**Mathematics: Grade 3: Number & Operations- Fractions**

## Develop understanding of fractions as numbers

3.NF.1 Understand a fraction 1/b as a 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.

**3.NF2**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 diagram by defining the interval from 0 to 1 as the whole and portioning 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.

Click here to order fractions with the same denominator on a number line (1/8, 2/8, 3/8 etc.)

**3.NF3**Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

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

Click here to model equivalent fractions

Click here to create equivalent fractions

Click here to use fraction tiles to make equivalents

Click here to create equivalent fractions

Click here to use fraction tiles to make equivalents

b. Recognize and generate simple equivalent fractions e.g.., ½ = 2/4, 4/6=2/3) Explain why the fractions are equivalent, by using a visual model.

Click here for a fraction tutorial

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3=3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or < and justify the conclusions, e.g., by using a visual fraction model.