This week your child multiplies one fraction by another — ½ × ½,
⅔ × ¾. The surprising part is that the answer comes out
smaller than what you started with. Every child expects multiplying to make things
bigger, because for years it has. Ten minutes of folding paper settles it more firmly than
any explanation.
The activity — ten minutes, one sitting
What you need: four sheets of any scrap paper — the back of an old handout, a page of newspaper,
a torn rice sack liner — and a pencil.
Take one sheet. Say “This whole sheet is one.”
Fold it in half and shade one half with the pencil, going across.
Without unfolding, fold it in half the other way. Shade one half again, this time
going up and down. Open it out.
Point at the part with both kinds of shading.
“How many pieces is the sheet in now?” Four.
“And how many have both marks?” One.
That piece is one quarter. Half of a half is a quarter — and a
quarter is smaller than a half.
Do it again on a fresh sheet with thirds and halves. Ask the same two questions in the same
order every time: how many pieces altogether, and how many carry both marks.
Last one, no folding. Say “Two thirds of three quarters. Bigger or
smaller than three quarters?” If the answer is “smaller” without a
fold, the week has landed.
Three things to avoid
Do not say “multiplying makes it bigger.” It is the belief this whole week
exists to correct. Let the folded paper say otherwise before you do.
Do not count only the second shading. If your child says ½ × ½ is
a half, point at the paper: “Only the piece with both marks
counts.”
Do not teach the shortcut yet — top times top, bottom times bottom. It is
Wednesday's lesson, and a child who has it early stops looking at the paper.
How to tell it is working
They fold the second time across the first fold, without being told, because they
want the overlap.
Asked for the answer, they point at a piece of paper rather than reaching for numbers.
They say something like “it got smaller because I only took part of
a part” — in their own words, not yours.
If they are stuck, stop at one fold. Just halves. Shade a half, then ask them
to shade half of that, and count. One clear quarter is worth more than four confusing
examples. The folded sheets are worth keeping — Wednesday's lesson uses the same idea.