Numerical and Algebraic Expressions

Lesson 8

Objective

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

Common Core Standards

Core Standards

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

Foundational Standards

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  • 6.EE.A.3

  • 6.EE.A.4

  • 7.NS.A.1

  • 7.NS.A.2

Criteria for Success

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  1. Look for and make use of structure in expressions (MP.7).
  2. Analyze student work to understand different approaches in simplifying expressions and to identify mistakes.
  3. Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

Tips for Teachers

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The numbers used in the problems in this lesson require skills working with positive and negative rational numbers. This is a good opportunity to spiral in skills from the previous unit aligned to 7.NS.1 and 7.NS.2. Resources in the Problem Set Guidance include a range of problems from simpler, with just integers, to more complex, with fractions and decimals. Students should get exposure to a wide range of difficulty levels.

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Anchor Problems

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Problem 1

A student solved the problem below as part of her homework. Review her work and check for any mistakes. For each line in her work, explain what she did to get her next step.

Homework Problem:

$${-\frac{1}{3}(5x-2y)-2\left ( \frac{1}{2}x+\frac{1}{3}y \right )}$$

 

Student’s Work:

$${-\frac{5}{3}x+\frac{2}{3}y-x-\frac{2}{3}y}$$

 

$${-\frac{5}{3}x-x+\frac{2}{3}y-\frac{2}{3}y}$$

 

$${\left ( -\frac{5}{3}-1 \right )x+0}$$

 

$${-\frac{8}{3}x}$$

Guiding Questions

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Problem 2

Find the perimeter of the parallelogram.

Guiding Questions

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Problem 3

An expression is given.

$${-2y+\frac{3}{2}x+\frac{7}{4}}$$

Which are equivalent to the given expression? Select each correct answer.

a.     $${-\frac{1}{2}xy+\frac{7}{4}}$$

b.     $${\frac{3}{2}x-2\left ( y+\frac{7}{2} \right )}$$

c.     $${-\frac{1}{4}y+\frac{3}{2}(y+x)}$$

d.     $${-2y+\frac{1}{2}\left ( 3x+\frac{7}{2} \right )}$$

e.     $${\frac{1}{4}(-8y+6x+7)}$$

Guiding Questions

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References

PARCC Released Items Math Spring Operational 2016 Grade 7 Released ItemsProblem 4

Math Spring Operational 2016 Grade 7 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, 10:59 a.m..

Problem Set

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With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample

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

  • Have students swap work every now and then to check and correct each other’s work (without an answer key). 

Target Task

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Which expressions are equivalent to the expression $${\frac{5}{8}(x-y)-\frac{1}{4}x+y}$$?

Select three correct answers.

a.  $${\frac{3}{8}x+\frac{3}{8}y}$$

b.  $${\frac{3}{8}x+1\frac{5}{8}y}$$

c.  $${\frac{5}{8}x-y-\frac{1}{4}x+y}$$

d.  $${\frac{5}{8}x-\frac{5}{8}y-\frac{1}{4}x+y}$$

e.  $${\frac{5}{8}x-\frac{1}{4}x+y-\frac{5}{8}y}$$

Mastery Response

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