# Fractions

## Objective

Explain equivalence by manipulating units and reasoning about their size.

## 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.

• 3.NF.A.3.C — Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Example: express 3 in the form 3 = 3/1; recognize that 6/1 = 6. Example: locate 4/4 and 1 at the same point of a number line diagram.

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• 2.MD.A.2

## Criteria for Success

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1. Understand that since equivalent fractions represent the same-sized part of the same-sized whole, the whole that is partitioned into more pieces must have more relevant pieces that constitute its equivalent fraction (MP.7, MP.8). Begin to see this relationship as a multiplicative one (although this explicit understanding is not required until Grade 4).
2. Generate simple equivalent fractions in all cases, including those with whole numbers.
3. Explain the equivalence of fractions in all cases, including those with whole numbers, using an area model, number line, or other method (MP.3, MP.5).

## Tips for Teachers

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This lesson previews the work of Grade 4 of developing an algorithm for finding equivalent fractions, but it also recaps every case of equivalent fractions students have seen thus far in the unit. Therefore, this lesson is optional though highly encouraged since it serves to summarize their work thus far as well as connect to future work on the topic.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

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1. Partition the following area model into thirds. Then write a fraction to represent the whole. 1. Partition the following area model into sixths. Then write a fraction to represent the whole. 1. Partition the following area model into ninths. Then write a fraction to represent the whole. 2. What do you notice about the number of parts and the size of each part in each model in #1? What do you wonder?

### Problem 2

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1. Partition the following number line into wholes. Label each tick mark with a fraction. 1. Partition the following number line into halves. Label each tick mark with a fraction. 1. Partition the following number line into fourths. Label each tick mark with a fraction. 1. Partition the following number line into eighths. Label each tick mark with a fraction. 2. What do you notice about the number of parts and the size of each part in each model in #1? What do you wonder?

## Problem Set & Homework

#### Discussion of Problem Set

• How did you use the patterns we noticed in the Anchor Tasks to solve #1 without needing to draw a model for every fraction?
• What happened to the size of the equal parts in #2a? What happened to the number of equal parts in #2a? How are those related?
• How did you share the chocolate bars equally? What fraction of a chocolate bar did each friend get? What fraction of all the chocolate bars collectively did each friend get? How do these questions demonstrate the importance of specifying the whole?
• Describe the approach you took to solving #5. Is there more than one correct answer?

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### Problem 1

Which fractions are equivalent to a whole number? Select the two correct answers.

A.  $\frac{4}{4}$

B.  $\frac{5}{4}$

C.  $\frac{3}{2}$

D.  $\frac{1}{2}$

E.  $\frac{3}{1}$

#### References

PARCC Released Items Math Spring 2018 Grade 3 Released ItemsQuestion #34

$\frac{3}{2}=\frac{\square}{6}$