# Fractions

## Objective

Partition a whole into equal parts, identifying and counting unit fractions using pictorial area models and tape diagrams, identifying the unit fraction numerically.

## Common Core Standards

### Core Standards

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• 3.G.A.2 — Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

• 3.NF.A.1 — Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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• 2.G.A.3

## Criteria for Success

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1. Understand a unit fraction to be a fraction that refers to just one equal part.
2. Write a unit fraction using unit form and fraction notation (e.g., “1 fourth” and “$\frac{1}{4}$", respectively).
3. Partition a pictorial area or length model to represent a unit fraction (MP.5).
4. Explain whether or not a pictorial area or length model represents a particular unit fraction or not (MP.3).
5. Determine the unit fraction represented by an abstract description of a situation (MP.2).
6. Count unit fractions up to a whole.

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### Problem 1

Each shape below represents one whole. What fraction of each shape is shaded?

1.

1.

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1.

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#### Guiding Questions

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### Problem 2

Make a model in which the shaded part represents the corresponding unit fraction.

 a. $\frac{1}{3}$ b. $\frac{1}{2}$ c. $\frac{1}{6}$

#### Guiding Questions

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### Problem 3

Kai says that each part of the shape below represents $\frac{1}{2}$. Do you agree or disagree? Explain your thinking.

#### Guiding Questions

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## Problem Set & Homework

#### Discussion of Problem Set

• Are the fractions in #2 unit fractions? How do you know?
• How did you determine the correct answer in #3? How did you know that was correct even though we’ve never discussed ninths as a class?
• Which two answer choices were you able to eliminate immediately in #4? How did you decide between the two remaining answer choices?
• How did you partition the cake in #6? Is there more than one correct way to do so?
• How did you determine the correct answer in #7 without an image?

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### Problem 1

Which figure is $\frac{1}{2}$ shaded?

 A. B. C. D.

#### References

#134030001_4 (p. 4)

From EngageNY.org of the New York State Education Department. New York State Testing Program Grade 3 Common Core Mathematics Test Released Questions with Annotations August 2014. Internet. Available from https://www.engageny.org/resource/new-york-state-common-core-sample-questions/file/103126; accessed Nov. 6, 2018, 1:35 p.m..

### Problem 2

A rectangle is shown below.

1. Draw line segments on the rectangle to divide the rectangle into 8 equal parts.
2. What fraction of the area of the whole rectangle is the area of each part?

#### References

Massachusetts Department of Elementary and Secondary Education Spring 2016 Grade 3 Mathematics TestQuestion #13

Spring 2016 Grade 3 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Oct. 15, 2018, 4:58 p.m..

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