Multi-Digit and Fraction Computation

Lesson 10

Unit 3: Multi-Digit and Fraction Computation

Topic A: Dividing with Fractions

1

6.NS.A.1

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.

2

6.NS.A.1

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

3

6.NS.A.1

Divide a whole number by a fraction using visual models.

4

6.NS.A.1

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

5

6.NS.A.1

Solve and write story problems involving division with fractions.

6

6.NS.A.1

Solve problems involving division with fractions.

Topic B: Computing with Decimals

7

6.NS.B.3

Add and subtract decimals using the standard algorithm.

8

6.NS.B.3

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

9

6.NS.B.3

Multiply decimals using the standard algorithm.

10

6.NS.B.2

Divide multi-digit whole numbers using the standard algorithm.

11

6.NS.B.2

6.NS.B.3

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

12

6.NS.B.3

Divide decimals by decimals using the standard algorithm.

13

6.NS.B.3

Solve problems involving decimals using all four operations.

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

14

6.NS.B.4

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

15

6.NS.B.4

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

16

6.NS.B.4

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

17

6.NS.B.4

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

Objective

Divide multi-digit whole numbers using the standard algorithm.

Common Core Standards

Core Standards

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.

Foundational Standards

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.

Criteria for Success

Divide multi-digit whole numbers using partial quotients.
Understand the connection between the standard algorithm for division and partial quotients.
Apply the standard algorithm for division to solve problems.

Tips for Teachers

In fifth grade, students found whole number quotients with up to 2 digit divisors and 4 digit dividends using various strategies. In sixth grade, dividing multi-digit whole numbers is a fluency expectation. This lesson reviews partial quotient strategies from fifth grade and students are guided toward understanding the standard algorithm as an efficient way to compute. Ensure students have opportunities to build towards fluency throughout the unit and the year. See our Guide to Procedural Skill and Fluency for additional information and strategies.
The following tools or materials are useful for this lesson: large graph or grid paper for computations, calculators to check answers.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 2 or 3 (benefit from worked examples). If students have a strong grasp on using the standard algorithm to divide whole numbers, then this Anchor Problem can either be skipped or done independently. Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

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Problem Set
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Anchor Problems

Problem 1

Find the quotient of $${ 67,764 \div 12}$$ using partial quotients.

Guiding Questions

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Problem 2

Solve $${70,072 \div 19}$$ using the standard algorithm.

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic C > Lesson 13 — Example 1

Grade 6 Mathematics > Module 2 > Topic C > Lesson 13 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Solve $${48,072 \div 24}$$ using the standard algorithm.

Guiding Questions

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Problem 4

Use the computation shown to find the products.

Guiding Questions

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References

Illustrative Mathematics Interpreting a Division Computation

Interpreting a Division Computation, accessed on Sept. 28, 2017, 3:31 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

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Include a few problems where there is a remainder. (Students are familiar with remainders from fourth and fifth grades.)

EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic C > Lesson 13 — Exercises and Problem Set

Illustrative Mathematics How Many Staples? — Challenge

Target Task

Use the standard algorithm to divide 462,308 by 76. Check your answer is correct using multiplication.

Mastery Response

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Multi-Digit and Fraction Computation

Lesson 10

Unit 3: Multi-Digit and Fraction Computation

Topic A: Dividing with Fractions

1

2

3

4

5

6

Topic B: Computing with Decimals

7

8

9

10

11

12

13

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

14

15

16

17

Objective

Common Core Standards

Core Standards

The Number System

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Criteria for Success

Tips for Teachers

Remote Learning Guidance

Fishtank Plus

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem 4

Guiding Questions

References

Problem Set

Target Task

Mastery Response

lesson 9

lesson 11