This week your child works with slope as a rate of change — how fast
something rises or falls, and what it is rising or falling per. The whole week hangs
on one question you can ask at home without knowing any algebra:
“per what?” A slope of 12 means nothing. Twelve pesos per kilo means
something.
The activity — ten minutes, one sitting
What you need: paper, a pencil, and something in the house that changes steadily — a water
container, load on a phone, money in a tin.
Pick the thing and measure it now. Write the number down with today's date.
Ask “What will it be tomorrow? And the day after?” Write
their guesses in a short list, one line per day.
Ask “How much does it change each day?” Whatever they
answer, ask the follow-up every single time:
“Per what?”Ten is not an answer. Ten pesos per day is. That habit is the week.
If the thing is going down — water used, load spent — say so and keep the
minus sign. Falling is a perfectly good rate.
Last, point at the very first number they wrote and ask
“Is this one a rate too?” It is not. It is where things
started. Two different kinds of number on the same page.
Three things to avoid
Do not let a slope be said as a bare number. Ask “per what?” every time,
even when you both know the answer. Especially then.
Do not treat a negative slope as a mistake. If the drum is emptying, negative is the
correct description, not an error to be fixed.
Do not confuse the starting amount with the rate. In “₱30 plus ₱12 a
kilo”, the 30 is an amount and the 12 is a rate. Mixing them up is this week's most
common slip.
How to tell it is working
They answer a “how fast” question with two words — a number and a
per-something.
They accept a negative rate without asking whether they have gone wrong.
They can say which number in a situation is the starting amount and which is the rate.
If they are stuck, use money, because the units say themselves. Ten pesos a
day for a week. How much on day four? Nobody needs a formula for that, and the formula they
meet at school is describing exactly this.