This week your child factors expressions — turning 2x − 4 into
2(x − 2). It looks like a topic only a teacher can judge, but it is not: every
answer can be checked by multiplying back out. That single fact is worth more than any
help you could give with the algebra itself, and you do not need to know algebra to give it.
The activity — ten minutes, one sitting
What you need: about twenty small identical things — bottle caps, beans, coins, torn paper
squares — and a pencil.
Put out twelve caps. Say “Arrange these into equal rows. Any number
of rows.” Let them choose.
Whatever they build, name it out loud: three rows of four, or two rows of six.
“So twelve is three times four.” Ask for another
arrangement. And another.
More than one arrangement is right. That is the point — there is
usually more than one way to factor, and none of them is the “real” one.
Now the useful part. Write their answer down and say
“Multiply it back. Do you get twelve?” Every single time.
Ask them to show you the same check on their homework: cover the question, multiply their
answer out, and see whether the original comes back.
If it does, say so plainly: “Then it is right, and you did not need
me to tell you.”
Three things to avoid
Do not treat factoring as guessing. If your child waits to be told whether an answer
is right, hand the check back to them — multiply it out.
Do not dismiss a plain number as “not a real factor”. In 2x − 4 the
2 is a factor exactly like an x would be.
Do not treat an unfinished answer as a wrong one. Factoring happens in stages; every
stage is correct as far as it goes. The question is whether anything is still shared —
“Look again. Is there anything left in every part?”
How to tell it is working
They check their own answer by multiplying out, without being asked.
Given twelve caps they find more than one arrangement and do not ask which is correct.
They look at their bracket a second time to see whether anything is still shared.
If they are stuck, drop the letters and stay with numbers. What do 15 and 20
share? Five. What is left? Three and four. That is the whole method, and the letters change
nothing about it.