Skip to content

Which holds more?

Measurement · level 1, lesson 3 of 6

A question to start

Fill a short, wide glass with water. Now, while someone watches, pour all of that water into a tall, thin glass. The water climbs up high! Ask them: "Is there more water now, or less, or the same?"

short and wide tall and thin the same water, poured

Many young children say "more now, because it is higher". But we did not add any water, and we did not spill any. It is the same water. It just got squeezed into a thinner glass, so it had to stand up taller. In this lesson you will learn how to find which container really holds more, without being fooled by how tall it looks.

The idea

Full, empty and holds

A container is anything that can hold something inside it: a cup, a bottle, a bucket, a bath, a box, a spoon.

  • A container is full when it cannot fit any more in.
  • It is empty when there is nothing in it.
  • It is half full when it has half of what it can hold.

How much a container holds is how much fits in it when it is full. Grown-ups call this its capacity. A bath holds a lot. A spoon holds a little. Which holds more, a bucket or a mug? The bucket, by far.

The same stuff, a new shape

Look back at the two glasses at the top. When you pour water from one glass to another, the water changes shape, but the amount stays the same. Nothing was added and nothing was taken away.

This is true for rice, sand and beans too. Pour a cup of rice onto a plate and it spreads out flat. Pour it into a tall bottle and it stands up high. It is still one cup of rice. The amount only changes if you add some or lose some.

Why did the water go higher in the thin glass? Because there is less room across. The same water has to go somewhere, so it goes up. Think of a crowd of children: in a wide room they stand in a short, wide group, and in a narrow hallway the same children make a long line.

The pouring test

Here is the fair way to find out which of two containers holds more. Call them A and B.

  1. Fill A right to the top.
  2. Pour all of it into B, which starts empty.
  3. Look at B.
spills over not full exactly full
  • If B spills over, then A held more than B can hold. A holds more.
  • If B is not full, then there is still room in B. B holds more.
  • If B is exactly full, they hold the same.

Why does this work? The water from A is exactly "what A holds". By pouring it into B, we are fitting all of A inside B. If it does not fit, B is smaller inside. If there is room to spare, B is bigger inside.

You can use dry rice or sand instead of water. It is less messy, and it pours almost as well.

Counting cups

The pouring test tells us which holds more. But how much more? Use a small cup again and again.

12345 the jug holds 5 cups

Fill the cup, tip it into the jug, and count: 1, 2, 3, 4, 5. The jug is full after 5 cups. So the jug holds 5 cups. If a bowl holds 3 cups, then the jug holds 2 cups more than the bowl.

Two rules keep the count honest:

  • Fill the cup to the top every time. A half-full cup is not a whole cup.
  • Use the same cup every time. A big mug and a tiny cup are not the same "cup".

Tall is not everything

How much a container holds depends on how tall it is, how wide it is, and how deep it is from front to back. A tall, skinny vase can hold less than a short, fat bowl. A wide, flat baking tray can hold a surprising amount of water. So never decide by height alone. Do the pouring test, or count cups.

Worked examples

Example 1. The pouring test. Maya fills a mug with water and pours it into a jar. The jar is only half full. Which holds more?

  1. All the mug's water went into the jar.
  2. The jar still has room: it is only half full.
  3. So the jar holds more than the mug. In fact, the jar holds about 2 mugs, because one mug filled half of it.

Example 2. Counting cups. A teapot is filled with cups of water. It takes 4 cups. A vase takes 7 cups. A bottle takes 4 cups.

  1. The vase took the most cups, 7. So the vase holds the most.
  2. The teapot and the bottle both took 4 cups. They hold the same.
  3. The vase holds 7 take away 4, which is 3 cups more than the teapot.

Example 3. Three containers in order. Ned does two pouring tests.

  • He pours a full bucket into the tub. The tub is not full.

  • He pours a full jug into the bucket. The bucket is not full.

  • The tub has room left after the bucket, so the tub holds more than the bucket.

  • The bucket has room left after the jug, so the bucket holds more than the jug.
  • From most to least: tub, bucket, jug.

Try it

  1. Which holds more: a bath or a cup? A spoon or a bowl?
  2. You pour a full glass of juice into a bowl. The juice spills over the top of the bowl. Which holds more, the glass or the bowl?
  3. Sara pours all the water from a wide bowl into a tall vase. The water now comes up high. Is there more water than before?
  4. A pot holds 6 cups of rice. A pan holds 9 cups. How many more cups does the pan hold?
  5. Leo fills a jar with cups of sand, but his cups are only half full each time. He counts 8 cups. Does the jar really hold 8 full cups? More or fewer?
  6. Two bottles: one is tall and thin, the other short and fat. How can you find out which holds more?
  7. A full jug fills exactly 3 glasses. A full bottle fills exactly 3 glasses too (the same glasses). What can you say about the jug and the bottle?
Answers
  1. The bath holds more than a cup. The bowl holds more than a spoon.
  2. The glass. All of the glass's juice did not fit in the bowl, so the glass holds more than the bowl.
  3. No. It is the same water. Nothing was added or spilled. It only looks higher because the vase is thinner, so the water has to stand up taller.
  4. 9 take away 6 is 3 cups more. Count on from 6: 7, 8, 9, that is 3.
  5. Fewer. Each half-full cup is only half a cup. Two half cups make one full cup, so 8 half cups make 4 full cups. The jar holds about 4 full cups.
  6. Do the pouring test. Fill one bottle to the top and pour it into the other. If it spills, the first holds more; if there is room left, the second holds more. Or fill each with the same small cup and count.
  7. They hold the same. Each one fills 3 of the same glasses, so each holds 3 glasses.

Common mistake

Thinking the taller container always holds more. Height is only part of it. A wide container can hold more than a tall, thin one. The pouring test is the fair way to decide.

Thinking water changes amount when it changes shape. Pouring water into a new container makes it look taller or flatter, but there is the same amount as before (unless you spill some).

Where it leads