# Fractions

## Objective

Place various fractions on a number line where the given interval is not a whole.

## Common Core Standards

### Core Standards

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• 3.NF.A.2 — Understand a fraction as a number on the number line; represent fractions on a number line diagram.

• 3.NF.A.3.D — Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

## Criteria for Success

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1. Given a unit fraction on a number line, plot the whole by making a certain number of copies of the unit fraction adjacent to one another (e.g., to create the whole given $\frac{1}{5}$, make copies of the unit fraction so that there are 5 equal pieces adjacent to one another).
2. Given a non-unit fraction on a number line, construct the whole by partitioning the given fraction into the appropriate number of equal pieces so that they represent the unit fraction, and then add copies of the unit fraction so that they make a whole (e.g., to create the whole given $\frac{3}{5}$, partition the given interval into 3 equal pieces so that they each represent $\frac{1}{5}$, then make copies of that unit fraction so that there are 5 equal intervals adjacent to one another).
3. Given a fraction greater than 1 on a number line, construct the whole by partitioning the given fraction into the appropriate number of equal pieces so that they represent the unit fraction, and then count the number of unit fractions that make a whole (e.g., to create the whole given $\frac{5}{3}$, partition the given interval into 5 equal pieces so that they each represent $\frac{1}{3}$, then plot a point at $\frac{3}{3}$ by counting up 3 intervals).
4. Given a fraction on a number line, plot another fraction of the same whole by using any of the strategies above to find the whole, then partition the whole into the relevant fractional pieces (e.g., to plot $\frac{2}{3}$ given $\frac{3}{4}$, partition the interval into three equal pieces, then make a fourth copy of it to construct a whole; then partition that whole into thirds and plot a point at $\frac{2}{3}$ by counting up 2 intervals).

## Tips for Teachers

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This lesson provides many opportunities for students make sense of problems and persevere in solving them (MP.1). Each task pushes students to make sense of the meaning of fractions and their numerators and denominators and use that understanding to relate them to the whole as well as other fractions of the same whole.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Some portion of a candy bar was eaten. There is now $\frac{3}{4}$ of the candy bar left. What did the whole candy bar look like if $\frac{3}{4}$ looks like this?

### Problem 2

Locate 1 on the number line. Label the point. Be as exact as possible.

#### References

Illustrative Mathematics Find 1Part b

Find 1, accessed on March 19, 2019, 9:45 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

### Problem 3

Locate $\frac{5}{6}$ on the number line. Label the point. Be as exact as possible.

#### References

Illustrative Mathematics Find 2/3

Find 2/3, accessed on March 25, 2019, 12:08 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

## Problem Set & Homework

#### Discussion of Problem Set

• Look at #1. How can you tell just by looking at the numerator and denominator that $\frac{3}{2}$ would be to the right of 1?
• Look at #4. Did anyone solve it without locating where 1 was? How did you know to do that?
• Look at #6. What number corresponds with the point Anna mislabeled?
• Look at #3 and #7. What do you notice about these number lines? What do you wonder?
• How did you decide to create 5 fractions in #8? How did you know how to place fractions in relation to one another on the number line? Where would you place a fraction with 1 as the denominator, such as $\frac{5}{1}$? Where would you place the fraction $\frac{4}{2}$ on the number line? Why?

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### Problem 1

The number line below shows two numbers, 0 and $\frac{6}{5}$.

Where is 1 on this number line?

#### References

Illustrative Mathematics Find 1

Find 1, accessed on March 19, 2019, 9:45 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by The Match Foundation, Inc.

### Problem 2

The number line below shows two numbers, 0 and $\frac{1}{3}.$

Where is $\frac{3}{4}$ on this number line?

#### References

Open Middle Identify a Fraction on a Number Line

Identify a Fraction on a Number Line by is made available on Open Middle under the CC BY-NC-SA 4.0 license. Accessed March 19, 2019, 11 a.m..

Modified by The Match Foundation, Inc.

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