# Decimal Fractions

## Objective

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

## 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.

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• 4.NBT.A.2

• 4.NF.A.1

## Criteria for Success

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1. Regroup 10 units into 1 of the next largest unit with numbers to hundredths.
2. Regroup 1 unit into 10 of the next smallest unit with numbers to hundredths.
3. Convert between nontraditional unit form (i.e., unit form with more than 9 of any kind of unit) and standard form.

## Tips for Teachers

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Students have dealt with regrouping decimal units in limited cases in previous lessons, e.g., 6 tenths = 60 hundredths. Today’s lesson extends that work to regrouping to various units, include ones that are not adjacent to the given unit. This serves a few purposes: (1) it helps to reinforce the 10-to-1 relationship in decimal numbers, (2) it helps students understand the value of a zero at the end of a decimal (e.g., 0.6 = 0.60), and (3) it prepares students for addition and subtraction of decimals, where students may need to convert a value in one unit to another unit in order to be able to add or subtract like units.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Tasks 2 and 3 (benefit from worked examples). You could consolidate these to be a single Anchor Task. Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

A dime is ${{1\over10}}$ of a dollar and a penny is ${{1\over100}}$ of a dollar.

Would you rather have 4 one-dollar bills and 1 dime, 42 dimes, or 413 pennies? Justify your answer.

### Problem 2

a.  Regroup each of the following values in terms of tenths. Then do the same in terms of hundredths.

i.  ${2{4\over10}}$ = ____ tenths = ____ hundredths

ii.  3 ones 5 tenths 7 hundredths = ____ tenths ____ hundredths = ____ hundredths

b.  How would you write each of the values in part (a) as decimals?

### Problem 3

a.  Fill in the blanks to make the following true.

i.  170 hundredths = _____ tenths _____ hundredths = _____ ones _____ tenths _____ hundredths

ii.  ${{407\over100}}$ = _____ tenths _____ hundredths = _____ ones _____ tenths _____ hundredths

b.  How would you write each of the values in part (a) as decimals?

## Problem Set & Homework

#### Discussion of Problem Set

• What strategies did you use when completing the number sentences in #7?
• How is decomposing hundreds to tens or tens to ones similar to decomposing ones to tenths or tenths to hundredths?

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1. Fill in the blanks below to make the following statements true.
1. 3 ones 2 tenths = ________ tenths = ________ hundredths
2. 4 ones 3 tenths 8 hundredths = ________ tenths ________ hundredths = ________ hundredths
3. 260 hundredths = ________ tenths = ________ ones ________ tenths
4. 601 hundredths = ________ tenths ________ hundredths = ________ ones ________ tenths ________ hundredths
2. Write each of the values in #1 above in decimal form below.
1.
2.
3.
4.

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic B > Lesson 8Exit Ticket, Question #1

Grade 4 Mathematics > Module 6 > Topic B > Lesson 8 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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