Numerical and Algebraic Expressions

Lesson 3

Math

Unit 3

7th Grade

Lesson 3 of 11

Objective


Expand and factor expressions using the distributive property and the greatest common factor.

Common Core Standards


Core Standards

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

Foundational Standards

  • 6.EE.A.3
  • 7.NS.A.2

Criteria for Success


  1. Use the distributive property to expand an expression by distributing a term through a sum or difference in parentheses.
  2. Model the distributive property using rectangular arrays and partial areas. 
  3. Factor out a greatest common factor from a sum or difference and write a new expression as a product.
  4. Understand that $${a(b+c)=ab+ac}$$.

Tips for Teachers


In Lessons 3 and 4, students expand and factor expressions with rational numbers. Students have prior experience with using the distributive property to generate equivalent expressions from 6th grade (6.EE.3). In Lesson 3, students see negative numbers inside a parentheses group written as subtraction, however, they will not distribute with a negative number outside a parentheses group until Lesson 4.

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Anchor Problems


Problem 1

a.   Write two equivalent expressions to represent the total area of the rectangle shown. Justify that your two expressions are equivalent.

b.   Expand the expression below using a rectangular array.

$${\frac{1}{3}(9x-12y-18)}$$

Guiding Questions

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Problem 2

a.   What could be the missing dimensions of the rectangular array? Which set of dimensions uses the greatest common factor of the two terms?

b.   Factor the expression below using a rectangular array. Use the greatest common factor as the representation of the width.

$${24d-8e+6}$$

Guiding Questions

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Problem 3

The table below includes expressions that are written in expanded form and in factored form. Complete the table. Use rectangular arrays as needed.

Factored Form Expanded Form
$$3(x-14y)$$  
  $$2x+3x$$
$$\frac{3}{4}(8a+16b)$$  
  $$24m+8n-12p$$
$$\frac{1}{2}\left(\frac{1}{3}x-8y+\frac{2}{3}z\right)$$  
  $$5xy+15y$$
$$2x(-3+y)$$  

Guiding Questions

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Problem Set

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Target Task


If we multiply $${\frac{x}{2}+\frac{3}{4}}$$ by $$4$$, we get $${{2x+3}}$$

Is $${{2x+3}}$$ an equivalent expression to $${\frac{x}{2}+\frac{3}{4}}$$? Explain your answer. 

References

Illustrative Mathematics Equivalent Expressions?

Equivalent Expressions?, accessed on Oct. 9, 2017, 9:10 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

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.

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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Evaluating Numerical and Algebraic Expressions

Topic B: Generating Equivalent Expressions

Topic C: Solving Multi-Step Problems using Expressions

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