Lesson 13 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

Objective

Solve problems involving decimals using all four operations.

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

Determine which operations are needed to solve a contextual problem.
Apply the standard algorithms for adding, subtracting, multiplying, and dividing with decimals to solve problems accurately and efficiently (MP.6).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Standard 6.NS.3 calls for fluent computation with decimals. This lesson engages students in computing with decimals in real-world applications. In providing feedback and in understanding students’ progression towards mastery of the standard, consider the calculations separately from the interpretation of the problem. 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.

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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

Solve each problem.

a. Juanita spent $24.50 on each of her 6 grandchildren at the fair. How much money did Juanita spend?

b. Nita bought some games for her grandchildren for $42.50 each. If she spent a total of $340, how many games did Nita buy?

c. Helen spent an equal amount of money on each of her 7 grandchildren at the fair. If she spent a total of $227.50, how much did she spend on each grandchild?

Guiding Questions

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References

Illustrative Mathematics Gifts from Grandma, Variation 3

Gifts from Grandma, Variation 3, accessed on Sept. 28, 2017, 3:59 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 2

A small inflatable pool holds 65.85 gallons of water. There are already 24.77 gallons of water in the pool. If water flows from a hose at a rate of 1.3 gallons per minute, how long will it take to fill the rest of the pool?

Guiding Questions

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Problem 3

Four friends are having a barbeque to celebrate a birthday. At the grocery store, the friends pick up the items shown in the list below:

2.6 lbs. of grapes at $2.90/lb.
6 ears of corn on the cob at $0.65 each
4.48 lbs. of ground beef at $3.75/lb.
2 packages of hamburger buns at $1.44 each

The friends split the cost of the groceries evenly. How much does each friend owe for the food?

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

You’re building a rectangular frame to go around your vegetable garden. The area of your garden is 1.96m$$^2$$ and length of the garden is 2.45m.

a. What is the width of your garden?

b. If the frame for your garden will go along the perimeter, how much wood will you need to build the frame?

Student Response

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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, covering all four operations, focused on where students need to build greater fluency.
Include word problems that involve one or more operations with decimals; this is a great opportunity to review rate problems from Unit 2.

Illustrative Mathematics Movie Tickets

Word Problems and Fluency Activities

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

Lesson 12

Lesson 14

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

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Word Problems and Fluency Activities

Lesson Map

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