Numerical and Algebraic Expressions

Lesson 3

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.

Fishtank Plus

Subscribe to Fishtank Plus to unlock access to additional resources for this lesson, including:

  • Problem Set
  • Student Handout Editor
  • Google Classrom Integration
  • Vocabulary Package

 

Anchor Problems

?

Problem 1

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

Expand the expression below by using a rectangular array.

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

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

Grade 7 Mathematics > Module 3 > Topic A > Lesson 3 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..

Modified by The Match Foundation, Inc.

Problem 2

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

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

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic A > Lesson 4Exercise 2

Grade 7 Mathematics > Module 3 > Topic A > Lesson 4 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..

Modified by The Match Foundation, Inc.

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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

?

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.

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.

Mastery Response

?

Create a free account or sign in to view Mastery Response