Decimal Fractions

Lesson 9

Math

Unit 6

4th Grade

Lesson 9 of 13

Objective


Add tenths with hundredths written as decimal fractions. 

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. Express a fraction with denominator 10 as an equivalent fraction with denominator 100 using visual models and multiplication. 
  2. Add decimal fractions in cases of adding tenths with tenths, hundredths with hundredths, and tenths with hundredths by using visual models or fraction addition strategies, including simplifying strategies like making one. 
  3. Write the sum of fraction addition in cases listed above as a decimal. 

Tips for Teachers


  • In this lesson, students find the sum of decimal fractions and are asked to write the sum in both fraction and decimal form. While students are asked to find the sum of decimal fractions, as well as to use decimal notation for fractions with denominators 10 and 100, the Common Core State Standards do not explicitly ask students to use both skills in a single task. Thus, you may just have students write their solutions as fractions. Be sure to change the Anchor Tasks, Problem Set, Target Task, and Homework if so. 
  • Lessons 9 and 10 each have four Anchor Tasks, but there are many options for consolidating their length. Anchor Task 4 in each lesson is optional, so you could eliminate those to save time. Or, Lesson 10 as a whole is optional, since students adding decimals to hundredths written in decimal form is not an explicit expectation of the grade level, so the entire lesson could be eliminated to save time.
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Anchor Tasks


Problem 1

A gardener plants $${{3\over10}}$$ of their garden with tomatoes. They also plant $${{4\over100}}$$ of their garden with chives. How much of their garden is planted with either tomatoes or chives? Write your answer as a fraction and decimal. 

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic D > Lesson 12Concept Development

Grade 4 Mathematics > Module 6 > Topic D > Lesson 12 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 2

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

a.   $${{6\over100} + {8\over10}}$$

b.   $${{2\over10} + {14\over100}}$$

c.   $$\frac{9}{10}+\frac{10}{100}$$

d.   $$\frac{9}{10}+\frac{23}{100}$$

e.   $$1\frac{4}{10}+2\frac{72}{100}$$

Guiding Questions

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References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic D > Lesson 12Concept Development

Grade 4 Mathematics > Module 6 > Topic D > Lesson 12 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 fraction in tenths or hundredths. Find the fraction that makes each equation true. 

a.   $$\frac{20}{100}$$ + ____ = $$\frac{28}{100}$$

b.   $$\frac{10}{100}$$ + ____ = $$\frac{30}{100}$$

c.   ____ + $$\frac{2}{10}$$ = $$\frac{80}{100}$$

d.   $$\frac{9}{100}$$ + ____ = $$\frac{8}{10}$$

e.   ____ + $$\frac{72}{100}$$ = $$\frac{102}{100}$$

f.   $$\frac{15}{100}$$ + ____ = $$1\frac{55}{100}$$

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 0 to 9, no more than one time each, to fill in the boxes to create a sum of $$1\frac{1}{10}$$.

Guiding Questions

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References

Open Middle Decomposing Tenths and Hundredths

Decomposing Tenths and Hundredths by is made available on Open Middle under the CC BY-NC-SA 4.0 license. Accessed May 30, 2018, 4:54 p.m..

Modified by Fishtank Learning, Inc.

Problem Set


Answer Keys

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Discussion of Problem Set

  • In #3(d), what do you notice about your answer? Can the answer be written using a unit other than hundredths? Does that apply to any solutions in #5? 
  • How can the model be used to solve $${{4\over10}+{50\over100}}$$ in #4? Is there another way you could use the models to solve if Part A wasn’t included in the problem? 
  • How did you solve #5d? Did anyone add the addends out of order? Why is it possible to do that? Why is it advantageous to? 
  • Did anyone solve #6? How? 

Target Task


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

a.   $${{2\over10} + {7\over100}}$$

b.   $${{63\over100} + {5\over10}}$$

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 8

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Lesson 10

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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