Volume does not change when it is poured

Why this exists

Pour water from a short cup into a tall thin glass and it rises higher; pour it into a wide dish and it spreads out low. A young child usually judges “how much” by how high the water comes, so the thin glass looks like more. It is not: no water was added and none was taken away, so there is just as much as before. These three days let the child see that for themselves, and the tool that settles every argument is the same one each time: pour it back into the cup it came from.

The child should already be able to compare two things side by side. Use plain words all week, “how much water”, “more”, “less”, “just as much”, and no measuring units.

Day 1: The thin glass

You need: two clear plastic cups of the same size (A and B), one tall thin clear glass, a pitcher of water, a towel. A drop of food coloring makes the water easy to see.

Fill cup A and cup B to the same height while the child watches. Put them side by side and ask, “Is there more water in A, more in B, or just as much?” Let the child check the tops of the water against each other until they agree it is just as much. Everything that follows depends on this starting agreement.

Now let the child pour cup A into the thin glass. Set the thin glass next to cup B and ask the same question: “Which has more water now, or is it just as much?”

Many children point to the thin glass because the water is higher. Do not tell them they are wrong. Ask, “Did we add any water? Did we spill any?” Then say, “Let’s find out. Pour it back into cup A.” Put A beside B again. The water is at the same height as before (a drop or two left in the glass makes no difference you can see), so it was just as much the whole time. Ask, “So when it was in the thin glass, was there more water, or did it only look taller?” A child who still is not sure has not failed; pour it back and forth a few more times, or come back to it tomorrow.

Practice.

1. Pour cup A into the thin glass and back again three times. Is the water in A still level with B? Answer: yes, just as much; nothing was added or spilled.
2. Before pouring, ask the child to guess: “In the thin glass, will the water come up higher or lower than in cup B?” Answer: higher, because the glass is narrow.
3. Higher in the thin glass means more water. True or not? Answer: not true; it is the same water, and pouring back shows it.
4. Leo pours his cup into a skinny glass and says, “Now I have more than you.” What can he do to find out? Answer: pour it back into his cup and put it next to yours; the levels match.

Day 2: The wide dish

You need: cups A and B again, a wide shallow dish or pie pan, a pitcher of water, a towel.

Start as on Day 1: fill A and B to the same height and agree that they hold just as much. Then pour cup A into the wide dish. The water spreads out and sits very low.

Ask, “Which has more water now, the dish or cup B?” This time the dish may look like less. Ask again whether anything was added or spilled, then pour the dish back into cup A (a dish pours better if you tilt it to one side and go slowly). The level matches B again.

Then try splitting: pour cup A into two small cups. Each small cup has only a little. Ask, “Is the water all still here?” Pour both small cups back into A. The level matches B, so splitting water into parts does not change how much there is in all.

Practice.

1. In the wide dish, is the water higher or lower than in cup B? Answer: lower, because the dish is wide and the water spreads out.
2. Lower in the dish means less water. True or not? Answer: not true; pouring back fills cup A to the same height as B.
3. Cup A is poured into two small cups. Is there more water, less water, or just as much as in cup B? Answer: just as much, shared between two cups; pouring both back shows it.
4. Ask the child, “How could you show me that the dish has just as much as the cup?” Answer: pour it back into the cup it came from and compare it with the other cup.

Day 3: Many shapes, one amount

You need: cups A and B, the thin glass, the wide dish, two small cups, a pitcher of water, a spoon, a towel.

Fill A and B to the same height. Pour cup A into the thin glass, then from the glass into the dish, then from the dish into the two small cups, then back into A. Before each pour, ask the child to guess where the water will come up to. After the last pour, put A beside B.

Ask the big question: “The water went into all those shapes. Did it ever get more or less?” The answer to listen for is something like “No, it is the same water, we didn’t add any or take any away.” That reason, not the height, is what decides how much.

Then show the other side. Pour A into the thin glass, add one spoonful of water from the pitcher, and pour it back into A. Now A is a little higher than B. Ask, “Why is it different this time?” Adding water changes the amount; pouring it into a new shape does not.

Practice.

1. Before pouring cup A into the dish, the child guesses the level. After pouring, is there more water, less, or just as much? Answer: just as much, whatever the guess about the height.
2. Water from cup A goes into the thin glass and a spoonful is added. Poured back, is A level with B? Answer: no, A is higher, because water was added.
3. Rice instead of water: fill two cups level, pour one into the thin glass and back. Answer: the cups match again; the same holds for rice or sand.
4. Ask, “How do you know the amount did not change?” Answer: nothing was added and nothing was taken away, and pouring back shows the same level.

Exercises

1. Fill two same-size cups to the same height. Pour one into a narrow vase (C) and the other into a flat pan (D). Ask, “Which has more water, the vase or the pan?” Then ask, “How can you show it?”
2. Fill two same-size cups to the same height. Pour one into a jar, and on purpose let a little splash onto the towel. Pour the jar back into its cup. Ask, “Is it still just as much as the other cup?”

Where this goes next

Saying how much water there is, not just whether it is more, is the start of measuring what a container holds with liters and milliliters or cups, pints, quarts and gallons. Filling a space with copies of one small piece becomes Volume as filling, the same way flat space is measured in Area as covering. The idea of this week, that moving something around does not change how much there is, is the same one a child meets with counters: spread a row out wide and it still has just as many, as in One-to-one correspondence.