Decimal Fractions

Lesson 10

Math

Unit 6

4th Grade

Lesson 10 of 13

Objective


Add tenths with hundredths written as decimals.

Common Core Standards


Core Standards

  • 4.NF.C.5 — Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Foundational Standards

  • 4.NF.A.1
  • 4.NF.B.3

Criteria for Success


  1. Write a decimal addition problem as a decimal fraction addition problem by replacing decimals with their equivalent fractions.
  2. Add decimals in cases of adding tenths with tenths, hundredths with hundredths, and tenths with hundredths by writing decimals as fractions and using fraction addition strategies from Lesson 9.
  3. Write the sum of fraction addition in cases listed above as a decimal.

Tips for Teachers


  • This lesson is optional since it is not an explicit part of the standards for students to add decimals together. However, because this is simply a combination of skills explicitly outlined in the standards (namely, writing a decimal as a fraction (4.NF.6) as well as adding decimal fractions together (4.NF.5)) and because it will aid students’ work with solving problems involving money (4.MD.2), it is included here. It is at your discretion to keep or skip.
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Anchor Tasks


Problem 1

a.   Solve.

  1. $${{3\over10} + {57\over100}}$$
  2. 0.3 + 0.57

b.   What do you notice about Part (a)? What do you wonder?

Guiding Questions

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Problem 2

Add. Show or explain your work. Write your answer as a decimal.

a.   0.4 + 0.5

b.   0.29 + 0.8

c.   1.52 + 0.39

d.   3.5 + 2.87

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic D > Lesson 13Concept Development

Grade 4 Mathematics > Module 6 > Topic D > 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

Each equation below is missing a decimal in tenths or hundredths. Find the decimal that makes each equation true. 

a.   0.30 + ____ = 0.36

b.   0.40 + ____ = 0.90

c.   ____ + 1.4 = 1.72

d.   1.10 + ____ = 1.5

e.   0.9 + ____ = 1.70

f.   0.28 + ____ = 1.78

Guiding Questions

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References

Illustrative Mathematics Illustrative Math Grade 4 Unit 3 Lesson 17 Activity 2

Illustrative Math Grade 4 Unit 3 Lesson 17 Activity 2, accessed on July 15, 2023, 8:48 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.

Problem 4

Using the digits 1 to 9, at most one time each, make the following statement true.

Guiding Questions

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References

Open Middle Open Middle, “Addding Parts of a Whole”

Open Middle, “Addding Parts of a Whole” by is made available on Open Middle under the CC BY-NC-SA 4.0 license. Accessed July 15, 2023, 11:10 p.m..

Problem Set


Answer Keys

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Discussion of Problem Set

  • I think I could solve #2a using tenths as a denominator. Do you agree or disagree? For what other computations in #2 could you use this strategy?
  • For #2b and 2d, explain how in the solution you could make 1 before adding the hundredths together. 
  • What was the added complexity of #3? How did your prior knowledge of adding fractions from Unit 5 and Lesson 9 help to make this task easier?

Target Task


Add. Show or explain your work. Write your answer as a decimal.

a.   0.4 + 0.72

b.   5.67 + 9.8

Student Response

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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

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

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Lesson 9

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Lesson 11

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Tenths

Topic B: Understanding Tenths and Hundredths

Topic C: Decimal Comparison

Topic D: Decimal Addition

Topic E: Money as a Decimal Amount

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