AC9M1M01 · YEAR 1 · MEASUREMENT

Comparing and Ordering

ACARA v9 CONTENT DESCRIPTION “compare directly and indirectly and order objects and events using attributes of length, mass, capacity and duration, communicating reasoning”
Builds on: Comparing attributes (Foundation, AC9MFM01). New this year: comparing indirectly with a go-between, and putting more than two things in order.

What makes a comparison fair?

Children compare things all day long: who is taller, whose bag is heavier, which glass has more, who finished first. Year 1 turns this everyday instinct into careful mathematics across four attributes — length, mass, capacity and duration. The key idea is fairness. Eyes are easily fooled: a straw can look longer because it sticks out further, a balloon can look heavy because it is big. A fair comparison makes things meet on equal terms — a shared start line, a balance scale, the same little cup, a steady clap. And when two objects cannot meet at all, mathematics sends a messenger. Just as important is saying what you found — longer than, heavier than, holds more than, takes longer than — and why.

Line them up
Two straws on the mat. Their ends can fool you until they share a start line.
Careful — they have different starting points. Can you really tell?

Length needs a start line

Length comparisons go wrong in one famous way: forgetting the start line. If two straws begin at different places, the eye judges only where they end, and the ends lie. Slide both back to a shared start line and the truth is instant — no measuring needed yet, just a fair line-up. This is direct comparison: putting the objects themselves side by side, on equal terms.

The balance scale
First guess by looking, then let the balance answer. It ignores size completely.
Look at the pair. Which side do you think is heavier?

Heavy is not the same as big

Mass hides from the eye completely. A balloon fills your arms; a pebble disappears in your palm; yet the pebble wins on the balance. Big tells you about space, not about heft. The balance scale is the fair test for mass: it ignores looks and answers only one question — which side pushes down harder? Children who have felt a few surprises on the balance stop trusting size alone.

Pour and compare
One shared cup is the fair test. Fill each container and count the pours.
The same little cup for every container. First, fill the tall glass.

Capacity hides inside

Capacity is the space inside, and the outside is a poor guide to it. A tall, narrow glass looks generous next to a short, wide jug — until the same little cup fills the glass in three pours and needs five for the jug. Filling everything with one shared unit is the fair test, and counting the pours also lets you put three containers in order, from least to most. That quiet counting plants the seed of measuring with units, which the next unit grows.

The clap clock
Time will not sit still on the mat, so we count it with a steady beat.
Press Clap to move time forward, one steady clap at a time.

Time you cannot see

Time cannot be lined up on the mat, which is why duration is the slipperiest attribute of all. Children often decide that whoever started first, or finished last, must have taken longer — but start order and finish order can both mislead. The fair test is a steady beat: clap evenly and count how many claps each event lasts. Three claps against six settles it, whatever order the events began.

The string trick
When two things cannot meet, send a go-between to carry the length.
The esky is on the lawn; the car is in the driveway. They cannot meet — so how do we compare?

When things cannot meet, send a messenger

Sometimes the two things simply cannot meet: the esky is on the lawn and the car boot is in the driveway. So we send a go-between. Cut a string to match the esky; the string now carries that length anywhere. If the string is as long as the esky, and the string fits across the boot opening with room to spare, then the esky fits too — reasoned out before anyone lifts a thing. This is indirect comparison, and that little chain of because-statements is the mathematics talking.

Quick self-check
1. Two ribbons end at the same line, but the red ribbon starts further back. Which is longer?
2. A balloon is much bigger than a spoon. Which is heavier?
3. A tall glass fills with 3 cups of water. A short jug fills with 5 cups. Which holds more?
4. Mia started her job after Tom and finished before him. Whose job took less time?
5. A string is cut to match the esky. The string fits across the boot opening with room to spare. What do you know?