Lesson 7 | Numerical and Algebraic Expressions | 6th Grade Mathematics

Objective

Identify equivalent expressions (Part 1).

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Expressions and Equations

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.

Expressions and Equations

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

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

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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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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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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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Problem 1

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

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

An example response to the Target Task at the level of detail expected of the students.

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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 $${5m}$$?

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

EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic D > Lesson 10 — Exercises and Problem Set (this lesson includes a Bingo game which could be used, time permitting)
EngageNY Mathematics Grade 6 Mathematics > Module 4 > Topic D > Lesson 14 — Exercises and Problem Set
Open Up Resources Grade 6 Unit 6 Practice Problems — Lesson 8
Open Middle Equivalent Expressions 1 — Challenge

Lesson 6

Lesson 8

Lesson Map

Topic A: Numerical Expressions with Exponents

Understand the meaning of exponents.

6.EE.A.1

Evaluate numerical expressions involving whole-number exponents.

6.EE.A.1

Topic B: Introduction to Algebraic Expressions

Use variables to write algebraic expressions.

6.EE.A.2 6.EE.A.2.C 6.EE.B.6

Evaluate algebraic expressions.

6.EE.A.2 6.EE.A.2.C

Write expressions for verbal statements and vice versa (Part 1).

6.EE.A.2.A 6.EE.A.2.B

Write expressions for verbal statements and vice versa (Part 2).

6.EE.A.2.A 6.EE.A.2.B

Topic C: Equivalent Expressions & Applications

Identify equivalent expressions (Part 1).

6.EE.A.3 6.EE.A.4

Identify equivalent expressions (Part 2).

6.EE.A.3 6.EE.A.4

Write equivalent expressions using the distributive property (Part 1).

6.EE.A.3 6.EE.A.4

Write equivalent expressions using the distributive property (Part 2).

6.EE.A.3 6.EE.A.4

Write algebraic expressions for application situations (Part 1).

6.EE.B.6

Write algebraic expressions for application situations (Part 2).

6.EE.B.6

Numerical and Algebraic Expressions

Objective

Common Core Standards

Core Standards

Expressions and Equations

Expressions and Equations

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Lesson Map

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