Numerical and Algebraic Expressions

Lesson 5

Objective

Add and simplify expressions by combining like terms.

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

Criteria for Success

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  1. Define and identify terms, like terms, constants, and coefficients in expressions.
  2. Understand why terms that have the same variable part can be combined using addition or subtraction. These are considered like terms.
  3. Simplify expressions with addition and subtraction of terms by combining like terms. 
  4. Add two expressions together and simplify by combining like terms.

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Anchor Problems

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Problem 1

Use the expression below to answer the questions that follow.

$${\frac{1}{3}x-2y-5x+8}$$

  1. How many terms are there in the expression?
  2. Which terms are “like terms”?
  3. Are there any constants? If so, what are they?
  4. What are the variables in the expression?
  5. What are the coefficients in the expression?

Guiding Questions

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Problem 2

Rewrite $${5x+3x}$$ and $${5x-3x}$$ by combining like terms.

  1. Do this by expanding each term using addition.
  2. Do this by factoring out a common factor and using the distributive property. 
  3. Can you rewrite $${5x+3y}$$ and $${5x-3y}$$ by combining terms? Why or why not? Use reasoning from parts a and b to support you answer. 

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic A > Lesson 1Example 1

Grade 7 Mathematics > Module 3 > Topic A > Lesson 1 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem 3

Find the sum of $${\left ( 0.75x-12y \right )}$$ and $$(-5+6y-0.5x)$$. Show each step in your work and explain why each step is equivalent to the expression in the step before. 

Guiding Questions

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Problem Set

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

  • Include items where students match equivalent expressions that are similar but differ by signs of coefficients.

Target Task

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Students in Mr. Jackson’s class are simplifying an expression written on the board:

$${{-12p-5n+8n+20p}}$$

Amal simplified the expression to be $${8p+3n}$$, and Andre simplified the expression to be $${-32p-13n}$$

 

Mr. Jackson saw a few different answers around the classroom, so he gave the students a hint on the board, writing:

$${{-12p-5n+8n+20p}}$$

$${-12p+20p-5n+8n}$$

$${(-12+20)p+(-5+8)n}$$

  1. What did Mr. Jackson do in each step he wrote on the board?
  2. Is either Amal or Andre correct? Explain why. 

Mastery Response

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