Year 2: Thirds and quarters of a length
Part of the Year 2 fractions chapter. Chapter overview · whole chapter on one page
Thirds and quarters of a length
A length can be shared into equal parts, just like a shape.
This ribbon is 12 cm long. We cut it into 3 equal pieces. Each piece is one third of the ribbon.
To find one third, share 12 into 3 equal parts: 12 ÷ 3 = 4. So one third of 12 cm is 4 cm.
Key ideas
- Share the whole length into equal pieces first.
- One third is one of three equal pieces.
- One quarter is one of four equal pieces.
- Write the answer in cm.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 12 cm into 3 equal pieces. Every piece needs the same number.12 ÷ 3 = 4
- Find what is in one piece. Each piece has 4 cm.4 in one piece
- Take one piece. One piece is one third of the whole.4
Check. Put the pieces back together: 4 + 4 + 4 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one quarter of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 9 cm into 3 equal pieces. Every piece needs the same number.9 ÷ 3 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one third of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 = 9. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Watch out
Watch out: share the whole length first.
Then count the length of one piece.
Exam tip
Grown-up tip. Use a strip of paper or ribbon. Fold it into three or four equal pieces. Ask: “How long is one piece?”
Exercise 4B Thirds and quarters of a length
Non-calculatorKey words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 6 cm into 3 equal pieces. Every piece needs the same number.6 ÷ 3 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one third of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 = 6. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 12 cm into 4 equal pieces. Every piece needs the same number.12 ÷ 4 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one quarter of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 15 cm into 3 equal pieces. Every piece needs the same number.15 ÷ 3 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one third of the whole.5
Check. Put the pieces back together: 5 + 5 + 5 = 15. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 16 cm into 4 equal pieces. Every piece needs the same number.16 ÷ 4 = 4
- Find what is in one piece. Each piece has 4 cm.4 in one piece
- Take one piece. One piece is one quarter of the whole.4
Check. Put the pieces back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one quarter of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 18 cm into 3 equal pieces. Every piece needs the same number.18 ÷ 3 = 6
- Find what is in one piece. Each piece has 6 cm.6 in one piece
- Take one piece. One piece is one third of the whole.6
Check. Put the pieces back together: 6 + 6 + 6 = 18. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 9 cm into 3 equal pieces. Every piece needs the same number.9 ÷ 3 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one third of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 = 9. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 20 cm into 4 equal pieces. Every piece needs the same number.20 ÷ 4 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one quarter of the whole.5
Check. Put the pieces back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 15 cm into 3 equal pieces. Every piece needs the same number.15 ÷ 3 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one third of the whole.5
Check. Put the pieces back together: 5 + 5 + 5 = 15. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one quarter of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Method. Share the 12 cm into 4 equal pieces, then check one piece.
- Share the ribbon. Share 12 cm into 4 equal pieces.12 ÷ 4 = 3
- Check one piece. Each piece is 3 cm, not 4 cm.3 cm in one piece
- Decide. Ben is not right. One quarter of 12 cm is 3 cm.No. One quarter of 12 cm is 3 cm.
Check. Four pieces of 3 cm make 12 cm: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Count the pieces, then share the length.
Method. Work out one piece of each ribbon, then compare.
- Ruby’s piece. Share 12 cm into 3 equal pieces.12 ÷ 3 = 4 cm
- Ali’s piece. Share 8 cm into 4 equal pieces.8 ÷ 4 = 2 cm
- Compare. 4 cm is more than 2 cm.4 > 2
- Write the answer. Ruby. Her piece is longer.
Check. Ruby’s piece is 4 cm and Ali’s is 2 cm. ✓
Watch out. Compare the pieces, not the whole ribbons.