Curriculum  /  Math  /  6th Grade  /  Unit 3: Multi-Digit and Fraction Computation  /  Lesson 4

Multi-Digit and Fraction Computation

Lesson 4

Math

Unit 3

6th Grade

Lesson 4 of 17

Objective

Use visual models and patterns to develop a general rule to divide with fractions.

Common Core Standards

Core Standards

  • 6.NS.A.1 — Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Foundational Standards

  • 5.NF.B.6
  • 5.NF.B.7

Criteria for Success

  1. Determine that dividing a number by a unit fraction is the same as multiplying by the denominator of the fraction; show this in a visual model.
  2. Determine that dividing a number by a fraction is the same as multiplying by the denominator and then dividing by the numerator of the fraction; show this in a visual model.
  3. Understand the reasoning behind the invert and multiply rule or multiplying by the reciprocal. 

Tips for Teachers

  • In this lesson, students use visual models and patterns to develop the general rule for dividing by fractions (MP.8). The focus of this lesson is on the development of the rule rather than on the use of it. Students will have opportunities for a lot of practice in upcoming lessons. 
  • There are several resources in the Teacher Tune Ups section of this SERP resource, including several short videos that demonstrate dividing with fractions using models and methods alternative to the general algorithm, as well as the post "Delaying 'Invert and Multiply'", a valuable resource for teachers to deepen their understanding of fraction division and to understand why the invert and multiply rule works prior to teaching the method to students.
Fishtank Plus

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

Anchor Problems

25-30 minutes

Problem 1

The number $$3$$ is divided by unit fractions $${\frac{1}{2}}$$, $$\frac{1}{3}$$, $${\frac{1}{4}}$$, and $${\frac{1}{5}}$$. For each division problem, draw a visual model to represent the problem and to find the solution. Then complete the rest of the chart and answer the questions that follow.

Division Problem Visual Model Quotient Multiplication Problem
$$3\div \frac{1}{2}$$                                                                                                                 
$$3\div \frac{1}{3}$$      
$$3\div \frac{1}{4}$$      
$$3\div \frac{1}{5}$$      

What pattern do you notice? What generalization can you make? Explain your reasoning.

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

The number 3 is now divided by fractions $${\frac {1}{4}}$$, $${\frac{2}{4}}$$, $${\frac{3}{4}}$$, and $${\frac{4}{4}}$$. For each division problem, draw a visual model to represent the problem and to find the solution. Then complete the rest of the chart and answer the questions that follow.

Division Problem Visual Model Quotient Multiplication Problem
$$3\div \frac{1}{4}$$                                                                                                                 
$$3\div \frac{2}{4}$$      
$$3\div \frac{3}{4}$$      
$$3\div \frac{4}{4}$$      

What pattern do you notice? What generalization can you make?

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 3

For each problem, draw a diagram and write a division problem. Find the solution using both the diagram and by calculating, and check that your answers are the same by each method.

a.   How many fives are in 15?

b.   How many halves are in 3?

c.   How many sixths are in 4?

d.   How many two-thirds are in 2?

e.   How many three-fourths are in 2?

f.   How many $${{\frac{1}{6}}}$$s are in $${\frac{1}{3}}$$?

g.   How many $${{\frac{1}{6}}}$$s are in $${{\frac{2}{3}}}$$?

h.   How many $${\frac{1}{4}}$$s are in $${{\frac{2}{3}}}$$?

i.   How many $${\frac{5}{12}}$$s are in $${\frac{1}{2}}$$?

Guiding Questions

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

Student Response

Upgrade to Fishtank Plus to view Sample Response.

References

Illustrative Mathematics How Many ___ Are in ... ?

How Many ___ Are in ... ?, accessed on Sept. 28, 2017, 12:55 p.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

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

Draw a visual model to represent the solution to the division problem $${6 \div \frac{2}{3}}$$. 

Then, use your model to explain why this can also be solved with the multiplication problem $${6 \times \frac{3}{2}}$$.

Student Response

Upgrade to Fishtank Plus to view Sample 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.

Word Problems and Fluency Activities

Next

Solve and write story problems involving division with fractions.

Lesson 5
icon/arrow/right/large

Lesson Map

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

Topic A: Dividing with Fractions

Topic B: Computing with Decimals

Topic C: Applying the Greatest Common Factor and the Least Common Multiple

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?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free