Numerical and Algebraic Expressions

Lesson 10

Math

Unit 5

6th Grade

Lesson 10 of 12

Objective


Write equivalent expressions using the distributive property (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.

Foundational Standards

  • 4.NBT.B.5

Criteria for Success


  1. Use area models to write equivalent expressions involving subtraction.
  2. Apply the distributive and commutative properties to write equivalent expressions involving addition and subtraction.
  3. Factor an expression to write it as a product of a number and a sum or difference.

Tips for Teachers


Lessons 9 and 10 focus on writing equivalent expressions using the distributive property. Lesson 10 continues the concepts from Lesson 9 but introduces expressions with subtraction.

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Anchor Problems


Problem 1

Jenny found the product of $${8 × {49}}$$ by doing $${8({50}) – 8(1)}$$

a.   Explain what strategy Jenny used to find the product. 

b.   Draw an area model to represent Jenny’s strategy. Include the labels $$8$$, $${50}$$, $${49}$$, and $$1$$. Shade in the area that represents the product.

c.   What is another expression that represents the product? 

Guiding Questions

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Problem 2

An area diagram is shown below. Write two equivalent expressions to represent the shaded area in the diagram.

Guiding Questions

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Problem 3

Which of the following expressions are equivalent? Defend your response. If an expression has no match, write two equivalent expressions to match it.

  1. $$2(x+4)$$
  2. $$8+2x$$
  3. $$2x+4$$
  4. $$3(x+4)-(4+x)$$
  5. $$x+4$$

Guiding Questions

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References

Illustrative Mathematics Equivalent Expressions

Equivalent Expressions, accessed on Dec. 19, 2017, 11:20 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.

Problem Set

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Target Task


Using properties of operations, complete the table so each row represents a pair of equivalent expressions. In the left column, write the missing product in factored form. In the right column, write the missing sum or difference in expanded form.

Factored Form Expanded Form
$${7(x-3)}$$  
$${{3\over5} (10m+20)}$$  
  $${12y-9y}$$
  $${15x+24y}$$

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 9

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Lesson 11

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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