Counting beyond one | Year 4

01 / LEARN

The idea, step by step

A whole is a landmark, not a stopping point

If one whole is split into four equal parts, each part is one quarter. Keep counting quarter-sized jumps: one quarter, two quarters, three quarters, four quarters, five quarters.

Four quarters make one whole. The next jump is five quarters, not five fifths. The denominator stays four because the piece size stays the same.

Use complete groups

The denominator tells how many pieces complete one whole. With thirds, every group of three thirds is a whole; with fifths, every group of five fifths is a whole.

Use these landmarks to check a fraction. Seven fifths is greater than five fifths but less than ten fifths, so it lies between one and two.

A common trap

Changing the denominator after reaching one whole.

Instead: The denominator describes the size of each part. It stays unchanged as more of those parts are counted.

02 / WORKED EXAMPLES

See the thinking

Example 1

Count fifths

Count seven fifth-sized pieces. How many wholes have been passed?

Five fifths make one whole.
There are two fifths left after making that whole.
Seven fifths lies between one whole and two wholes.

\frac{7}{5}

, or

1 \frac{2}{5}

Example 2

Count halves on a walk

Each marked section of a path is $\frac{1}{2}$ km. How far is six sections?

Two half-kilometre sections make 1 km.
Six sections form three pairs.
The total is 3 km.

\frac{6}{2} = 3

Check your understanding

What comes after $\frac{5}{3}$ when counting in thirds?

Show answer

$\frac{6}{3} = 2$

Add one more third; six thirds form two wholes.

03 / WORKSHEET

Your turn

6 questions · 8 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Count the first seven quarter-sized jumps. Write the final fraction.
1 mark
Complete: $\frac{2}{3}, \frac{3}{3}, □, \frac{5}{3}$ .
1 mark
How many whole lengths are eight halves?
1 mark
Does $\frac{9}{5}$ lie between 0 and 1, 1 and 2, or 2 and 3?
1 mark
A student says $\frac{4}{4}$ means 4 wholes. Explain the mistake.
2 marks
A jug receives five pours of $\frac{1}{4}$ litre. Write the total in quarters and as a mixed number.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Count the first seven quarter-sized jumps. Write the final fraction.
1 mark
Each jump adds one quarter; seven jumps make seven quarters.
$\frac{7}{4}$
Complete: $\frac{2}{3}, \frac{3}{3}, □, \frac{5}{3}$ .
1 mark
The numerator increases by one; the denominator stays three.
$\frac{4}{3}$
How many whole lengths are eight halves?
1 mark
Each pair of halves makes one whole; eight halves form four pairs.
4
Does $\frac{9}{5}$ lie between 0 and 1, 1 and 2, or 2 and 3?
1 mark
$\frac{5}{5} = 1$ and $\frac{10}{5} = 2$ ; nine fifths is between them.
Between 1 and 2.
A student says $\frac{4}{4}$ means 4 wholes. Explain the mistake.
2 marks
The four equal parts together fill one whole; four wholes would be sixteen quarters.
Four quarters make 1 whole.
A jug receives five pours of $\frac{1}{4}$ litre. Write the total in quarters and as a mixed number.
2 marks
Four pours make 1 L, with one quarter-litre pour left.
$\frac{5}{4}$ L, or $1 \frac{1}{4}$ L.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Equivalence; counting beyond one; mixed numbers; number lines.

Official curriculum source ↗

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