Comparing length, height, mass, area, and capacity

Measuring by comparing

Before we use rulers and scales, we can compare things directly. Is this pencil longer than that one? Is the bag of apples heavier than the bag of bread? Comparing is the first step in measurement.

Five things we can compare

Comparing length and height

Line the objects up at the same starting point, like the bottom of a table edge. Then see which one sticks out farther. Without a fair start, a short pencil could look longer than a long one.

Comparing mass

Hold one object in each hand: which pulls your hand down more? For a fairer test, use a balance scale. The heavier side goes down; the lighter side goes up. If they balance, they have the same mass.

Big doesn’t always mean heavy. A big balloon is lighter than a small rock!

Comparing area

Put one shape on top of the other. The one that covers more is bigger. You can also cover each shape with the same small squares and count them.

Comparing capacity

Fill one container with water, rice or sand, then pour it into the other.

• If it overflows, the second container holds less.
• If it doesn’t fill up, the second container holds more.

Tall containers don’t always hold more. A wide bowl may hold more than a tall, thin glass.

Ordering three or more

You can put objects in order: shortest to longest, or lightest to heaviest. Compare two at a time until all are in place.

Worked examples

Example 1: A crayon and a pencil start at the same line. The pencil sticks out past the crayon. Which is longer?

The pencil.

Example 2: On a balance scale, the apple side goes down and the grape side goes up. Which is heavier?

The apple.

Example 3: A jug of water fills cup A and overflows. The same amount doesn’t fill cup B. Which cup holds more?

Cup B.

Common mistakes

• Not lining up the starting point when comparing length.
• Thinking bigger always means heavier.
• Thinking taller containers always hold more.

Try it yourself

1. Which is usually heavier: a feather or a book?
2. How should you line up two ribbons to compare length?
3. On a balance, which side goes down: the heavier or lighter one?
4. Name a container that holds more than a cup.

Answers: 1) a book 2) Start them at the same point. 3) the heavier side 4) e.g. a bucket

Quick recap

• We can compare length, height, mass, area and capacity.
• Use a fair start for length; use a balance for mass.
• Size can be tricky: bigger doesn’t always mean heavier.