Numerical and Algebraic Expressions

Lesson 4

Objective

Expand and factor expressions with negative rational numbers.

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

  • 7.NS.A.2

Criteria for Success

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  1. Use the distributive property to expand an expression by distributing a negative term through a sum or difference in parentheses.
  2. Model the distributive property with a negative factor using rectangular arrays. 
  3. Apply the rules of multiplying signed numbers to expanding and factoring expressions.

Tips for Teachers

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In Lessons 3 and 4, students expand and factor expressions with rational numbers. In Lesson 4, students see negative numbers both inside and outside a parentheses group. They will need to recall rules of multiplying signed numbers, specifically a negative times a negative is a positive number. 

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Anchor Problems

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Problem 1

For each problem, fill in the blanks around the diagram, and then write equivalent expressions in the form:

___ ( _______) = ___________

Guiding Questions

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Problem 2

What are the values of $$q$$ and $$r$$ in each set of equivalent expressions? 

a.     $$q(6x+4)=3x+r$$

b.     $$q\left ( \frac{1}{2}x+\frac{1}{3} \right ) = 3x+r$$

c.     $$q(3x+4)=r-8$$

Guiding Questions

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Problem 3

Expand or factor each expression.

a.     $${-\frac{1}{2}(-5x+4y-16)}$$

b.     $${-2\left ( 4-\frac{1}{2}h \right )}$$

c.     $${-\left ( \frac{2}{3}a-\frac{3}{4}b-1 \right )}$$

d.     $${-16xy+8y}$$

e.     $${\frac{1}{2}x-1}$$

Guiding Questions

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Problem Set

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Target Task

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The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use a diagram if needed.

Factored Form Expanded Form
$$-5(a-b+1)$$  
  $$18xy-6y$$
$$-\frac{2}{5}(-20x+10y)$$  
  $$-12d+9e-15$$

Mastery Response

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