Lesson 2 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

Objective

Divide a fraction by a whole number using visual models and related multiplication problems.

Common Core Standards

Core Standards

The core standards covered in this lesson

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?

The Number System

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

The foundational standards covered in this lesson

5.NF.B.7

Number and Operations—Fractions

5.NF.B.7 — Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Draw and interpret a visual model to represent a fractional amount being divided by a whole number.
Write a division problem to represent a context.
Understand that dividing an amount by a whole number, $$n$$, is the same as taking $$\frac{1}{n}$$th of the amount or multiplying by $$\frac{1}{n}$$. (For example, dividing by $$3$$ is the same as multiplying by $$\frac{1}{3}$$.)

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students may need to be reminded of Criteria for Success #3. This can be done using visual models, dividing a whole unit by a certain number, $$n$$, and then observing that each piece represents $$\frac{1}{n}$$ th of the whole unit.
The focus of this lesson is on using visual models to solve fraction-divided-by-whole-number problems. Students should not be using the “invert and multiply” rule as an algorithm yet in order to continue to build conceptual understanding. This concept will be introduced in Lesson 4 and reinforced throughout the lessons to follow.
Note that standard 6.NS.1 is a culminating standard; it is the last standard in the progression of standards that extends on the operations to include fractions.

Fishtank Plus

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

Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Leonard made $${\frac{1}{4}}$$ of a gallon of lemonade and poured all of it into $$3$$ glasses, divided equally. How much lemonade is in each glass? Write a division problem and draw a visual model.

Guiding Questions

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

Problem 2

$${\frac{3}{4}}$$ quart of soup is split equally between two people. How much soup does each person get?
Write a division problem and draw a visual model.

Guiding Questions

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

Problem Set

A set of suggested resources or problem types that teachers can turn into a 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

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

You follow a recipe to make a dipping sauce for chicken. The recipe makes $${\frac{2}{3}}$$ cup of sauce and serves $$4$$ people. How many cups of sauce are in each serving?

a. Draw a visual model to represent the situation and solution.

b. Write a division and multiplication problem to represent the situation. Show that your solution from your calculations is the same as from your model.

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.

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic A > Lesson 1 — Examples, Exercises, and Problem Set
Illustrative Mathematics Salad Dressing
Illustrative Mathematics Painting a Room

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 1

Lesson 3

Lesson Map

Topic A: Dividing with Fractions

Interpret division problems as the number of items in each group or the number of groups of a given number of items. Write corresponding multiplication and division problems.

6.NS.A.1

Divide a fraction by a whole number using visual models and related multiplication problems.

6.NS.A.1

Divide a whole number by a fraction using visual models.

6.NS.A.1

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

6.NS.A.1

Solve and write story problems involving division with fractions.

6.NS.A.1

Solve problems involving division with fractions.

6.NS.A.1

Topic B: Computing with Decimals

Add and subtract decimals using the standard algorithm.

6.NS.B.3

Multiply decimals using strategies, and develop an understanding of the standard algorithm.

6.NS.B.3

Multiply decimals using the standard algorithm.

6.NS.B.3

Divide multi-digit whole numbers using the standard algorithm.

6.NS.B.2

Divide numbers with decimal quotients. Divide decimals by whole numbers.

6.NS.B.2 6.NS.B.3

Divide decimals by decimals using the standard algorithm.

6.NS.B.3

Solve problems involving decimals using all four operations.

6.NS.B.3

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

Use prime factorization to represent numbers as products of prime factors.

6.NS.B.4

Find the greatest common factor of two numbers. Solve application problems using the greatest common factor.

6.NS.B.4

Find the least common multiple of two numbers. Solve application problems using the least common multiple.

6.NS.B.4

Solve mathematical and real-world problems using the greatest common factor and least common multiple.

6.NS.B.4

Multi-Digit and Fraction Computation

Objective

Common Core Standards

Core Standards

The Number System

Foundational Standards

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Word Problems and Fluency Activities

Lesson Map

Request a Demo

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?

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

Effective Instruction Made Easy