Comparing Length, Mass and Capacity

What you will learn

• Use comparing words for length, mass and capacity, such as longer, heavier and holds more.
• Order three objects, from the shortest to the longest, or the lightest to the heaviest.
• Measure with equal units such as cubes or paper clips, and say how many more or fewer.

Before you start: you should be able to compare two numbers. Comparing and Ordering Numbers covers this.

The idea

Which is longer, your arm or your leg? Which is heavier, a bag of feathers or a bag of bricks of the same size? You can answer these without a ruler or scales. Comparing is the first step in measuring.

We compare three things in this lesson.

• Length is how long, tall or far something is.
• Mass is how heavy something is.
• Capacity is how much a container can hold.

Comparing length

Put two things side by side with their ends lined up at the same place. The one that sticks out further is longer, and the other is shorter. For height we say taller and shorter. For distance across we say wider and narrower.

The words change as you compare more things. Long, longer (two things) and longest (three or more). Short, shorter and shortest.

To compare lengths that you cannot put side by side, use something equal to measure them with, such as cubes or paper clips laid end to end with no gaps.

Comparing mass

You can feel which of two things is heavier by holding one in each hand. A balance scale is more reliable. Put one object in each pan. The heavier object pulls its pan down. If the pans stay level, the two objects have the same mass.

Size can fool you. A big balloon is bigger than a stone, but the stone is heavier. Do not guess mass from size alone.

The comparing words are heavy, heavier and heaviest, and light, lighter and lightest.

Comparing capacity

Capacity tells you how much a container can hold. A bucket can hold more than a cup, so it has a bigger capacity. You can compare by pouring: fill one container, pour it into the other, and see whether it overflows, fits exactly or has room left over.

Be careful not to mix up how tall a container is with how much it holds. A tall thin glass and a short wide bowl can hold the same amount.

When containers are the same size, how full they are tells you how much is inside. Full holds more than half full, and half full holds more than empty.

Why we need equal units

Suppose you measure a table with your hand span and your friend measures it with theirs. You get $9$ and they get $7$. Both of you are right, but the numbers do not match, because your hand is bigger. Counting only works for comparing if every unit is the same size. That is why people agreed on standard units, such as centimetres, grams and litres, which are the same everywhere. Units of Measurement introduces these.

Worked examples

Example 1: Ordering by length

Maya measures three ribbons in cubes: red is $8$ cubes, blue is $12$ cubes and green is $5$ cubes. Put them in order, shortest first.

1. Compare the numbers: $5$, $8$, $12$.
2. The smallest is $5$, so the green ribbon is the shortest.
3. Then $8$ is red, and $12$ is blue, the longest.

Answer: Green, red, blue.

Example 2: How much longer?

A snake is $14$ cubes long and a worm is $9$ cubes long. How much longer is the snake?

1. Both are measured in cubes, so the units match.
2. Find the difference: $14 - 9 = 5$.

Answer: The snake is $5$ cubes longer than the worm.

Example 3: Reading a balance

An apple is in the left pan of a balance and a plum is in the right pan. The right pan is lower. Which is heavier?

1. The heavier object pulls its pan down.
2. The right pan is lower, so the plum is in the heavier pan.

Answer: The plum is heavier than the apple.

Always use the same unit for the things you compare. If one length is in paper clips and the other is in cubes, the numbers cannot be compared.

Why it matters

Comparing helps you make choices every day. Which box is big enough? Which bag is too heavy to carry? Which bottle has more juice? Cooks, builders and shoppers all compare before they measure. It also prepares you for measuring with numbers, because you now know what you are checking: how long, how heavy or how much a container holds.