Halves, quarters and eighths

A fraction describes equal parts of one whole. Before naming a half, quarter or eighth, first decide what the whole is and check that it has been divided into equal parts.

Learning sequence: Whole → split equally → count equal parts → name the fraction → connect it to a real situation.

• Half: 2 equal parts make one whole.
• Quarter: 4 equal parts make one whole.
• Eighth: 8 equal parts make one whole.

Each model shows the same whole divided into more equal parts. More parts means each part is smaller: one eighth is smaller than one quarter, and one quarter is smaller than one half.

1. Is this really one half?

A sandwich is cut into 2 pieces, but one piece is much larger. The pieces are not halves because halves must be equal in size.

2. Halving again

Cut one whole into 2 equal halves. Halve each half again: now there are 4 equal quarters. Halve every quarter again: now there are 8 equal eighths.

3. Measuring cup

If 2 half-cups fill one cup, each half-cup represents one half of the whole cup. Four quarter-cups fill the same whole cup.

4. Position

The halfway point of a race is a position that divides the full race distance into 2 equal lengths.

5. Time

Half an hour is half of 60 minutes, so it is 30 minutes. A quarter of an hour is one of 4 equal parts of 60 minutes, so it is 15 minutes.

AC9M2M02: identify common uses and represent halves, quarters and eighths in relation to shapes, objects and events.

• E1: food items divided into equal halves, quarters and eighths
• E2: half- and quarter-cup/spoon measures
• E3: paper folding into equal halves and quarters
• E4: halves and quarters describing lengths, positions and distances
• E5: halves and quarters describing durations and sporting-event sections

• Two pieces automatically mean halves. No: the 2 pieces must be equal.
• A larger denominator means a larger piece. For the same whole, eighths are smaller than quarters because the whole is split into more equal parts.
• The whole can change halfway through a comparison. Fractions can only be compared fairly when the same-sized whole is being considered.
• Fractions only describe shapes. They also describe measures, positions, distances, durations and events.

1. Fold and prove: fold paper into halves, then quarters, then eighths. Open it and check that all parts are equal.
2. Fair-share challenge: decide whether pictured food portions are fair halves or quarters and explain why.
3. Measure the whole: fill one cup using halves and quarters and record how many equal parts make the whole.
4. Human number line: mark the start, halfway point and finish of a path, then discuss what “halfway” means.
5. Time connection: connect 15 minutes to quarter of an hour and 30 minutes to half an hour.

• Always identify the whole first.
• Fraction parts must be equal.
• 2 halves = 1 whole.
• 4 quarters = 1 whole.
• 8 eighths = 1 whole.
• Half an hour = 30 minutes.
• Quarter of an hour = 15 minutes.

Quick check

1. How many quarters make one whole?
2. Why are two unequal pieces not halves?
3. Which is smaller for the same whole: one quarter or one eighth?
4. How many minutes are in a quarter of an hour?
5. Give one example of a fraction used to describe a position or event.