Decimal Fractions

Lesson 4

Math

Unit 6

4th Grade

Lesson 4 of 13

Objective


Represent decimals to hundredths more than one. Write a decimal value in fraction, decimal, unit, and decimal and fraction expanded form for some number to hundredths.

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

  • 4.NBT.A.2
  • 3.NF.A.2
  • 4.NF.A.1

Criteria for Success


  1. Write a decimal value in 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 pictorial base ten blocks to help (MP.7). 
  3. Understand that place value is symmetric about the ones place, as opposed to the decimal point.

Tips for Teachers


  • As mentioned in Lesson 3, 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, 217.35 is read “two hundred seventeen and thirty-five hundredths,” not “two hundred and seventeen and thirty-five hundredths” or “two hundred and seventeen and thirty-five hundredths”. 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).
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Anchor Tasks

25-30 minutes


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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Student Response

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Problem 2

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

  1. 1.57
  2. 5.03
  3. 98.30
  4. 623.46

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

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

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

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Discussion of Problem Set

  • How do the base ten blocks in #1 help to show the value of each digit?
  • In #2f, express this number in ones and tenths. Is this equivalent to 7 ones 70 hundredths? How do you know? 
  • In #3, how did you determine the value of each digit? Did anyone draw base ten blocks to help? 
  • Why is there one more item in the center column of #4 than in the other columns? 
  • 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? 
  • 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

5-10 minutes


Problem 1

Use the number below to answer the following questions.

268.39

a.   What digit is in the hundreds place? What is its value? 

b.   What digit is in the tens place? What is its value? 

c.   What digit is in the ones place? What is its value? 

d.   What digit is in the tenths place? What is its value? 

e.   What digit is in the hundredths place? What is its value? 

Student Response

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Problem 2

Complete the following chart.

Fraction form Fraction expanded form Decimal expanded form Decimal form
$$21\frac{9}{100}$$      
      50.48

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.

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.

Next

Regroup decimal numbers with more than 9 tenths or 9 hundredths into simplest unit form and vice versa.

Lesson 5
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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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