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Heavier and lighter

Measurement · level 1, lesson 2 of 6

A question to start

Here is a big, round party balloon, as big as your head. Here is a small stone from the garden, as small as a grape. Which one is heavier?

Most people point at the balloon first, because it is so much bigger. But pick them both up and you will feel the truth: the little stone pulls your hand down, and the balloon hardly pulls at all. The small thing is the heavier one!

So being big and being heavy are not the same thing. In this lesson you will learn how to find out which thing is heavier, even when your eyes and your hands are not sure, and why big things can be light.

The idea

Heavy and light

When you pick something up, you feel it pull down on your hand. A bag of potatoes pulls hard. A feather hardly pulls at all. How hard a thing pulls down is how heavy it is. Grown-ups call this its weight.

We use these words:

  • Heavier: it pulls down more. A cat is heavier than a mouse.
  • Lighter: it pulls down less. A leaf is lighter than a book.
  • The same weight: neither one is heavier.
  • Heaviest and lightest: the most and the least, when there are three or more things.

Testing with your hands

The first way to compare is to hold one thing in each hand. Stand still, hold your arms out in front of you, and feel which hand is pulled down more. That is the heavier thing.

This works well when the two things are very different, like a shoe and a sock. But your hands can be fooled when two things are nearly the same weight. Try an orange and an apple of the same size. Can you really tell? Your two arms are not exactly the same, and you might already think you know the answer. When it is close, we need a fairer test.

The balance

A balance is a fair judge. It is a bar that rests on a point in the middle, with a pan (a little dish) at each end. Put one thing in each pan.

  • The heavier side goes down.
  • The lighter side goes up.
  • If the bar stays flat and level, the two things weigh the same.

In the picture, the stone's side went down. So the stone is heavier than the balloon, just as your hands told you.

Why is a balance fair? Because it is like a seesaw. When a big kid and a small kid sit at the two ends of a seesaw, the big kid's end goes down. Both ends are the same distance from the middle, so the only thing that matters is which side pulls down more. A balance does not care how big the things are, what colour they are, or which hand you like best. It only feels the pull.

Why can a big thing be light?

Things are made of different stuff, and some stuff is packed tight while some is very loose.

  • A stone is packed tight. Even a small stone has a lot of stuff in it, so it is heavy.
  • A balloon is mostly air inside a thin skin. Air is very, very light. So a big balloon is light.
  • A pillow is big, but full of soft fluff with air between. It is light.
  • A small tin of beans is packed full. It is heavy for its size.

So you cannot tell how heavy something is just by how big it looks. You have to lift it, or put it on a balance.

Balancing with blocks

A balance can do more than say "heavier" or "lighter". Put an apple on one side. Now add blocks to the other side, one at a time, until the bar is level.

The bar is level with 6 blocks. So the apple weighs the same as 6 blocks. Now we can say how heavy the apple is, with a number! A pear that balances 8 blocks is heavier than the apple, by 2 blocks.

This is a big idea. We picked a small thing (one block) and counted how many it took. You will use the same idea for length in Measuring with hands and feet. All the blocks must be the same kind, or the count does not mean anything.

Putting three things in order

If a book is heavier than an apple, and the apple is heavier than a grape, then the book is heavier than the grape. You do not even need to test it! The apple is in the middle. So with a balance you can put many things in order from heaviest to lightest, by testing them two at a time.

Lighter on Mars

If you took a stone to Mars, it would feel much lighter in your hand: a bit more than one third as heavy as it feels on Earth. Mars is a smaller planet, and it pulls things down less strongly than Earth does. An astronaut on Mars could lift a box that feels too heavy to lift at home.

But here is a clever fact. A balance on Mars would still work exactly the same way. If an apple balances 6 blocks on Earth, it balances 6 blocks on Mars too. Why? Mars pulls less on the apple, but it also pulls less on the blocks, and both sides get lighter together. The seesaw stays level.

Worked examples

Example 1. Read the balance.

  1. The book's side is down.
  2. The heavier side goes down.
  3. So the book is heavier than the apple. The apple is lighter.

Example 2. Which is heavier? A toy car is put on a balance with 4 blocks.

  1. This time the left side, with the car, is up. The side with the blocks is down.
  2. So the 4 blocks are heavier than the car.
  3. The toy car weighs less than 4 blocks. If we took a block away, we might find that the car balances 3 blocks.

Example 3. Heaviest to lightest. Jo tests three fruits on a balance.

  • The melon goes down when it is weighed against the orange.

  • The orange goes down when it is weighed against the plum.

  • The melon is heavier than the orange.

  • The orange is heavier than the plum.
  • The orange is in the middle. So the order from heaviest to lightest is melon, orange, plum.
  • Jo does not need a third test to know the melon is heavier than the plum.

Try it

  1. Which is heavier: a school bag full of books, or an empty school bag?
  2. On a balance, a spoon's side goes up and a cup's side goes down. Which is heavier?
  3. A pencil and 2 erasers make a balance level. What can you say about their weights?
  4. Ali says, "The beach ball is bigger than the ball of clay, so it must be heavier." Is Ali right? Why or why not?
  5. A shoe balances 9 blocks. A sock balances 1 block. How many more blocks does the shoe weigh than the sock?
  6. A cat is heavier than a rabbit. A dog is heavier than the cat. Which of the three is the lightest?
  7. Tim weighs a toy on a balance with 5 red blocks. Then he weighs it again with 5 big wooden blocks, and the balance tips the other way. Did the toy change? What went wrong?
  8. On Mars, a box of toys would feel lighter to lift. Would it still balance the same number of blocks as on Earth?
Answers
  1. The full bag. It has the same bag plus all the books, and each book adds more pull.
  2. The cup. Its side went down, and the heavier side goes down.
  3. They weigh the same. When the bar is level, the two sides are equal: the pencil weighs the same as the two erasers together.
  4. No. A beach ball is big but full of air, which is very light. Clay is packed tight, so a ball of clay is heavy even when it is small. Big does not always mean heavy. You must lift them or use a balance.
  5. 9 blocks take away 1 block is 8 blocks. The shoe is 8 blocks heavier.
  6. The rabbit. The cat is heavier than the rabbit, and the dog is heavier than the cat, so the dog is heaviest, the cat is in the middle and the rabbit is lightest.
  7. No, the toy did not change. The blocks changed! Big wooden blocks are heavier than small red blocks. "5 blocks" only means something if all the blocks are the same kind. To compare, always use the same blocks.
  8. Yes. Mars pulls less on the box, but it also pulls less on every block, so the two sides stay balanced. The balance gives the same answer on Earth and on Mars.

Common mistake

Thinking bigger means heavier. A big thing is often heavy, but not always. Balloons, pillows, popcorn and boxes of tissues are big and light. Stones, coins and tins of food are small and heavy. Always test, never guess from the size.

Reading a balance the wrong way round. The side that goes down is the heavier one, not the lighter one. Think of a seesaw: the bigger kid sinks down.

Where it leads