# Fractions

## Objective

Understand two fractions as equivalent if they are the same point on a number line referring to the same whole. Use this understanding to generate simple equivalent fractions.

## Common Core Standards

### Core Standards

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• 3.NF.A.3.A — Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

• 3.NF.A.3.B — Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

## Criteria for Success

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1. Understand that equivalent fractions are fractions that are equal, i.e., they represent the same point on the number line.
2. Generate simple equivalent fractions with the use of a number line (MP.5).
3. Recognize that comparisons (which include the possibility of equivalence) are valid only when the two fractions refer to the same whole, which in the case of a number line, is the same length unit interval (MP.6).
4. Explain the equivalence of fractions using an area model or other method (MP.3, MP.5).

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Ebony and Shaun both have the same length string. Ebony cuts her string into three equal-length pieces to make necklaces, and Shaun cuts his string into six equal-length pieces to make bracelets. Ebony uses two of her pieces of string and Shaun uses four of his pieces of string. Who used more string, Ebony or Shaun? Draw a picture to support your reasoning.

### Problem 2

1. Place the following fractions on the number line below.

a.  $\frac{2}{4}$

b.  $\frac{1}{2}$

1. Are these fractions equivalent? How do you know?
2. Find another fraction that is equivalent to the fraction in Part (b).

### Problem 3

Scott drew this picture:

Then he said

This shows that $\frac{\mathbf{1}}{\mathbf{4}}$ is equal to .$\frac{\mathbf{4}}{\mathbf{8}}$.

1. What was his mistake?
2. Replace either fraction with a different fraction so that they are equivalent to one another. Then draw a number line to support your answer.

#### References

Illustrative Mathematics Comparing Fractions with a Different Whole

Comparing Fractions with a Different Whole, accessed on March 28, 2018, 1:21 p.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

• In #2c, did anyone list $\frac{3}{6}$? How do you know that is equivalent to 1 half even though the second number line was not partitioned into halves?
• How did you complete the number sentence for #3? Can you write a non-fractional number that is equivalent to all of these fractions? How do you know it is equivalent?
• What fractions did you write for #4b? What are all of the possibilities?
• What fractions did you write for #4d? How do you know those fractions are equivalent to 1 whole?
• What is another fraction that is equivalent to the fractions in #7 and #8? How do you know it is equivalent?

Find a fraction that is equivalent to $\frac{2}{4}$. Show or explain how you know they are equivalent using a number line.