Graphs with fractions: a gentle walkthrough for Grade 3

1 · A graph is a picture of counts

We asked 12 kids, "What is your favorite pet?" and made a tally mark for each answer. Then we turned the tallies into bars.

The taller the bar, the more kids picked it. Dog wins: its bar is the tallest.

2 · How to read a bar graph

Every bar graph has three helpers: a title (what it is about), labels along the bottom (the choices), and numbers up the side (how many).

To read a bar, put your finger on the top of the bar and slide it left to the numbers. Leo's bar stops at 3, so Leo read 3 books.

3 · When the numbers skip

Sometimes the side counts by 2s: 0, 2, 4, 6, 8, 10. Then a bar can stop between two lines.

Halfway between 4 and 6 is 5. Halfway between 6 and 8 is 7. Green stops halfway between 4 and 6, so Green is 5.

4 · Pictographs: a picture stands for a number

A pictograph uses little pictures instead of bars. The key at the bottom tells you what one picture is worth.

Here ★ = 2 apples. Sam has 3 stars, so Sam picked 2 + 2 + 2 = 6 apples. Ren has 4 stars: 8 apples.

5 · Half a picture

Here is where fractions sneak in. If ★ = 2, then half a star = half of 2 = 1.

Sam now has 2 stars and a half: 2 + 2 + 1 = 5 apples. Ren has 3 and a half: 2 + 2 + 2 + 1 = 7.

If the key were ★ = 4, a half star would be half of 4 = 2. Always look at the key first!

6 · Line plots: Xs on a number line

A line plot counts how many times each number happens. Every X is one thing.

We looked in 10 desks and counted the pencils. Three desks had 5 pencils, so there are 3 Xs above 5. The most common number is 4 (the tallest stack).

7 · Line plots with halves

When we measure things, the answers are often not whole numbers. A leaf can be 2 inches, or 2½ inches.

So the number line is marked in halves: 2, 2½, 3, 3½. Count the Xs above 2½: 4 leaves are 2½ inches long.

8 · Line plots with quarters

Measure more carefully and you get quarters: 1, 1¼, 1½, 1¾, 2.

Remember from fractions: 2/4 is the same as 1/2, so the middle mark can be called 1½ or 1 2/4. The tallest stack shows the most common length: 1½ inches.

9 · Bars that stop at a half

Bar graphs can measure too, not just count. This one shows rain. The side numbers count by halves: 0, ½, 1, 1½, 2.

Monday's bar stops at ½ inch. Wednesday's stops at 1½ inches. Slide your finger left, just like before.

10 · How many more? Compare two bars

"How many more" means subtract, or count the steps from the shorter bar up to the taller one.

From Monday (½) up to Wednesday (1½) is 2 half-steps, and 2 halves make 1 whole. So Wednesday had 1 inch more rain than Monday.

11 · What fraction of the whole?

Add all the bars to get the whole group: 4 + 2 + 2 = 8 kids.

Apple was picked by 4 of the 8 kids: 4/8, which is the same as 1/2. Banana was picked by 2 of 8: 2/8 = 1/4.

12 · Two steps at once

The hardest questions ask you to do two things: read the graph, then add, subtract, or find a fraction.

Sam has 3½ stars and Jo has 2½ stars. With ★ = 2, that is 7 books and 5 books. How many more did Sam read? 7 − 5 = 2.

Read the key, read the graph, then do the math. That is the whole trick. 🎉