Decimal Fractions

Lesson 10

Objective

Add tenths with hundredths written as decimal fractions.

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.

Foundational Standards

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  • 4.NF.A.1

  • 4.NF.B.3

Criteria for Success

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

Tips for Teachers

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In Lesson 10, 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 convert tenths and hundredths to decimals, 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. 

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Tasks

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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 The Match Foundation, 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 The Match Foundation, Inc.

Problem Set & Homework

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? 
  • Did anyone solve #7? Is there more than one correct answer? 

Target Task

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

1.  $${{1\over10} + {9\over100}}$$

2.  $${{73\over100} + {4\over10}}$$

References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic D > Lesson 12Exit Ticket, Question #1

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 The Match Foundation, Inc.

References

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