Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 17

Operations with Rational Numbers

Lesson 17

Math

Unit 2

7th Grade

Lesson 17 of 18

Objective

Multiply and divide with rational numbers using properties of operations.

Common Core Standards

Core Standards

  • 7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
  • 7.NS.A.2.C — Apply properties of operations as strategies to multiply and divide rational numbers.

Foundational Standards

  • 4.NBT.B.5
  • 3.OA.B.5

Criteria for Success

  1. Apply the commutative property of multiplication to rearrange factors in more efficient ways.
  2. Apply the associative property of multiplication to group factors in more efficient ways. 
  3. Apply the distributive property of multiplication to create equivalent expressions, which lend to different ways to solve.
  4. Rewrite expressions with division as problems using multiplication as a strategy to solve.

Tips for Teachers

  • There are many different approaches students can take to multiply and divide with rational numbers, and some of these approaches may be more efficient or easier than others, especially when looking carefully at the structure of the expression and thinking quantitatively about the values (MP.7 and MP.2). Using the examples, have students brainstorm various approaches to tackling each one; in addition to the strategies mentioned in the notes and guiding questions, students are bound to come up with other great approaches. 
  • Continue building fluency with mental math and other activities.
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Anchor Problems

25-30 minutes

Problem 1

Evaluate each expression below. Compare your approaches with others in the class to determine the most efficient approach.

a.   $${-6 \times 2 \times (-2) \times (-5) \times (-3)}$$

b.   $${4 \times {1\over 3} \times (-8) \times 9 \times \left( -{1\over2} \right)}$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 — Example 1 and Exercise 2

Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 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..

Problem 2

Evaluate the expression below. Compare your approach with others in the class to determine the most efficient approach.

$${1 \div {2\over3} \times (-8) \times 3 \div \left ( -{1\over2} \right )}$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 — Example 4

Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 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..

Problem 3

Evaluate the expression below. Can you determine an approach to solving this problem using the distributive property?

$${-6 \times \left(5{1\over3} \right)}$$

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 — Example 2

Grade 7 Mathematics > Module 2 > Topic B > Lesson 16 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..

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

Use the properties of operations to evaluate the expression below. 

$$-\frac{5}{6}\times24\times(-9)\div(-\frac{3}{2})\div\frac{25}{12}$$

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.

  • Challenge: Evaluate: $$\frac{2(-8)+(-4)^2+2(-2)(-4)}{32\div2}$$

Next

Solve problems with rational numbers and all four operations.

Lesson 18
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Lesson Map

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

Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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