Numerical and Algebraic Expressions

Lesson 8

Math

Unit 5

6th Grade

Lesson 8 of 12

Objective


Identify equivalent expressions (Part 2).

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. Understand that two algebraic expressions are equivalent to each other if they are equal for every value the variable(s) may be.
  2. Write equivalent expressions for given expressions.
  3. Determine if two expressions are equivalent.

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. 

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Anchor Problems


Problem 1

Watch the video "Consecutive Sums" by Mike Wiernicki

a.   What do you notice? What do you wonder?

b.   How can the performer know the sum so quickly for any number chosen? Determine how the trick works and how you can quickly find the sum for any number chosen.

Guiding Questions

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References

Under the Dome Consecutive Number Sums

Consecutive Number Sums by Mike Wiernicki is made available on Under the Dome at https://mikewiernicki.com/consecutive-number-sums/. Accessed Dec. 18, 2017, 5:01 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

A pentagon and a rectangle are shown below.

Do the two polygons have equivalent perimeters? Explain your reasoning.

Guiding Questions

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Problem 3

Are the two expressions below equivalent? Explain your reasoning.

$${4+x+2+y}$$                    $${4x+2y}$$

 

Guiding Questions

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Problem Set

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Target Task


Students were asked to write a pair of equivalent expressions. The work of four students is shown below. 

Harry $${3ab=a+a+a+b+b+b}$$
Iris $${3a^2=3\times3\times a\times a}$$
Jill $${a+a+1+a+2=3a+3}$$
Kevin $${2a+3b=2+a+3+b}$$

 

Which student(s) wrote an equivalent pair of expressions? Justify your answer. 

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 examples where students write simplified, equivalent expressions with one or more variables (not including distributive property)
  • Spiral in review of Lessons 1 and 2, evaluating numerical expressions with exponents
  • Spiral in review of greatest common factor from Unit 3 in preparation for Lesson 9; there is a sprint of finding GCF at the end of Lesson 11 in EngageNY, Grade 6, Module 4
  • Under the Dome Triangle Mystery...A more challenging take on the consecutive number sums
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Lesson 7

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Lesson 9

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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