 7.NS.2.a, 7.NS.2.b, 7.NS.2.d, 7.NS.3, 7.RP.3

Lesson Title / Subtitle

Standards Lesson Summary

Equal Groups 1

Multiplying and Dividing Integers

7.NS.2.a 7.NS.3

Students use number lines and two-color counters to model the product of two integers. They use the models to develop rules for multiplying integers. Using fact families, students apply rules for the multiplication of integers to the division of integers.

Be Rational! 2

Quotients of Integers

7.NS.2.b Students write the quotients of integers as fractions and decimals. They learn that the decimal representation of 7.NS.2.d rational numbers terminates or repeats.

Building a Wright Brothers' Flyer 3

Simplifying Expressions to Solve Problems

7.NS.3 7.RP.3

Students solve real-world problems involving numeric expressions and signed rational numbers, including problems about percent error.

Properties Schmoperties

4

Using Number Properties to Interpret

Expressions with Signed Numbers

7.NS.1.d 7.NS.2.c 7.NS.3

Students apply the distributive property to expanding and factoring with -1 and learn that subtraction is the same as adding the opposite. They identify properties in expressions with rational coefficients.

Learning Individually with MATHia or Skills Practice

7.NS.2 7.NS.3

Students use fact families to explore dividing integers. They then practice simplifying a variety of numeric expressions using order of operations.

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Course 2, Module 3, Topic 1: Algebraic Expressions

Students explore algebraic expressions with rational coefficients. They apply the Distributive Property as a strategy to write equivalent expressions and to factor linear expressions. Students

combine like terms, including like linear terms, and use properties of operations to add and subtract expressions.

Standards: 7.EE.1, 7.EE.2, 7.EE.3

Lesson Title / Subtitle

Standards Lesson Summary

No Substitution for Hard Work 1

Evaluating Algebraic Expressions

7.EE.3

Students review variables, algebraic expressions, and evaluating algebraic expressions. They practice evaluating expressions with rational numbers.

Mathematics Gymnastics

2

Rewriting Expressions Using the Distributive

Property

7.EE.1

Students rewrite algebraic expressions with rational coefficients using the Distributive Property. They then expand linear expressions. Students will factor linear expressions in a variety of ways, including by factoring out the greatest common factor and the coefficient of the variable.

All My Xs 3

Combining Like Terms

7.EE.1 7.EE.2

Students simplify expressions by combining like terms, with integer, fraction, and decimal coefficients. They use properties to simplify the expressions. Students add and subtract algebraic expressions, using addition of the opposite to subtract.

Learning Individually with MATHia or Skills Practice

7.EE.1

Students model the product of two factors and explore different factors of expressions. They then use the Distributive Property to factor and expand expressions. Students simplify variable expressions by combining like terms, by using number properties, and by using order of operations.

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Course 2, Module 3, Topic 2: Two-Step Equations and Inequalities

Students use bar models and double number lines to reason about and solve two-step linear equations. Then they use inverse operations to fluently and efficiently solve two-step equations

with rational coefficients. Finally, students investigate, solve, and graph two-step inequalities.

Standard: 7.EE.4

Lesson Title / Subtitle

Standards Lesson Summary

Picture Algebra 1

Modeling Equations by Equal Expressions

7.EE.4.a Students use bar models to write expressions and equations and to solve for unknown quantities.

Expressions That Play Together ... 2

Solving Equations on a Double Number Line

7.EE.4.a Students model contextual and mathematical situations using double number lines.

Formally Yours 3

Using Inverse Operations to Solve Equations

7.EE.4.a

Students formalize the process and language of solving two-step equations. They refer to the Properties of Equality and use inverse operations flexibly to solve equations. Students consider efficient strategies for solving problems with different types of rational numbers. They practice solving two-step equations.

Be Greater Than 4

Solving Inequalities with Inverse Operations

7.EE.4.b

Students solve inequalities. They compare solving equations with solving inequalities. Students informally develop the Properties of Inequalities before analyzing them formally. They then solve and graph inequalities.

Learning Individually with MATHia or Skills Practice

7.EE.4

Students create visual models to represent real-world situations and solve using reasoning. They then write and solve expressions from a given real-world problem using tables. Students solve a variety of two-step equations and inequalities using formal strategies.

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