## Objective

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

## Common Core Standards

### Core Standards

The core standards covered in this lesson

7.EE.A.1— Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

### Expressions and Equations

7.EE.A.1— Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

### Foundational Standards

The foundational standards covered in this lesson

6.EE.A.3

### Expressions and Equations

6.EE.A.3— Apply the properties of operations to generate equivalent expressions.

*For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.*6.EE.A.4

### Expressions and Equations

6.EE.A.4— Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).

*For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.*7.NS.A.1

### The Number System

7.NS.A.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.

7.NS.A.2

### The Number System

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

## Criteria for Success

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

- Look for and make use of structure in expressions (MP.7).
- Analyze incorrect answers to highlight and correct misconceptions.
- Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

## Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 7 and 8 pull together the concepts from the previous four lessons and engage students in simplifying complex expressions. In Lesson 7, students look at and discuss common misconceptions, and the problems become progressively more complex and challenging by the end of Lesson 8. Students will need to draw on their skills of computing with rational numbers from Unit 2.

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## Anchor Problems

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

25-30 minutes

### Problem 1

In math class, students are attempting to simplify the expression written on the board:

$${7-2(3-8x)}$$

Three students make an attempt at a first step:

Len writes: $${5(3-8x)}$$

Monty writes:$${7-2(-5x)}$$

Nailany writes: $${7-6-16x}$$

a.Do you agree with any of the students? Explain your reasoning for each one.

b.Oscar is a little stuck, so he rewrites the problem in a different way to help him determine what to do. He writes $${ 7+(-2)(3-8x)}$$. How might this new expression help Oscar simplify the expression?

#### Guiding Questions

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#### Student Response

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#### References

Institute for Mathematics and Education *Draft 6–8 Progression on Expressions and Equations*

*Draft 6–8 Progression on Expressions and Equations*, by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents.All contents copyrighted. All rights reserved. Accessed Oct. 9, 2017, 10:34 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Modified by Fishtank Learning, Inc.

### Problem 2

Which expressions below are equivalent to$${4-3(6x-3)}$$? Select **all **that apply.

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#### Guiding Questions

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#### Student Response

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### Problem 3

Determine which expression is equivalent to $${\frac{3}{4}-x\left ( \frac{1}{2}-\frac{5}{8} \right )+\left ( -\frac{3}{8}x \right )}$$.

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#### Guiding Questions

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#### Student Response

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#### References

PARCC Released Items *Math Spring Operational 2015 Grade 7 End of Year Released Items*—Problem 13

*Math Spring Operational 2015 Grade 7 End of Year Released Items* is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC). Copyright © 2017 All Rights Reserved. Accessed Oct. 9, 2017, 10:41 a.m..

## Problem Set

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

15-20 minutes

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

5-10 minutes

Simplify the expressions.

a.$${-2x+15-4(3x-1)}$$

b.$${-(a+b)-\frac{3}{2}(a-b)}$$

#### 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.

- Smarter Balanced Assessment Consortium: Sample Items
*Item #3609* - EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic A > Lesson 4—Exit Ticket, Problem Set #6-7
- EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic A > Lesson 6—Exercises 2 and 3, Example 3, and Problem Set (This lesson focuses on rational numbers.)
- Kuta Software Free Pre-Algebra Worksheets
*Algebraic Expressions - Simplifying Variable Expressions* - Algebra By Example
*1.4 Distributive Property*—Basic review through error analysis

Lesson 6

Lesson 8