This week your child works with percentage rise and fall. There is one idea underneath
all of it: a percentage is always a percentage of something, and that something
changes. Put a price up 20% and then down 20% and you do not get back to where you
started. Ten minutes with real peso amounts shows why.
The activity — ten minutes, one sitting
What you need: paper, a pencil, and one real price your child knows — a sachet of shampoo, a
ride, a kilo of rice.
Pick the price and write it down. Say a hundred pesos if you want the arithmetic easy.
“The store puts this up by twenty per cent. What is it now?”
Work it together: twenty per cent of one hundred is twenty, so the new price is
₱120. Write both numbers, one under the other.
Now say “Next week the store takes twenty per cent off. Guess the
price before you work it out.” Let them guess. Almost everyone says a hundred.
Work it out. Twenty per cent of 120 is 24, so the price is ₱96.
Four pesos short. Not a trick and not an error — the second
twenty per cent was taken from a bigger number than the first.
Ask the question the whole week turns on:
“Twenty per cent of what?” Ask it about the rise, then
about the fall. Two different answers.
Three things to avoid
Do not let percentages be added or subtracted straight. “Up twenty and down
twenty is zero” is the mistake. Show the two peso amounts side by side: 20 and 24 do
not cancel.
Do not say the shop is cheating. Both discounts are honest. The arithmetic simply is
not symmetric, and saying so plainly is better than a story about tricks.
Do not let 20% be read as “divide by 20”. Twenty per cent means twenty per
hundred. Anchor on ten per cent first — that one they can do in their head.
How to tell it is working
Before calculating anything, they ask “per cent of what?”
They can find 10% in their head and build 20% or 5% from it.
Shown a rise and a fall by the same percentage, they say the answer will be lower
— and can say why.
If they are stuck, forget percentages and use halves. Double a price, then
take half off: that one comes back exactly. Then try adding half and taking half off —
it does not. The asymmetry is the same idea, without the arithmetic in the way.