Lesson 15 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

Solve two- and multi-step word problems involving addition and subtraction of decimals.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

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.

Foundational Standards

The foundational standards covered in this lesson

4.OA.A.3

Operations and Algebraic Thinking

4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Criteria for Success

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

Make sense of a three-act task and persevere in solving it (MP.1).
Solve two- and multi-step word problems that involve the addition and subtraction of decimals (MP.4).
Assess the reasonableness of an answer to a word problem involving the addition and subtraction of decimals (MP.1).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Let students work on each problem on the Problem Set independently and circulate to see whether students are solving correctly. If not, come back together to discuss how/what to draw on a tape diagram, then allow them to try again on their own. Encourage students to use a strategy of their choice to assess the reasonableness of their answer.

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Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

Act 1: Watch the first 27 seconds of the following video from the 2016 Olympics.

a. What do you notice? What do you wonder?

b. Who won the relay race? By how much? Make an estimate.

Guiding Questions

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References

YouTube Video: “USA takes gold in Men's 4x100m Freestyle Relay”

“USA takes gold in Men's 4x100m Freestyle Relay” by is made available by YouTube under the Standard YouTube License. Accessed Feb. 11, 2018, 2:37 p.m..

Problem 2

Act 2: Use the following information to determine who won the relay race and by how much.

Nation

Swimmers

United States

Caeleb Dressel (48.1)

Michael Phelps (47.12)

Ryan Held (47.73)

Nathan Adrian (46.97)

France

Mehdy Metella (48.08)

Fabien Gilot (48.2)

Florent Manaudou (47.14)

Jeremy Stravius (47.11)

Guiding Questions

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Problem 3

Act 3: The United States won the race. They beat France's time by 0.61 seconds.

Was your answer reasonable? Why or why not?

Guiding Questions

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Problem 4

Act 4 (the sequel): What was the winning team's time in minutes and seconds?

Guiding Questions

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Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

Look at #1b. I got 2.36 seconds. Is my answer reasonable? Why or why not? What mistake do you think I made?
Look at #5. What did you get for the cost of the notebooks? What multiplication sentence can I write to describe this relationship? What do you notice about the factors and product?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Naja brought $20 to the corner store.

She spent $3.49 on candy.
She spent $5.79 on a Jamaican beef patty.

How much money did Naja have left?

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 Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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

Lesson 14

Lesson Map

Topic A: Addition and Subtraction of Fractions

Recognize and generate equivalent fractions.

5.NF.A

Add fractions with like denominators.

5.NF.A

Subtract fractions with like denominators.

5.NF.A

Add fractions with unlike denominators whose sum is less than 1.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 1 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is less than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is greater than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions greater than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers.

5.NF.A.2

Add and subtract more than two fractions.

5.NF.A.1

Solve two- and multi-step word problems involving addition and subtraction of fractions.

5.NF.A.2

Topic B: Addition and Subtraction of Decimals

Add decimals.

5.NBT.B.7

Subtract decimals.

5.NBT.B.7

Solve two- and multi-step word problems involving addition and subtraction of decimals.

5.NBT.B.7

Addition and Subtraction of Fractions/Decimals

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem 4

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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