Decimal Fractions

Lesson 3

Math

Unit 6

4th Grade

Lesson 3 of 13

Objective


Represent decimals to hundredths less than one, understanding the equivalence of some number of tenths and ten times as many hundredths. Write a decimal value in fraction, decimal, and unit form.

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.
  • 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

  • 3.NF.A.2
  • 4.NF.A.1

Criteria for Success


  1. Understand hundredths as a further extension of the place value system to represent values that are 1 tenth of 1 tenth (or 1 hundredth of 1) (MP.7)
  2. Explain why some number of tenths is equivalent to ten times as many hundredths, using a visual model or multiplication/division to demonstrate this understanding (MP.3).
  3. Represent decimals to hundredths less than one written in decimal, fraction, or unit form as well as with area models (MP.5).

Tips for Teachers


  • There are many ways to read decimals aloud, but to help ensure students have a strong concept of the value of decimals, try to use place value language to read them for now. Further, for the sake of avoiding confusion, we recommend only using the word “and” in place of the decimal point and nowhere else. For example, “2.35” is read “two and thirty-five hundredths” rather than “two point three five”. As time goes on, you can read them as “zero point _” or “point _”, as many mathematicians and scientists do. This will be especially helpful later in the unit, since “[d]ecimals with many non-zero digits are more easily read aloud in this manner. (For example, the number π, which has infinitely many non-zero digits, begins 3.1415…)” (NBT Progression, p. 14).

Lesson Materials

  • Base ten blocks
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Anchor Tasks


Problem 1

a.   Fill in the following blanks to make true statements. Use base ten blocks to help you.

  1. 1 thousand is the same as _______ hundreds. 
  2. 1 hundred is the same as _______ tens. 
  3. 1 ten is the same as _______ ones. 
  4. 1 one is the same as _______ tenths. 

b.   Below is an area model that represents 1 one. It is partitioned into tenths. Partition it to show what you would expect the next smallest unit to look like so that it continues the pattern in Part (a).

c.   Use what you notice in Part (a) and (b) to write a similar sentence that starts “1 tenth is the same as…” 

Guiding Questions

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Problem 2

The shaded part of this diagram represents 1 hundredth. We can write this as the fraction $$\frac{1}{100}$$ or as the decimal 0.01. 

Fill out the following table to represent each given number. 

Diagram Unit Form Fraction Form Decimal Form

7 hundredths    

  $$\frac{32}{100}$$  

    0.85

     

Guiding Questions

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Problem 3

a.   Explain why $${{1\over10}={10\over100}}$$. Draw a picture to illustrate your explanation.

b.   Explain why $${0.20 = 0.2}$$. Draw a picture to illustrate your explanation.

Guiding Questions

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References

Illustrative Mathematics Fraction Equivalence

Fraction Equivalence, accessed on May 29, 2018, 11:07 a.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

Jani and Kai are representing a decimal number. Here are the area models they drew:

Jani Kai

a.   What value do you think Jani and Kai are trying to model? How do you know?

b.   Draw pictures to show what Kai might have drawn for each area model in Anchor Task 2.

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • What decimal was modeled in #1d? How do you know? How was this area model different from the previous ones? 
  • How did the models in #2 show that 0.3 = 0.30?
  • What are two ways you could have modeled $${{6\over10}}$$ in #3a?
  • Compare the answers to #4d and #4f. Did you write the same equivalent numbers? Why are there several possibilities for answers in these two problems? Where have we seen that before? 

Target Task


Problem 1

a.   Model 53 hundredths on the area model below.

b.   What is 53 hundredths written as a decimal?

Student Response

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Problem 2

Damien says 0.78 is equivalent to 78 hundredths. Kelly says 0.78 is equivalent to 7 tenths and 8 hundredths. Who is right? Explain how you know.

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

Answer Keys

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Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

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Lesson 2

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Lesson 4

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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