# Fractions

## Objective

Understand two fractions as equivalent if they are the same sized pieces of the same sized wholes, though not necessarily the same shape. 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 sized piece of the same whole, though not necessarily the same shape.
2. Generate simple equivalent fractions with the use of an area model (MP.5).
3. Explain the equivalence of fractions using a number line or other method (MP.3, MP.5).

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## Anchor Tasks

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### Problem 1

Mrs. Allen and Ms. Roll each got the same kind of chocolate bar at the grocery store. Mrs. Allen broke her chocolate bar into three equal-sized pieces and ate one of those pieces. Ms. Roll broke her chocolate bar into six equal-sized pieces and ate two of those pieces. Who ate more chocolate, Mrs. Allen or Ms. Roll? Use the models below to support your reasoning.

#### Guiding Questions

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### Problem 2

Jessie drew the following area model to represent a fraction.

Which of the following fractions are equivalent to the one represented above?

A.  $\frac{8}{6}$

B.  $\frac{3}{4}$

C.  $\frac{12}{16}$

D.  $\frac{9}{12}$

E.  $\frac{6}{9}$

#### Guiding Questions

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## Problem Set & Homework

#### Discussion of Problem Set

• In #1, which shapes were most difficult to match? Why?
• Look at #2. What pattern do you notice between the three sets of models? How does this pattern relate to other parts of today’s lesson?
• How did you determine the other models that were equivalent to Figure Y? Which one was the most difficult to figure out? Why?
• In #8, how do you know the way you shaded Figure B was equivalent to the way you shaded Figure C?

## Target Task

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### Problem 1

Shade the model below to create a fraction that is equivalent to $\frac{4}{8}$.

### Problem 2

Explain how you know the model above represents a fraction that is equivalent to $\frac{4}{8}$.

### Mastery Response

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