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Before, now and after

Change and motion · level 1, lesson 3 of 6

A question to start

Fill a glass with water right up to the very top. Then gently put in some ice cubes, and top it up until the water is exactly at the rim. Part of each ice cube sticks up above the water.

Now wait while the ice melts. Will the water spill over the top?

Most people think it will, because the ice sticking up has to go somewhere. But try it: the water level stays just the same, and nothing spills. By the end of this lesson you will be able to explain why, by asking two detective questions: what changed, and what stayed the same?

The idea

Three little words: before, now, after

To talk about a change, we need words for different times.

  • Before means earlier, in the past. "Before lunch I was hungry."
  • Now means at this moment. "Now I am eating."
  • After means later, in the future. "After lunch I will be full."

A change is when something is one way before and a different way after. If it is exactly the same before and after, nothing changed.

before now after

The orange dashed line shows the water's top. It is at the same height before, now and after.

Question 1: what changed?

Look at the ice in the glass.

  • Before: the ice was hard, cold, and shaped like a cube. It floated.
  • Now: the ice cube is smaller. Some of it has turned into water.
  • After: there is no ice left. It has all turned into water, and the water has spread out to fill the glass.

So the ice changed from solid (hard, keeps its shape) to liquid (runny, takes the shape of its container). This change is called melting. It happens because the room is warmer than the ice.

Question 2: what stayed the same?

This is the cleverer question, and it is easy to forget. When the ice melted:

  • the glass stayed the same;
  • the amount of water stayed the same! The ice was made of water, and the melted water is the same water. None of it disappeared and no new water came from nowhere. If you put the glass on a kitchen scale, it would weigh the same before and after.
  • the water's top stayed at the same height.

Why the glass does not spill

Here is the secret. When water freezes into ice, it puffs up a little. The same water takes up a bit more room as ice than it did as water. (That is why a full bottle of water in the freezer can crack, and why ice floats.)

So an ice cube is like a puffed-up bit of water. The part that sticks up above the water is the "puffed-up" extra. When the ice melts, it un-puffs and becomes water again, and it fits exactly into the space that the underwater part of the ice was using. Nothing extra is left to spill over.

You do not need to remember all of that. The big lesson is: when something changes, check what stayed the same, because that is often the key to the puzzle.

A balloon losing air

Blow up a balloon and tie it. Leave it for a few days.

before a few days after
What changed What stayed the same
It got smaller It is still orange
Its skin got wrinkly and soft It is still the same balloon
It has less air inside The knot and the string are the same
It may float lower or sink

Where did the air go? It did not vanish. Tiny bits of air slowly squeeze out through the balloon's rubber and go into the room. The air is still there, only now it is outside the balloon.

Changes you can undo, and changes you cannot

Some changes can be undone, so things go back to how they were before:

  • Melted ice can be put back in the freezer, and it becomes ice again.
  • A flat balloon can be blown up again.
  • A ball of play dough squashed flat can be rolled back into a ball.

Other changes cannot be undone:

  • An egg that has been cooked cannot be uncooked.
  • Bread that has been toasted cannot be untoasted.
  • A paper that has been burnt cannot be made into paper again.

This is another detective clue for putting pictures in order (lesson 1). If a picture shows a cooked egg, the raw egg picture must have come before it, never after.

Worked examples

Example 1. A sandcastle at the beach. Before: a tall sandcastle near the water. After the waves come in: a low bump of wet sand.

  1. Changed: the shape (castle to bump), the height (tall to low), the sand got wetter.
  2. Stayed the same: it is still sand; it is still at the same place on the beach; most of the sand is still there (some was washed away).
  3. Can you undo it? Yes, you can build the castle again from the sand.

Example 2. Play dough. You have a ball of play dough. You roll it into a long snake.

  1. Changed: the shape (round to long and thin).
  2. Stayed the same: the colour, and the amount of dough. You did not add or take away any dough. If you rolled the snake back up, you would get the same size ball.

This is a famous puzzle for young children: many think the long snake has "more" dough because it is longer. But it is the same dough, only spread out.

Example 3. Cooking pasta. Before: hard, thin, dry pasta. After cooking: soft, fat, wet pasta.

  1. Changed: hard to soft, dry to wet, thinner to fatter (the pasta soaked up water, so it got heavier too).
  2. Stayed the same: it is still pasta, still the same colour (about), same number of pieces.
  3. Can you undo it? No, you cannot make cooked pasta hard and dry the same way again.

Example 4. Now, before and after with numbers. A tower has 6 blocks now. Before, it had 4 blocks. After you add one more, how many will it have?

  1. Before: 4. Now: 6. So 2 blocks were added between before and now.
  2. After: one more than now, so 7 blocks.

Try it

  1. You leave a chocolate bar in the hot sun. Say one thing that changes and one thing that stays the same.
  2. A puddle dries up in the sun. Where does the water go?
  3. You pour water from a tall thin glass into a short wide bowl. Is there more water, less water, or the same amount?
  4. Sort these into "can be undone" and "cannot be undone": freezing juice into an ice lolly, baking a cake, folding a paper, cutting a paper into pieces, blowing up a balloon.
  5. A plant had 3 leaves last week. Now it has 5 leaves. How many new leaves grew?
  6. Finish the sentences: "Before I was a baby. Now I am ______. After many years I will be ______."
  7. Ice puffs up when water freezes. What do you think happens to a glass bottle full to the top with water, left in the freezer? (Do not try this at home!)
  8. Grown-up question: in the play dough snake example, how could you show a child that the amount of dough stayed the same?
Answers
  1. For example: changed: it gets soft and melty, it loses its shape. Same: it is still chocolate, the wrapper is the same, the amount of chocolate is the same (if nobody eats it!).
  2. It goes up into the air as tiny drops that are too small to see. (This is called evaporation. Later the water can come down again as rain.)
  3. The same amount. Only the shape changed. It may look like less in the wide bowl because it is lower, but no water was added or taken away (as long as you did not spill any).
  4. Can be undone: folding a paper (unfold it), blowing up a balloon (let the air out), freezing juice (let it melt). Cannot be undone: baking a cake, cutting a paper into pieces (you can tape it, but it is not the same as before).
  5. From 3 to 5 is 2 new leaves: 3, then 4, 5 (two more counts).
  6. For example: "Now I am a child. After many years I will be a grown-up."
  7. The water turns to ice and puffs up, but there is no room, so the bottle can crack or break.
  8. Roll the snake back into a ball and put it next to a ball you did not touch, or weigh the dough on a kitchen scale before and after rolling. The number on the scale stays the same.

Common mistake

Thinking that taller, longer or more spread out means "more". When water is poured into a different glass, or dough is rolled into a snake, the shape changes but the amount does not. Ask: was anything added or taken away? If not, the amount stayed the same.

Thinking that something that vanished from sight is gone. The air from the balloon and the water from the puddle did not disappear. They went somewhere else. Looking for where things went is a good habit.

Where it leads