Half, quarter or not equal?: what children learn
A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts. The word equal matters: if a pizza is cut into two pieces of different sizes, neither piece is a half.
In this sorting game children decide whether each piece is a half, a quarter or a part that is not equal. The examples use pizzas, cakes, sandwiches and shared sweets, so children apply the idea to both shapes and quantities.
This topic covers the Year 1 statutory requirement in the National Curriculum in England (Number – fractions): pupils should be taught to “recognise, find and name a half as 1 of 2 equal parts of an object, shape or quantity; recognise, find and name a quarter as 1 of 4 equal parts”. Year 1 pupils are usually aged 5–6.
For families following US standards, the closest Common Core standard is 1.G.A.3, which is taught in Grade 1.
How to play
Sort the cards into the right groups. Tap a card, then its group. You can also drag a card, or press the number on its group. Each game has 3 rounds with no timer. Every card is checked as soon as you place it: a card in the wrong group comes back with a hint, and you get a point for each card you place right first time. For a quicker go, choose Quick quiz: 10 multiple-choice questions in 150 seconds (choose Relaxed for more time).
Step by step
- Count the parts. How many parts is the whole split into? 2 parts could be halves; 4 parts could be quarters.
- Check the parts are equal. Halves and quarters must be the same size. Unequal parts are not halves or quarters, however many there are.
- Sharing works the same way. 8 sweets shared equally between 2 gives 4 each, so 4 is half of 8. Shared equally between 4 gives 2 each, so 2 is a quarter of 8.
- Name the part. 1 of 2 equal parts is a half. 1 of 4 equal parts is a quarter.
Worked examples
Example 1: A cake is cut into 4 equal slices. Is one slice a half or a quarter?
Working: 1 of 4 equal parts.
Answer: A quarter
Example 2: A bar is broken into 2 pieces, one much bigger than the other. Is the small piece a half?
Working: The pieces are not equal.
Answer: No, the parts are not equal
Example 3: 10 marbles are shared equally between 2. Is 5 marbles a half or a quarter?
Working: 2 equal groups of 5.
Answer: A half
Common mistakes and how to fix them
- Calling any piece of two 'a half'. Ask: are the two pieces exactly the same size? Lay them on top of each other to check.
- Thinking a quarter is bigger than a half. Fold a paper circle in half, then in half again, and compare the pieces.
- Counting the pieces you have rather than the pieces in the whole. Ask 'how many equal pieces make the whole?' first.
Activities to try at home
- Cut toast into halves and quarters, and sometimes into unequal pieces, and ask which is which.
- Share a handful of pasta or buttons equally between 2 and 4 bowls.
- Fold a napkin in half and in quarters.
Ideas for the classroom
- Show shapes split into equal and unequal parts and ask pupils to vote: half, quarter or not equal?
- Pupils fold paper shapes to make quarters in different ways.
- Share cubes between 2 or 4 pupils and talk about what each share is called.
Free printable game and worksheet
The free printable starts with a game sheet, such as a colour-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
Why include parts that are not equal?
The most common mistake with fractions is forgetting that the parts must be equal. Sorting unequal parts makes that rule clear.
Is three quarters included?
No. Year 1 covers a half and a quarter. Three quarters comes in Year 2.
Can it be played with a keyboard?
Yes. Tab to a card, press Enter to pick it up, then choose its group.