Curriculum  /  Math  /  4th Grade  /  Unit 6: Decimal Fractions  /  Lesson 2

Decimal Fractions

Lesson 2

Math

Unit 6

4th Grade

Lesson 2 of 13

Objective

Represent decimals to tenths greater than one with pictorial base ten blocks. Write a decimal value in fraction, decimal, unit, and fraction and decimal expanded form.

Common Core Standards

Core Standards

  • 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

Criteria for Success

  1. Understand that fraction expanded form is a decimal fraction written as a sum of base ten decimal fractions (e.g., $$(1 \times 10) + (5 \times 1) + \left (8 \times \frac{1}{10} \right )$$).
  2. Understand that decimal expanded form is a decimal number written as a sum of base ten decimal numbers (e.g., $$(1 \times 10) + (5 \times 1) + (8 \times 0.1)$$).
  3. Represent decimals to tenths greater than one in decimal, fraction, unit, or decimal or fraction expanded form as well as with pictorial base ten blocks (MP.5).
  4. Understand that 1 one can be regrouped as 10 tenths, and flexibly write numbers greater than one in fraction and unit form based on that understanding.

Tips for Teachers

  • Some resources find that expanded form seems more aligned to 5.NBT.1, given that’s the first place it is explicitly mentioned in the Common Core State Standards in relation to decimals. However, given that expanded form deepens students’ understanding of the value of each digit in a decimal and there are reliable sources such as this Illustrative Mathematics task that include it in Grade 4, it has been included throughout this unit. However, it is at your discretion to cut it.
  • For the sake of avoiding confusion, we recommend only using the word “and” in place of the decimal point and nowhere else. For example, 217.5 is read “two hundred seventeen and five tenths,” not “two hundred and seventeen and five tenths.”
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Anchor Tasks

25-30 minutes

Problem 1

Below are representations for a ten, a one, and a tenth.

Based on the base ten block diagrams below, fill in the table with the value of each diagram (a)-(c).

a.

b.

c.

 

Diagram Decimal Form Fraction Form Fraction Expanded Form Decimal Expanded Form
a        
b        
c        

Guiding Questions

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Student Response

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Problem 2

Danny writes a value in decimal, fraction, and unit form below:

Decimal Form Fraction Form Unit Form
3.9 $$\frac{39}{10}$$ 39 tenths

Are these values equivalent? Why or why not? Use a picture to support your reasoning.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #1. For the third row in the chart, I wrote the decimal 3.4. Do you agree or disagree with my answer? Why?
  • Look at #2b. How did you represent this number with pictorial base ten blocks?
  • In #2c and #2d, we have the same number of tens as tenths. Explain to your partner the difference in value between the tens place and the tenths place. Notice that the ones are sandwiched between the tens and tenths. 

Target Task

5-10 minutes

Complete the chart.

Decimal Form Fraction Form Fraction Expanded Form Decimal Expanded Form
  $$2\frac{9}{10}$$    
$${40.6}$$      

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

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.

Lesson 3
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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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