Curriculum  /  Math  /  4th Grade  /  Unit 6: Decimal Fractions  /  Lesson 1

Decimal Fractions

Lesson 1

Math

Unit 6

4th Grade

Lesson 1 of 13

Objective

Represent decimals to tenths less than or equal to one with area models. Write a decimal value in fraction, decimal, and unit 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

  • 3.NF.A.2

Criteria for Success

  1. Look for and make use of structure to understand the importance of the unit tenths as an extension of the place value system to represent values smaller than one (MP.7).
  2. Understand a decimal fraction to be a fraction whose denominator is 10 (or, as explored in later lessons, another power of ten like 100).
  3. Understand a decimal number to be a way of writing a decimal fraction using a decimal point followed by digit(s) which represent the fractional part of a decimal fraction. 
  4. Understand that a decimal point helps to delineate between the whole number and fractional parts of a decimal number when writing a number in decimal form. 
  5. Represent decimals to tenths less than one in decimal, fraction, or unit form as well as with an area model (MP.5).
  6. Understand that 1 one can be regrouped as 10 tenths, and flexibly write 1 in fraction and unit form based on that understanding. 

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. For example “0.4” is read “four tenths” rather than “zero point four” or “point four”. 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 (10 ones, 10 tens, 10 hundreds, and 1 thousand per student or small group) — You could just use one set for the teacher if materials are limited
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Anchor Tasks

25-30 minutes

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. 

b.   Imagine the following model is a zoomed-in ones cube. 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 Parts (a) and (b) to write a similar sentence that starts “1 one is the same as…” 

Guiding Questions

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Student Response

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Problem 2

The shaded part of this diagram represents 1 tenth. We can write this as the fraction $$\frac{1}{10}$$ or as the decimal 0.1. 

Fill out the following table to represent each given number.

Diagram

Unit Form

Fraction Form

Decimal Form

2 tenths    

  $$\frac{3}{10}$$  

     

    0.8

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • What relationship does 1 tenth have to 1? 
  • How did your work with decimal fractions like $${{3\over10}}$$, $${{7\over10}}$$, or $${{9\over10}}$$ prepare you for this lesson?
  • Today, we studied decimal numbers and we wrote them in fraction form and decimal form. How are the two forms alike? How are they different?
  • What purpose does a decimal point serve?

Target Task

5-10 minutes

Problem 1

Match each value written in unit form with its equivalent value written in fraction form and decimal form. 

Student Response

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Problem 2

Draw an area model to match each decimal below.

a.   0.9

b.   0.2

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

Lesson 2
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Lesson Map

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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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