Fractions and Equal Parts: Year 3 Study Guide
A fraction describes equal parts of a whole. The bottom number tells how many equal parts there are.
When something is shared into equal parts, each part is a fraction of the whole. A pizza cut into 4 equal slices has 4 quarters. One slice is 1/4 (one quarter). The bottom number, the denominator, says how many equal parts. The top number, the numerator, says how many parts you are talking about.
A unit fraction has a numerator of 1, such as 1/2, 1/3, 1/4, 1/5 and 1/8. In Year 3 you learn to recognise and name these, to make equal parts of shapes and collections, and to see that the larger the denominator, the smaller each piece is.
Equal parts matter
A fraction only works when the parts are the same size. If a chocolate bar is broken into two unequal pieces, neither piece is a half. You can check by folding or laying one piece over the other.
| Name | Symbol | Parts in whole |
|---|---|---|
| Half | 1/2 | 2 |
| Third | 1/3 | 3 |
| Quarter | 1/4 | 4 |
| Fifth | 1/5 | 5 |
| Eighth | 1/8 | 8 |
Fractions of a collection
Fractions can describe a group. If 8 apples are shared into 4 equal groups, each group is 1/4 of the apples and has 2 apples. So 1/4 of 8 is 2. To find 1/2 of a collection, share it into 2 equal groups. To find 1/3, share it into 3.
Comparing unit fractions
The more pieces a whole is cut into, the smaller each piece is. So 1/8 is smaller than 1/4, and 1/3 is larger than 1/5. Thinking about pizza helps: would you rather have 1/2 of a pizza or 1/8?
Bigger denominator, smaller piece.
Use rectangles of the same size.
The shaded parts show which is larger.
Worked examples and common mistakes
Example: What is 1/5 of 15? Share 15 into 5 equal groups: 3 in each. Answer: 3. Example: Is 1/3 shaded? Count equal parts first. A common mistake is to count the shaded parts against the unshaded parts; the denominator counts all parts. Another is to think 1/8 is bigger than 1/4 because 8 is bigger than 4.
Check your understanding: model answers
1. Draw a rectangle and divide it into 3 equal parts, then shade one. 2. Share 20 into 4 equal groups: 5 in each, so 1/4 of 20 is 5. 3. 1/2 is larger. Halves are cut into 2 big pieces, but fifths are cut into 5 smaller pieces.
✨ Key Takeaways
- A fraction is an equal part of a whole or collection.
- The denominator counts all the equal parts.
- A unit fraction has 1 as its numerator.
- Bigger denominators make smaller pieces.
💬 Questions for Discussion & Reflection
- Draw a rectangle and shade 1/3.
- Find 1/4 of 20 and explain how you worked it out.
- Which is larger, 1/2 or 1/5? Why?
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