Lesson 11 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

6.NS.B.2 — Fluently divide multi-digit numbers using the standard algorithm.

The Number System

6.NS.B.2 — Fluently divide multi-digit numbers using the standard algorithm.
6.NS.B.3 — Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

The Number System

6.NS.B.3 — Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Foundational Standards

The foundational standards covered in this lesson

4.NBT.B.6

Number and Operations in Base Ten

4.NBT.B.6 — Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.B.6

Number and Operations in Base Ten

5.NBT.B.6 — Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
5.NBT.B.7

Number and Operations in Base Ten

5.NBT.B.7 — Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Criteria for Success

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

Represent remainders as decimals in division problems.
Understand how the standard algorithm (long division) can be extended to include decimal quotients and decimal dividends.
Apply the standard algorithm for division to solve problems.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Dividing multi-digit decimals is a fluency expectation in sixth grade. Lessons 11 and 12 demonstrate how the standard algorithm for division can be applied to problems with decimals in the dividend, divisor, or quotient. This lesson focuses on decimals in the quotient or in the dividend; students will see decimals in the divisor in Lesson 12.

Lesson Materials

Graph Paper (2-3 sheets per student)
Optional: Calculators (1 per student) — Calculators can be used to check answers.

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Anchor Problems

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

Problem 1

Eight people need to divide $62 equally so that each person gets the same amount of money. How much money will each person get?

Solve this problem using any method of your choice. Then use long division to support your answer.

Guiding Questions

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Problem 2

What is the decimal value of $${1 \div 20}$$?

Use long division to show your answer.

Guiding Questions

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Problem 3

A scientist is dividing 48.85 ounces of a liquid equally into 5 beakers. How many ounces of liquid should she put in each beaker?

Guiding Questions

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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

Problem 1

Find the decimal value of $${3 ÷ 50}$$ using any strategy. Then find the quotient using long division and show the answers are the same.

Problem 2

After 6 months, you’ve paid $512.34 to your phone company. Assuming you pay the same amount each month, what is your monthly phone bill? Show your work.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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 procedural problems of
- Dividing whole numbers by whole numbers that result in a decimal quotient
- Dividing decimals by whole numbers
- Dividing whole numbers by whole numbers that result in a whole number (review from Lesson 10)
- Multiplying decimals, especially to check answers to division problems
Include problems similar to anchor problems with light context.

Illustrative Mathematics What Is the Best Way to Divide? — The second question of part c involves a whole number divided by a decimal, which is covered in the next lesson

Word Problems and Fluency Activities

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

Lesson 10

Lesson 12

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

The Number System

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations in Base Ten

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Problem 1

Problem 2

Student Response

Additional Practice

Word Problems and Fluency Activities

Lesson Map

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