Halves, Thirds and Quarters

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What this lesson covers

  • A fraction needs equal parts.
  • The bottom number is how many equal parts make the whole.
  • The top number is how many parts we are counting.
  • Two quarters are the same as one half.
Key idea

Equal parts

  • Cut a pizza into 4 slices that are all the same size. Each slice is one quarter.
  • If the slices are different sizes, they are not quarters.
  • Fractions always use equal parts.
Key idea

Top and bottom numbers

  • Look at 3/4.
  • The bottom number, 4, is the denominator: the whole is cut into 4 equal parts.
  • The top number, 3, is the numerator: we are counting 3 of those parts.
FractionEqual parts in the wholeParts counted
1/221
2/332
3/443
Key idea

Try it: change the top and bottom

Worked example

Names, words and symbols

  • A fraction can be a name, words or a symbol.
SymbolWords
1/2one half
1/3one third
2/3two thirds
1/4one quarter
2/4two quarters
3/4three quarters
Worked example

A fraction of a shape, a set and an amount

  • A shape: a pizza cut into 4 equal slices. Eat 1 slice and 1/4 is gone.
  • A set: 6 feijoas in 3 equal groups of 2. One group is 1/3 of the feijoas.
  • An amount: half of a 2 litre bottle of water is 1 litre.
KindExampleFraction
shape1 of 4 equal pizza slices1/4
set1 of 3 equal groups of feijoas1/3
amount1 litre of a 2 litre bottle1/2
Key idea

Try it: split a set into equal groups

Key idea

Two quarters make a half

  • Fold a paper in half. Fold it in half again. Now there are 4 quarters.
  • Colour 2 of the quarters. They cover exactly one half.
  • So 2/4 and 1/2 are the same amount.
Key idea

Maths blocks

Common mistakes

  • Any 2 pieces are halves.
    Halves must be the same size. Two pieces that are not equal are not halves.
  • In 1/4, the 4 means 4 pieces are coloured.
    The 4 is how many equal parts make the whole. The 1 is the part you count.
  • 2/4 is more than 1/2, because 2 is more than 1.
    2/4 and 1/2 cover the same amount. Quarters are just smaller pieces.

Your turn

1

A cake is cut into 4 equal pieces. What is one piece called?

2

In 2/3, how many equal parts are in the whole?

3

Write three quarters as a fraction.

4

8 shells are put in 2 equal groups. How many shells are in 1/2?

5

Is 2/4 more than, less than, or the same as 1/2?

Show answer

1. one quarter 2. 3 3. 3/4 4. 4 5. the same

Summary

What to take away

  • Fractions need equal parts.
  • Bottom number: parts in the whole. Top number: parts counted.
  • 1/2, 1/3 and 1/4 can be written in words or symbols.
  • 2/4 is the same as 1/2.
Report a mistake

More in Number

Numbers to 120: Read, Write and CompareNotesGroups of Ten and Where Numbers Sit on a LineNotesRounding, Skip Counting, Odd and EvenNotesAdding and Taking Away: Facts to 20 and TensNotesStory Problems: Adding and Taking Away to 100NotesTimes and Share: 2s, 5s and 10sNotesHalves, Thirds and QuartersNotesComparing Fractions and Finding the WholeNotesNZ Coins and Notes: Count and Make MoneyNotes

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