Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 15

Operations with Rational Numbers

Lesson 15

Math

Unit 2

7th Grade

Lesson 15 of 18

Objective

Divide signed rational numbers and interpret quotients in real-world contexts.

Common Core Standards

Core Standards

  • 7.NS.A.2.B — Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.
  • 7.NS.A.2.C — Apply properties of operations as strategies to multiply and divide rational numbers.

Foundational Standards

  • 6.NS.A.1

Criteria for Success

  1.  Apply the rules of dividing signed numbers to find the quotients of rational numbers.
  2. Write and solve division problems with signed rational numbers to represent contexts.
  3. Apply the concept of rate to situations with a negative rate of change.

Tips for Teachers

  • This lesson mainly deals with fractional rational numbers and does not involve converting fractions to decimals, which will come in Lesson 16.
  • Continue building fluency with mental math and other activities.
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Anchor Problems

25-30 minutes

Problem 1

Over time, houses can sink slightly due to shifts in the soil below. One house was built with its ground at sea level, and over a period of 7 years, it sank to an elevation of  $${-1 {5\over 16}}$$ inches. On average, what is the rate of change in elevation of the house? 

Guiding Questions

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Student Response

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Problem 2

Find the quotients:

a.      $${{5\over 4} \div \left ( -{2\over 3} \right)}$$

b.      $${-18 \div \left( {1\over 5} \right )}$$

c.      $${- \left( {9\over 4} \div 6 \right)}$$

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

A red-throated loon is a type of diving bird that dives for its food. One particular loon dives for 8 seconds to a depth of 12 feet under the surface of the water.

a.   Assume the loon dives at a constant rate. Write an equation that can be used to represent the elevation, $$y$$, of the loon after $$x$$ seconds into the dive.

b.   If the loon is at a depth of 22.5 feet under the surface of the water, how long was it diving for?

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 like $${-6 \times ? = 5{1\over 3}}$$; determine the missing value.
  • Include procedural practice of finding the quotient of signed numbers. (Note, students are not converting fractions into decimals yet.)
  • Kuta Software Free Pre-Algebra Worksheets Arithmetic — Multiplying and Dividing Fractions and Mixed Numbers

Next

Convert rational numbers to decimals using long division and equivalent fractions.

Lesson 16
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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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