Fractions of amounts: what children learn
Find halves, thirds and quarters of amounts in a timed quiz. Free Grade 3 math game.
Supplemental fraction practice: finding a fraction of a set. This is not the Grade 2 shape-partitioning standard in the original England cross-reference.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 120-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- The bottom number says how many equal parts. The denominator (bottom number) tells you how many equal groups to share the amount into. For ¼ of 12, share 12 into 4 equal groups.
- Find one part first. 12 shared into 4 equal groups gives 3 in each group, so ¼ of 12 = 3.
- The top number says how many parts you take. The numerator (top number) tells you how many of the groups to take. For ¾ of 12, take 3 groups of 3, which is 9.
- Spot equivalent fractions. 2/4 means 2 of 4 equal parts, which is the same as half. So 2/4 of 8 = 4, just like ½ of 8 = 4.
Worked examples
Example 1: ½ of 14 = ?
Working: Share 14 into 2 equal groups: 7 in each. Or halve 14.
Answer: 7
Example 2: ⅓ of 15 = ?
Working: Share 15 into 3 equal groups: 5 in each.
Answer: 5
Example 3: ¾ of 16 = ?
Working: ¼ of 16 is 4 (16 shared into 4). Three quarters is 3 × 4.
Answer: 12
Common mistakes and how to fix them
- Dividing by the top number instead of the bottom. Always share by the denominator first. Use objects so children can see the equal groups.
- Stopping at one part for ¾. After finding ¼, ask 'how many quarters do we need?'
- Making groups that are not equal. Fractions need equal parts. Share objects one at a time into each group, like dealing cards.
Activities to try at home
- Share candies, grapes or Lego bricks into halves, thirds and quarters.
- Cut a pizza or a sandwich into quarters and talk about ¼, 2/4 and ¾.
- Ask fraction questions about time: what is half of an hour? A quarter of an hour?
Ideas for the classroom
- Use bar models: draw a bar for the whole amount and split it into equal parts.
- Fold paper strips into halves and quarters to show 2/4 = ½.
- Ask students to find ½ and ¼ of a length using string and a ruler.
Free printable game and worksheet
The free printable starts with a game sheet, such as a color-by-answer picture, an answer maze or a secret-code joke, followed by a worksheet. Both use the same checked questions as the online game, and the answers are on the last page. Print it, or save it as a PDF from your browser’s print menu.
Open the free printable game and worksheet
Frequently asked questions
How should I choose this game for my learner?
Supplemental fraction practice: finding a fraction of a set. This is not the Grade 2 shape-partitioning standard in the original England cross-reference.
How should I choose this game for my learner?
Supplemental fraction practice: finding a fraction of a set. This is not the Grade 2 shape-partitioning standard in the original England cross-reference.
Does the US curriculum teach this in 1st grade?
The Common Core works with equal shares of shapes (halves, thirds and fourths) in Grade 2 (2.G.A.3) and treats fractions of a set more formally later, so the match is approximate.