Lesson 12 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

Objective

Divide decimals by decimals using the standard algorithm.

Common Core Standards

Core Standards

The core standards covered in this lesson

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

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

Understand that multiplying a dividend and divisor by the same power of ten creates equivalent division problems with the same solution.
Create equivalent division problems with whole number divisors that can be solved using the standard algorithm.
Apply the standard algorithm for division to solve problems.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Dividing with decimals is a fluency expectation in sixth grade. Ensure students have opportunities to build towards fluency throughout the unit and the year. See our Guide to Procedural Skills and Fluency for additional information and strategies.

Lesson Materials

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

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

Consider the division problem $$19.2 \div 1.6$$.

Written as a fraction, the problem becomes $${\frac{19.2}{1.6}}$$.

a. Multiply the fraction by $${\frac{10}{10}}$$ to create an equivalent division problem with whole numbers. Then use the standard algorithm for division to find the quotient.

b. How can you apply this approach to solve other decimal division problems?

Guiding Questions

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

Problem 2

Divide: $$526.76 \div 1.3$$

First, write an equivalent division problem with a whole number divisor. Then solve and check your answer using multiplication.

Guiding Questions

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

Problem 3

Which division problems below will have the same solution as $$580.6 \div 8.44$$?

Explain your reasoning for each equivalent problem.

A. $${580.6 \div 844}$$

B. $${5,806 \div 844}$$

C. $${58,060 \div 844}$$

D. $${580,600 \div 844}$$

E. $${5,806 ÷ 84.4}$$

F. $${58.06 ÷ 0.844}$$

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

Sophia’s dad paid $43.25 for 12.5 gallons of gas.

a. What is the cost of one gallon of gas?

b. Approximately how many gallons of gas can you get for $1? Round to the nearest hundredth.

Student Response

Create a free account or sign in to view Student Response

References

Illustrative Mathematics Buying Gas

Buying Gas, accessed on Sept. 28, 2017, 3:55 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.

Modified by Fishtank Learning, Inc.

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 involving all types of decimal division problems.
Include examples where the decimal answer is rounded to a given place value.
Include error analysis problems.

Illustrative Mathematics Reasoning about Multiplication and Division and Place Value, Part 1 — Parts e-g
Illustrative Mathematics Reasoning about Multiplication and Division and Place Value, Part 2
EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic C > Lesson 15 — Exercises, Examples, and Problem Set; this lesson focuses on using some mental math and reasonability strategies to solve problems
Illustrative Mathematics Changing Currency
EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic C > Lesson 14 — Exercises, Examples, and Problem Set

Word Problems and Fluency Activities

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

Lesson 11

Lesson 13

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 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

Student Response

References

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