Third Grade Math Study Guide Understanding Fractions

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Third Grade Math Study Guide

Understanding Fractions: Unit 4

Standard: MCC3.NF.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is portioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. Grade 3 expectations in tis domain are limited to fractions of 2, 3, 4, 6, and

8.

Vocabulary

Fraction A number that names part of a whole or part of a group

1 of the whole 1 of the group

3 3

Numerator The number above the fraction bar. It tells how many parts or pieces of the whole/group that you are talking about

Denominator The number below the fraction bar. It tells how many equal parts the whole/group has been portioned (divided) into

It also tells the size of the parts.

The denominator is 3, so the size of the parts is thirds

Whole All of an object or all of the group.

Unit Fraction A fraction with one as the numerator.

Equal Parts or

Equal Shares

Part of an object/group that has been divided equally

Partition An action to divide shapes or groups into equal parts.

You can partition by drawing lines or circles; by cutting; or by folding.

Understandings/Skills:

Fractional parts must be equal-sized.

Be able to partition shapes equally.

Be able to recognize situations when shapes have been partioned equally.

When shown a partitioned shape or group, be able to name the size of the parts

Example Non-Example

These are thirds. These are not thirds.

This shape has been divided into six equal parts.

The size of the parts is sixths.

Each part is one-sixth,

When given a model, be able to write the fraction that represents the part asked for.

Be able to explain how each part of the fraction represents the model.

5

8 names the shaded part. 5 is the numerator.

It tell how many parts are shaded.

8 is the denominator. It tells how many parts are in the whole.

Standard: MCC3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram. a.

Represent a fraction 1/b on a number line by defining the interval from 0 and 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b.

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from

0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Grade 3 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 6, and 8.

Vocabulary

Number Line A line on which points can be located.

Interval The distance between two points

Understandings/Skills:

Draw a number line to represent one whole by labeling the endpoints 0 and 1.

Explain the interval or space between 0 and 1 represents one whole

Draw a number line to represent one whole and partition it into a given number of parts.

The space between 0 and

1, the whole, has been partitioned into 2 equal parts.

The size of each part is ½.

0 1

Draw a number line and partition it into halves.

This number line has been partioned into thirds, 3 equal parts. The size of each part is 1/3.

This number line has been partioned into fourths, 4 equal parts. The size of each part is 1/4.

This number line has been partioned into sixths, 6 equal parts. The size of each part is 1/6.

This number line has been partioned into eighths, 8 equal parts. The size of each part is 1/8.

Represent a fraction on a number line diagram.

Partition the number line into fourths. Represent ¾.

Explanation: I divided the whole into 4 equal parts. Each part has a size of ¼. I started at 0 and counted off 3 one-fourth lengths and then circled ¾ to locate ¾ on the number line

Standard: MCC3.G.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.

Understanding/Skills:

Partition a shape into a given number of parts and describe the shape of each part.

Notice that the shape of the part can be different.

Partition a shape into a given number of parts and describe the size of each part.

Every Fraction is a combination of unit fractions.

Each whole rectangle is the same size. Each has been portioned into fourths. Notice that each represents fourths, but the shape of each ¼ is different.

The rectangle has been portioned into thirds. The size of each part is 1/3.

4/6 of the whole rectangle has been shaded.

4/6 = 1/6 + 1/6 + 1/6 + 1/6

The fraction 4/6 is a combination of four unit fractions of sixths.

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