She is completely solid on a half and a quarter and can shade them in on a drawing. Where it falls apart is comparing two fractions that are not obviously related, specifically whether two thirds is bigger than three quarters. We have twenty minutes of homework time in the evening and she gets frustrated fast, so I would rather pick one approach and do it properly than confuse her with two.
A strip of paper is the other option worth knowing, and it costs nothing. Two identical strips, she folds one into thirds and the other into quarters, colour in two parts and three parts, then lay them next to each other. The comparison is physically visible and, importantly, she does the folding, so it is her result rather than your demonstration. Same length strips is the entire trick, and it is the thing pizzas cannot do.
Doing it themselves matters more than the medium. A demonstration is watched; a folded strip is remembered because their hands were involved.
One extra trick for that specific pair: ask how much is missing rather than how much is there. Two thirds is missing one third, three quarters is missing one quarter, and she already knows a quarter is smaller than a third. Less missing means more there. It works beautifully whenever both fractions are one piece short of the whole, and it feels like a magic trick to a child.
That reframing is genuinely elegant and I am slightly annoyed nobody showed it to me at school.
Whatever you pick, stop at the first correct answer she gets on her own rather than consolidating with three more. Ending on a win is most of what makes her willing to sit down tomorrow.
@chapter_cass · 6mo ago · 3 replies
Money, because the thing she is stuck on needs a common unit and money hands you one for free.
Pizza is excellent for what a fraction is, and it is bad for comparing, because two pizzas cut into thirds and quarters are two different pictures and the eye cannot reliably judge them. Money is all the same unit, so two thirds and three quarters end up as two numbers you can put side by side.
Use twelve of something rather than a random amount, because twelve divides neatly by two, three, four and six, which covers almost everything at this age. Twelve coins, twelve counters, twelve grapes. Two thirds of twelve is eight, three quarters of twelve is nine, nine is more than eight, done. She can do that with her hands in about four minutes and she will not need to be told the answer.
Once that lands, the pizza comes back in usefully for equivalence, because two quarters visibly being one half is much better seen than counted.
And twenty minutes is too long. Do eight good minutes and stop while it is still going well.
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@question_jar · 6mo ago
Twelve is the number to build everything on. I taught for years and the difference between using twelve counters and using ten was night and day.
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@peer_review_pat · 6mo ago
Did it with twelve one cent coins. She got there herself in about five minutes and then made up two more comparisons to test me.
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