Lesson 7 | Multi-Digit and Fraction Computation | 6th Grade Mathematics

Objective

Add and subtract 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 the role that place value plays in addition and subtraction of decimals.
Accurately use the standard algorithm to add and subtract decimals.
Use addition and subtraction to solve decimal word problems.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

In fifth grade, students computed with decimals using all four operations and various strategies. In sixth grade, adding and subtracting with decimals is a fluency expectation. Use the problems in this lesson to review any strategies from fifth grade as needed so that students have a conceptual understanding to support the standard algorithm. 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.

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

Jayden has $20.56. He buys an apple for 79 cents and a granola bar for $1.76.

a. How much money did Jayden spend?

b. How much money does Jayden have now?

Guiding Questions

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

References

Illustrative Mathematics Jayden's Snacks

Jayden's Snacks, accessed on Sept. 28, 2017, 2:25 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

Dan is hiking along the Pacific Coast Trail. On Sunday morning, he hikes 5.83 miles before stopping for lunch. At the end of the day, Dan has hiked a total of 12.4 miles. How many miles did he hike after lunch?

Guiding Questions

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

Problem 3

The two problems below have been solved incorrectly. Explain the error in each problem and then correctly solve each one.

$${ 244.038+18.65 }$$	$${95.75-37.424}$$

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

A pitcher of water holds 48.2 ounces of water in it. The water is poured into two glasses, 12.08 ounces into one glass and 18.86 ounces into a second glass.

a. How much water is poured out of the pitcher?

b. How much water is left in the pitcher?

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.

Include fluency practice with adding and subtracting decimals.
Include error analysis problems of the standard algorithm applied incorrectly.

Illustrative Mathematics Adding Base Ten Numbers, Part 2
Illustrative Mathematics Adding Base Ten Numbers, Part 1 — Good problem if students need review of strategies to add and subtract decimals
EngageNY Mathematics Grade 6 Mathematics > Module 2 > Topic B > Lesson 9 — This lesson takes the approach of having students write decimals from fractions before computing
MARS Formative Assessment Lessons for Grade 6 Using Standard Algorithms for Number Operations — This includes error analysis studies of algorithms with positive integers; may be good for review or remediation
Open Middle Adding Decimals 2
Decimal Magic Square — Challenge
Open Middle Adding Decimals to Make Them as Close to One as Possible

Word Problems and Fluency Activities

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

Lesson 6

Lesson 8

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

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