Grade 3 Math Unit 3

Understand Fractions

Unit description: Students will deepen their understanding of parts and wholes. They will begin to learn about unit fractions and non-unit fractions and how to represent them and compare them. They will also start thinking about equivalent fractions.

Download the complete Grade 3 Math Unit 3 framework to customize for your own planning.

Essential Outcomes

Number & Operations – Fractions

NY-3.NF.1 Understand a unit fraction, 1b, is the quantity formed by 1 part when a whole is partitioned into b equal parts. Understand a fraction abis the quantity formed by a parts of size 1b. Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

NY-3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line. Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

NY-3.NF.2a Represent a fraction 1bon a number line by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1band that the endpoint of the part starting at 0 locates the number 1b on the number line.

NY-3.NF.2b Represent a fraction ab on a number line by marking off a lengths 1b from 0. Recognize that the resulting interval has size aband that its endpoint locates the number abon the number line.

NY-3.NF.3 Explain equivalence of fractions and compare fractions by reasoning about their size.

Note: Fractions are limited to those with denominators 2, 3, 4, 6, and 8.

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

NY-3.NF.3b Recognize and generate equivalent fractions. e.g., 12= 24; 46= 23. Explain why the fractions are equivalent. e.g., using a visual fraction model.

NY-3.NF.3c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. e.g., Express 3 in the form 3 = 31, recognize that 63= 2, and locate 44and 1 at the same point on a number line.

NY-3.NF.3d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons rely on the two fractions referring to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions. e.g., using a visual fraction model.

NY-3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. e.g., Partition a shape into 4 parts with equal area, and describe the area of each part as 14 of the area of the shape.

Essential Questions and Big Ideas

What is a fraction? What is a unit fraction?

A fraction represents a part of a whole.
A unit fraction represents one part of a whole broken into equal parts.

How can a fraction be represented on a number line?

The number one represents one whole.
To represent a fraction on a number line, break the whole (1) into the number of parts.

What are equivalent fractions?

Equivalent fractions are equal.
A whole can be broken in different ways that create equal amounts.

How can I compare fractions?

Fractions can be compared by comparing the size of the parts.
Fractions can be compared by comparing the number of parts.
Fraction bars can be used to compare fractions.
Number lines can be used to compare fractions.

Prerequisite Skills

NY-1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
NY-2.MD.6 Represent whole numbers as lengths from 0 on a number line with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line.
NY-2.G.3 Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, etc. Describe the whole as two halves, three thirds, four fourths.