Numerical and Algebraic Expressions

Lesson 7

Objective

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

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 incorrect answers to highlight and correct misconceptions.
  3. Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

Tips for Teachers

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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

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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:  $${7-6-16x}$$

 

  1. Do you agree with any of the students? Explain your reasoning for each one.
  2. 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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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 The Match Foundation, Inc.

Problem 2

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

a.     $${(4-18)x+9}$$

b.     $${(4+9)-18x}$$

c.     $${4-(18x-9)}$$

d.     $${4-18x-3}$$

e.     $${4-18x+9}$$

f.     $${6x-3 }$$

Guiding Questions

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Problem 3

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

 

a.     $${-\frac{3}{4} x}$$

 

b.     $${\frac{1}{2} x}$$

 

c.     $${\frac{1}{8}-\frac{7}{8}x}$$

 

d.     $${\frac{3}{4}-\frac{1}{4}x}$$

Guiding Questions

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References

PARCC Released Items Math Spring Operational 2015 Grade 7 End of Year Released ItemsProblem 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

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Target Task

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Simplify the expressions.

a.     $${-2x+15-4(3x-1)}$$

b.     $${-(a+b)-\frac{3}{2}(a-b)}$$

Mastery Response

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