Counting beyond one | Year 4

01 / LEARN

Understand the idea.

A whole is a landmark, not a stopping point

Count fractions by keeping the piece size fixed. With quarters, the jumps are $\frac{1}{4}$ , $\frac{2}{4}$ , $\frac{3}{4}$ , $\frac{4}{4}$ , then $\frac{5}{4}$ . One whole is a landmark on the number line, and counting continues beyond it.

The denominator stays four after you pass one whole because the jumps are still quarter-sized. Only the numerator increases. Changing the denominator would change the size of the pieces you were counting.

Use complete groups

Use the denominator to group pieces into complete wholes. Three thirds make one whole; five fifths make one whole. Count those complete groups first, then describe the pieces left over. This helps you see the size of a fraction beyond one.

For $\frac{7}{5}$ , the nearby whole-number landmarks are $\frac{5}{5} = 1$ and $\frac{10}{5} = 2$ . Seven fifths lies between them. It contains one complete group of five fifths and two fifths more.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Count fifths

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

Worked solution

1
Identify one complete whole in fifths.
$\frac{5}{5} = 1$
Five fifth-sized pieces fill one whole.
2
Separate seven pieces into a full group and leftovers.
$7 = 5 + 2$
After one group of five, two fifth-sized pieces remain.
3
Name the total amount.
$\frac{7}{5} = 1 \frac{2}{5}$
One whole has been passed, with two fifths of the next whole.

Answer

$\frac{7}{5}$ , or $1 \frac{2}{5}$

EXAMPLE 02

Count halves on a walk

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

Worked solution

1
Pair two half-kilometre sections.
$\frac{1}{2} km + \frac{1}{2} km = 1 km$
Two halves of a kilometre make one whole kilometre.
2
Count the pairs in six sections.
$6 \div 2 = 3$
Six half-sized sections form three complete pairs.
3
State the complete distance.
$\frac{6}{2} km = 3 km$
Each of the three pairs contributes one kilometre.

Answer

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

03 / YOUR TURN

Try it yourself.

Check your understanding

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

Show answer & reasoning

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

Add one more third: $\frac{5}{3} + \frac{1}{3} = \frac{6}{3} = 2$ . Six thirds form two groups of three thirds, so the next number is two.

Keep practising

6 worksheet questions · 8 marks

Open worksheet 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 ↗

In this lesson

Understand the idea.

A whole is a landmark, not a stopping point

Use complete groups

See the method in action.

Count fifths

Identify one complete whole in fifths.

Separate seven pieces into a full group and leftovers.

Name the total amount.

Count halves on a walk

Pair two half-kilometre sections.

Count the pairs in six sections.

State the complete distance.

Try it yourself.

Check your understanding

Keep practising