Operations with Rational Numbers

Lesson 14

Math

Unit 2

7th Grade

Lesson 14 of 18

Objective


Determine the rules for dividing signed numbers.

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

  • 5.NF.B.3
  • 3.OA.B.6

Criteria for Success


  1. Use the relationship between multiplication and division to determine the rules for dividing signed numbers (MP.8).
  2. Write division problems of signed numbers as multiplication problems, and vice versa.
  3. Understand that the division problem $${p \div q}$$, where $$p$$ and $$q$$ are integers and $$q \neq 0$$, can be represented as $$p\over q$$, and vice versa. 
  4. Understand that for integers $$p$$ and $$q$$, where $$q \neq 0$$, the following are equivalent: $$-{p\over q} = {-p\over q} = {p\over-q}$$.

Tips for Teachers


  • Lessons 14 and 15 address dividing signed numbers. Lesson 14 introduces the concept and Lesson 15 involves real-world applications.
  • The equivalence between $$-\frac{p}{q}$$, $$\frac{-p}{q}$$, and $$\frac{p}{-q}$$ is an important concept for students to understand when they study slope, the change in $$y$$ values over the change in $$x$$ values for a linear relationship, in 8th grade.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

Four multiplication problems are shown in the table. Write each one as a division problem and then find the solution. What can you conclude about the rules for dividing signed numbers?

Multiplication Problem Division Problem Solution
$$2\times\square=6$$ $$6\div2=\square$$

$$\square=$$

$$2\times\square=-6$$  

$$\square=$$

$$-2\times\square=-6$$  

$$\square=$$

$$-2\times\square=6$$  

$$\square=$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Write each division problem as a fraction, and then find each quotient. What do you notice about the three problems? Why do you think this happened?

a.   $$-24 \div 6$$

b.   $$24 \div (-6)$$

c.   $$-(24\div6)$$

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

Which expressions are equivalent to $${5\div (-12)}$$? Select all that apply.

Create a free account or sign in to view multiple choice options

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.

a.   $$-0.25$$ and $$\frac{1}{-4}$$

b.   $$-\left ( \frac{1}{4} \right )$$ and $$\frac{-1}{-4}$$

c.   $$\frac{-1}{4}$$ and $$-\frac{1}{4}$$

Student Response

Create a free account or sign in to view Student Response

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 determine if the quotient will be positive or negative, without computing.
  • Include problems where students write or identify equivalent expressions, similar to Anchor Problem #3.
  • Include problems where students find the quotient, involving either integer or fraction answers (decimal representation is coming up in Lesson 16).
icon/arrow/right/large copy

Lesson 13

icon/arrow/right/large

Lesson 15

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

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free