Mathematics K–6 · Years 5–6

A half, a quarter, a fifth and a tenth of real quantities

Number and algebra

PracticalLow risk

The idea

A unit fraction of a quantity is found by dividing the quantity into that many equal parts, so 1/4 of 2 L is 500 mL and 1/5 of 1 m is 20 cm, and measuring one part checks the division.

What you need

2 L of water in a jug and a 1 L measuring jug marked every 50 mL or finer
4 identical clear cups that each hold at least 600 mL
a metre ruler and a 1 m length of string
a 1 kg bag of rice and a kitchen scale reading to 1 g
a clock with a second hand

How to do it

Share the 2 L of water equally among the 4 cups by pouring until the levels match. Measure the water from one cup in the measuring jug.
Fold the 1 m string into 5 equal parts by trial, mark the folds and measure one part with the ruler.
Find 1/10 of 1 kg of rice by calculating first (1000 g ÷ 10), then weigh out that amount. Pour the 100 g back into the bag, make ten piles by eye from the whole 1 kg, and weigh one of them.
Find 1/2, 1/4 and 1/5 of an hour in minutes and check 1/4 of an hour against the clock.
Record each result as a number sentence, for example 1/4 of 2000 mL = 2000 mL ÷ 4 = 500 mL.

What you should see

Each cup holds 500 mL, read on the jug to the nearest marking. One fifth of the string measures 20 cm, and a fold in the wrong place shows as a part longer or shorter than 20 cm. One tenth of 1 kg is 100 g; the scale shows how far a pile made by eye is from 100 g. Half an hour is 30 minutes, a quarter of an hour 15 minutes and a fifth of an hour 12 minutes. Every measured part multiplied by its denominator gives the whole back: 4 × 500 mL = 2 L, 5 × 20 cm = 1 m and 10 × 100 g = 1 kg.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

One fifth of 1 m is 5 cm.
Finding a quarter of a quantity means taking 4 away from it.

Safety card

Low riskLearners carry it out

Hazards

spilled water on the floor
spilled rice is a slip hazard

Controls

pour over a tray
sweep up spills at once

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-RQF-02 MAO-WM-01
Australian Curriculum v9AC9M6N07

Sources

The pages the author read to write this activity.

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