Fractions of amounts: what children learn
Finding a fraction of an amount means splitting it into equal parts and taking some of them. Year 2 pupils find ½, ⅓, ¼, 2/4 and ¾ of lengths, shapes, sets of objects and quantities. They write statements such as ½ of 6 = 3 and learn that 2/4 is the same as ½.
In the game, children answer questions such as '¾ of 12 = ?' against the clock. All amounts divide exactly, so the answers are whole numbers. The questions use the fractions named in the Year 2 programme of study, plus ½, so children meet halves, thirds and quarters as well as their first non-unit fraction, ¾.
This topic covers the Year 2 statutory requirement in the National Curriculum in England (Number – fractions): pupils should be taught to “recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity; write simple fractions, for example 1/2 of 6 = 3”. Year 2 pupils are usually aged 6–7.
For families following US standards, the closest Common Core standard is 2.G.A.3, which is taught in Grade 2. Closest match only: Common Core works with equal shares of shapes in Grade 2 and finds fractions of a quantity later.
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 sweets, 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 pupils to find ½ and ¼ of a length using string and a ruler.
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
Which fractions do Year 2 pupils learn?
The programme of study names ⅓, ¼, 2/4 and ¾, as well as halves (introduced in Year 1). Pupils also learn that 2/4 is equivalent to ½.
Why does the game include 2/4?
To show that 2/4 of an amount is the same as half of it, which is a Year 2 objective.
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.