# Decimal Fractions

## Objective

Add tenths with hundredths written as decimals.

## Common Core Standards

### Core Standards

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• 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.

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• 4.NF.A.1

• 4.NF.B.3

## Criteria for Success

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1. Convert a decimal addition problem to 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 converting decimals to fractions and using fraction addition strategies from Lesson 10.
3. Convert the sum of fraction addition in cases listed above to a decimal.

## Tips for Teachers

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• 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, converting between fraction and decimal form (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.
• As a supplement to the Problem Set, students can play the game Make Two by the San Francisco Unified School District Mathematics Department. The hundreds grids for the game can be found here. There are two versions of game cards that students could use, which can be found here and here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

1. Solve.

a.  ${{3\over10} + {57\over100}}$

b.  0.3 + 0.57

2. What do you notice about #1? What do you wonder?

### Problem 2

a.  0.4 + 0.5

b.  0.29 + 0.8

c.  1.52 + 0.39

d.  3.5 + 2.87

#### 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 The Match Foundation, Inc.

## Discussion of Problem Set

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• What other conversion could you have used for #2a and #2c?
• 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 6 and Lesson 12 help to make this task easier?

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1.  0.3 + 0.95

2.  8.29 + 5.9

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic D > Lesson 13Exit Ticket, Questions #1 and #2

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 The Match Foundation, Inc.

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