Decimal Fractions

Lesson 5

Objective

Represent decimals to hundredths more than one. Convert between fraction, decimal, unit, and fraction and decimal expanded form.

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.

  • 4.NF.C.6 — Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Foundational Standards

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  • 4.NBT.A.2

  • 3.NF.A.2

  • 4.NF.A.1

Criteria for Success

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  1. Convert between fraction form, decimal form, unit form, and decimal and fraction expanded form for some number to hundredths.
  2. Understand the value of each digit in a multi-digit decimal to hundredths, using a place value chart to help (MP.7). 
  3. Understand that place value is symmetric about the ones place, as opposed to the decimal point.

Tips for Teachers

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When saying a number in word form, make sure to only use the word “and” in place of the decimal place and nowhere else. For example, 217.35 is read “two hundred seventeen and thirty-five hundredths,” not “two hundred and seventeen and thirty-five hundredths.” Also recall from Lesson 4 that “there are several ways to read decimals aloud, but even though ‘mathematicians and scientists often read 0.15 aloud as “zero point one five” or “point one five”,’ refrain from using this language until you are sure students have a strong sense of place value with decimals” (NF Progression, p. 15).

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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  • Student Handout Editor
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Anchor Tasks

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Problem 1

Complete the following table. Draw models for each row if they will help you.

Unit Form Fraction Form Fraction Expanded Form Decimal Expanded Form Decimal Form
     

$$1\times1+5\times0.1+7\times0.01$$

 
   

$$(5\times 1)+\left(0 \times \frac{1}{10} \right) + \left(3\times\frac{1}{100}\right)$$

   
       

$$98.30$$

 

$$623 \frac{46}{100}$$

     

Guiding Questions

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References

Open Up Resources Photo: Grade 6 Unit 5 Lesson 2 Teacher Version

Grade 6 Unit 5 Lesson 2 Teacher Version is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed June 1, 2018, 2:08 p.m..

Modified by The Match Foundation, Inc.

Problem 2

Use the following numbers to answer each of the following questions: 

a. 1.57

b. 5.03

c. 98.30

d. 623.46

1. What is the value of the digit 1 in (a)? The digit 5?

2. What is the value of the digit 3 in (b), (c), and (d) above? How are those values related to one another? 

3. What is the value of the digit in the hundreds place in (c)? What is the value of the digit in the hundredths place in (c)? How are these similar? How are they different? 

Guiding Questions

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References

Institute for Mathematics and Education Progressions for the Common Core State Standards in Mathematics (Numbers and Operations - Fractions, 3-5)Image from p. 14

Progressions for the Common Core State Standards in Mathematics (Numbers and Operations - Fractions, 3-5), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed April 16, 2018, 11:23 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Problem Set & Homework

Discussion of Problem Set

  • In #1a, how did you estimate the location of your point? 
  • In #2f, express this number in ones and tenths. Is this equivalent to 7 ones 70 hundredths? How do you know? 
  • Why is there one more item in the center column of #3 than in the other columns? 
  • How do the place value disks in #4 help to show the value of each digit? How did the unit language help you to write the total value of the number disks?
  • In #5, how did you determine the value of each digit? Did anyone use a place value chart to help? 
  • In #6, we can write the expanded notation of a number in different ways. What is similar about each of the ways? What is different?
  • Ten is found in the word “tenths,” and hundred is found in the word “hundredths.” We say that these place values are symmetric. What are they symmetric around? How can we see that in the place value chart? 
  • Why is the number zero important? What role does it play in the number 100? The number 0.01? Based on that understanding, is 7 the same as 7.0? Why or why not?

Target Task

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Problem 1

Fill in the blanks below to make each statement true about the number below. 

827.64

a. The digit _____ is in the hundreds place. It has a value of ________.

b. The digit _____ is in the tens place. It has a value of ________.

c. The digit _____ is in the tenths place. It has a value of ________.

d. The digit _____ is in the hundredths place. It has a value of ________.

References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic B > Lesson 7Exit Ticket, Question #1

Grade 4 Mathematics > Module 6 > Topic B > Lesson 7 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

Complete the following chart.

References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic B > Lesson 7Exit Ticket, Question #2

Grade 4 Mathematics > Module 6 > Topic B > Lesson 7 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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