Fractions start with equal parts, and rounding starts with a number line

What a fraction is

A fraction is a number made by cutting one whole into equal parts. The bottom number says how many equal parts the whole is cut into. The top number says how many of those parts we take.

1 of 4 equal parts is one fourth, written 1/4.

A picture walk-through

Halves: 2 equal parts. One part is 1/2. Grade 1 starts here, with the words “half” and “fourth”.
Thirds: 3 equal parts. Each part is smaller than a half.
3 of 8 equal parts is 3/8. In grade 3, kids name fractions up to eighths.

Fractions on a number line

In grade 3, fractions become numbers with their own spot on the number line, just like 1, 2 and 3.

From 0 to 1, cut into 4 equal hops. The dot is 3 hops along, so it's at 3/4.

Comparing fractions

Same top number: 1/3 is more than 1/4, because the whole is cut into fewer, bigger parts.

With the same bottom number it's easier: 3/8 is more than 2/8, just as 3 slices are more than 2 slices of the same size.

Rounding

Rounding finds the nearest easy number. On a number line from 40 to 50, kids look at which end 47 is closer to.

47 is closer to 50 than to 40, so 47 rounds to 50. A number exactly in the middle, like 45, rounds up.

The same idea works for bigger places: 362 rounds to 400 to the nearest 100, and 2,750 rounds to 3,000 to the nearest 1,000.

Things to say at home

“Are the pieces fair? Are they all the same size?”
“Which would you rather have: 1/2 or 1/8 of the pizza?”
“Is 47 closer to 40 or to 50?”

Common mix-ups

Parts that aren't equal. A pizza cut into 4 uneven slices isn't cut into fourths.
A bigger bottom number means a bigger fraction. It's the other way round: 1/8 is less than 1/2.
Rounding down by habit. 47 rounds to 50, not 40. Look at the digit just right of the place you're rounding to.