# Fractions

## Objective

Compare and order fractions using various methods.

## Common Core Standards

### Core Standards

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• 3.NF.A.3 — Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

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• 2.MD.A.2

## Criteria for Success

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1. Compare fractions in all cases by reasoning about their size and/or distance from 0 on the number line (MP.2, MP.5).
2. Order a set of fractions using various strategies by comparing two fractions in the set at a time.
3. Record the results of comparisons with the symbols >, =, or <.
4. Justify comparisons of fractions using an area model or number line or by reasoning about the size of the fractional pieces or the number of fractional pieces (MP.3, MP.5).

## Tips for Teachers

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Choose either fraction cards with pictures or fraction cards without pictures for this lesson (see Note in Anchor Task 1).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Play the following game with a partner using a set of cards (either with pictures or without, see lesson materials). The goal is to compare the two fractions appearing on each card, determining if they are equivalent and, if not, which is larger. Instructions for the activity are as follows:

1. Go through the following steps with the fraction cards:
1. Select a card.
2. Individually decide whether the fractions are equal and, if not, which is greater. Then show each other your choices.
3. If you both agree, take turns explaining your reasoning. If you disagree, discuss until you reach a consensus.
4. Repeat 1 through 3 with a new card.
2. After 10 rounds, record observations about what methods you used to compare the fractions.

#### References

Illustrative Mathematics Comparing Fractions Game

Comparing Fractions Game, accessed on March 19, 2019, 11:35 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

1. Place the following fractions on the number line.

$\frac{2}{4},\ \frac{4}{4},\ \frac{1}{4},\ \frac{2}{2},\ \frac{1}{2},\ \frac{4}{2},\ \frac{4}{1}$

1.     Compare each of the following pairs of fractions. Record your answer with <, >, or =.

i.  $\frac{1}{4}$ and $\frac{1}{2}$

ii.  $\frac{2}{4}$ and $\frac{4}{4}$

iii.  $\frac{4}{2}$ and $2$

iv.  $\frac{2}{4}$ and $\frac{4}{2}$

1. Order the fractions in Part (a) from least to greatest.

### Problem 3

Which is closer to 1 on the number line, $\frac{4}{5}$ or $\frac{5}{4}$? Explain.

#### References

Illustrative Mathematics Which is Closer to 1?

Which is Closer to 1?, accessed on March 19, 2019, 11:36 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 Set & Homework

#### Discussion of Problem Set

• How did you compare the fractions in each part of #2?
• Which fractions were the least and greatest in #3? How could you tell just by looking at their location on the number line?
• You were not given the fractions that represented each point on the number line in #5. Did you need to write them to be able to determine who has the shortest time? Why or why not?
• How did you approach #6? What fraction did you come up with?
• What did you choose in #7, Part B? How do you know that is correct?
• Which statement of Landon’s was incorrect? How did you correct it?

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### Problem 1

a.  $\frac{3}{8},\frac{3}{3},\frac{3}{4}$

b.  $\frac{4}{6},\frac{2}{6},\frac{7}{6}$

### Problem 2

Two fractions have different numerators and denominators. Is it possible for the two fractions to be located at the same point on the number line? Why or why not?

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