Curriculum  /  Math  /  6th Grade  /  Unit 5: Numerical and Algebraic Expressions  /  Lesson 7

Numerical and Algebraic Expressions

Lesson 7

Math

Unit 5

6th Grade

Lesson 7 of 12

Objective

Identify equivalent expressions (Part 1).

Common Core Standards

Core Standards

  • 6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
  • 6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

Criteria for Success

  1. Use tape diagrams to model expressions and determine if they are equivalent.
  2. Understand that two algebraic expressions are equivalent to each other if they are equal for every value the variable(s) may be.
  3. Identify equivalent forms of terms that involve multiplication and division.

Tips for Teachers

  • Lessons 7 and 8 introduce the concept of equivalent expressions to students. In these two lessons, they develop the understanding that $${y+y+y}$$ is equivalent to $${3y}$$, regardless of what $$y$$ represents. Lessons 9 and 10 will address the distributive property.
  • The commuative property appears again in Anchor Problem 3, this time with multiplication and division, when students consider if $$6m$$ is equivalent to $$m\times6$$. While students are familiar with the concept of the commutative property from elementary work using numbers, they may not be familiar with the formal term, and should begin hearing and using the formal vocabulary in 6th grade. 
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Anchor Problems

25-30 minutes

Problem 1

Three questions below explore what it means for two expressions to be equivalent. Use tape diagrams to draw models for each expression and determine if and when the expressions are equal. 

An example using numerical expressions is shown below:

Is $${1+3=2+1+1}$$?

Tape diagram: 

Conclusion: The tape diagrams are the same length, so the two numerical expressions are equivalent.

a.   Is $${x+x+x+2=3x+2}$$?

b.   Is $${x+x+x+2=4x}$$?

c.   Is $${ x+x+x+2=3x}$$?

Guiding Questions

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Student Response

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Problem 2

Which expressions below are equivalent to the expression $${5m}$$? Choose all that apply. Justify your reasoning for each expression.

a.   $${m+m+m+m+m}$$

b.   $${m+5}$$

c.   $${3m+m+m}$$

d.   $${2m+3m}$$

e.   $${3+2m}$$

f.   $${ m+m+m+2}$$

g.   $${4m+m}$$

Guiding Questions

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Student Response

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Problem 3

For each row in the chart below, determine if the expression given is equivalent to $${{6m}}$$, $${{m\over6}}$$, or neither. Place a check mark to indicate equivalent expressions.

 

  $${{6m}}$$ $${{m\over6}}$$ Neither
$${m\times6}$$      
$${m\div{1\over6}}$$      
$${{1\over6} \cdot m}$$      
$${6\div m}$$      
$${2\cdot 3(m)}$$      
$${m\div6}$$      

 

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Problem 1

Write three different expressions that are equivalent to $${4y+5}$$.

Student Response

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Problem 2

Match each expression on the left with an expression on the right.

a.     $${8+8+2(8)}$$                                          i.     $${4(8)}$$

b.     $${8+8+8\times8}$$                                        ii.      $${8^3+8}$$

c.     $${8\times8\times8+8}$$                                        iii.      $${2^2+8^2}$$

d.     $${2\times2+8\times8}$$                                        iv.      $${2(8)+8^2}$$

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.

  • Include problems where students reason with subtraction. For example:

Which expressions are equivalent to $${5m}$$?

  1. $${6m-1}$$
  2. $${6m-m}$$
  3. $${3m+4m-m-m}$$
  4. $${8-3m}$$
  5. $${(8-3)m}$$
  6. $${5m}+0$$

Next

Identify equivalent expressions (Part 2).

Lesson 8
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Lesson Map

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

Topic A: Numerical Expressions with Exponents

Topic B: Introduction to Algebraic Expressions

Topic C: Equivalent Expressions & Applications

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