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 trickiest 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.
13 · Tables and tally charts
A tally chart counts with marks: each line is 1, and a line across four lines closes a group of 5. Count the bundles by fives, then the single lines.
Pizza has one bundle and 4 more lines: 5 + 4 = 9. A table shows the same counts as numbers, so you can skip the counting.
14 · Which statement is true?
Some questions give four sentences about a graph and ask which one is true. Check each sentence against the graph, one at a time, and cross it off as soon as one part is wrong.
On the pet graph: "Fish was chosen by 4 kids" is false (2). "Cat beat Dog" is false. "Dog was chosen by 3 times as many kids as Fish" is true: 6 is 3 times 2.
Watch the words more than, fewer than, twice as many, and in all. Each one asks for a different calculation.
15 · Certain, likely, unlikely, impossible
Probability words say how sure we are. Certain: it will happen every time. Impossible: it can never happen. Likely: it happens more often than not. Unlikely: it can happen, but not often.
This bag has 5 red marbles and 1 blue. Pick one without looking. Red is likely, blue is unlikely, and green is impossible because there is no green marble in the bag.
16 · Which is most likely?
The color with the most marbles in the bag, or the biggest space on a spinner, is the most likely. The smallest is the least likely.
On this spinner, Red covers half the circle, Blue a quarter, and Green and Yellow an eighth each. Red is most likely. Green and Yellow are equally likely, because their spaces are the same size.
If every space is the same size, every result has an equal chance: that spinner is fair.
17 · Counting the ways
Ivy has 3 shirts (red, blue, green) and 2 skirts (black, white). How many different outfits can she make? List them in order so you miss none: each shirt goes with each skirt.
Red with black, red with white. Blue with black, blue with white. Green with black, green with white. That is 6 outfits, which is 3 × 2.
Ready to practice?
The quiz gives you new questions each time and explains every answer. You'll also find more quizzes and full practice tests.