Lesson 10 | Numerical and Algebraic Expressions | 7th Grade Mathematics

Objective

Solve multi-step real-world problems with rational numbers.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.EE.B.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. 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.

Expressions and Equations

7.EE.B.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. 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.

7.NS.A.3 — 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.

The Number System

7.NS.A.3 — 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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Develop a strategy to solve real-world problems involving computation with rational numbers.
Use properties and order of operations to compute with rational numbers in any form.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 10 and 11 engage students in solving multi-step real-world problems, drawing on skills from Units 1–3. There is only one Anchor Problem in this lesson that can be introduced as a whole class and then completed by the students in pairs or small groups. For these challenging problems, students would benefit from a mix of peer collaboration time, independent work time, and teacher-led discussion.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Below is a table showing the number of hits and the number of times at bat for two Major League Baseball players during two different seasons:

Season	Derek Jeter	David Justice
1995	12 hits in 48 at bats	104 hits in 411 at bats
1996	183 hits in 582 at bats	45 hits in 140 at bats

A player's batting average is the fraction of times at bat when the player gets a hit.

Who has the better batting average? Justify your answer.

Guiding Questions

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References

Illustrative Mathematics Who is the Better Batter?

Who is the Better Batter?, accessed on Oct. 9, 2017, 11:34 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

You have a large sheet of paper that measures $$18\frac{1}{2}$$ inches by $$20$$ inches. You need to cut it into $$6$$ equal-sized rectangles.

a. Find two different sets of dimensions for the smaller rectangle pieces of paper.

b. Will the areas of the two rectangles you found in part a be the same? Explain and give the area(s) in square inches.

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

MARS Formative Assessment Lessons for Grade 7 Modeling: Hot and Cold — Given time, this would be a good lesson to incorporate into whole-group instruction with small groups.
PARCC Released Items Math Spring Operational 2016 Grade 7 Released Items — Problem 38
Illustrative Mathematics Shrinking
PARCC Released Items Math Spring Operational 2015 Grade 7 End of Year Released Items — Problem 22

Lesson 9

Lesson 11

Lesson Map

Topic A: Evaluating Numerical and Algebraic Expressions

Evaluate numerical expressions with rational numbers using the order of operations.

7.EE.A.1 7.NS.A.3

Write and evaluate expressions for mathematical and contextual situations.

7.EE.A.1 7.NS.A.3

Topic B: Generating Equivalent Expressions

Expand and factor expressions using the distributive property and the greatest common factor.

7.EE.A.1

Expand and factor expressions with negative rational numbers.

7.EE.A.1

Add and simplify expressions by combining like terms.

7.EE.A.1

Subtract and simplify expressions.

7.EE.A.1

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).

7.EE.A.1

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).

7.EE.A.1

Write and interpret expressions in different ways to shed new meaning on a context.

7.EE.A.2

Topic C: Solving Multi-Step Problems using Expressions

Solve multi-step real-world problems with rational numbers.

7.EE.B.3 7.NS.A.3

Model real-world problems involving rational numbers using reasoned estimates.

7.EE.B.3 7.NS.A.3

Numerical and Algebraic Expressions

Objective

Common Core Standards

Core Standards

Expressions and Equations

The Number System

Criteria for Success

Tips for Teachers

Anchor Problems

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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