# Decimal Fractions

## Objective

Represent decimals to tenths greater than ten with pictorial base ten blocks. Convert between fraction, decimal, unit, and fraction and decimal expanded form.

## Common Core Standards

### Core Standards

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• 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

• 3.NF.A.2

## Criteria for Success

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

## Tips for Teachers

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When saying a number in word form, make sure to only use the word “and” in place of the decimal place and nowhere else. For example, 217.5 is read “two hundred seventeen and five tenths,” not “two hundred and seventeen and five tenths.”

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### 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

#### References

Open Up Resources Photo: Grade 6 Unit 5 Lesson 2 Teacher Version

Modified by The Match Foundation, Inc.

### Problem 2

Draw a different base ten diagram to represent 15.8 from Anchor Task #1, Part (a). Explain why both diagrams represent the same value.

## Discussion of Problem Set

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• Look at #2b. Today, we showed mixed numbers in decimal expanded form and fraction expanded form. How did you represent this number with pictorial base ten blocks?
• Look at the first row in #1. How would you represent this number using only tenths? With your partner, use the number line or centimeter ruler to prove that 39 tenths is the same as 3 ones and 9 tenths.
• 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.
• How did you locate points on the number line?

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Complete the chart.

 Decimal Form Fraction Form Fraction Expanded Form Decimal Expanded Form 1. ${12{9\over10}}$ 2. ${70.7}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic A > Lesson 3Exit Ticket, Question #2

Grade 4 Mathematics > Module 6 > Topic A > Lesson 3 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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