L6 · The same fraction of different-sized wholes; representations clinic

Learning goal

“I can explain why the same fraction (like 1/2) can name different AMOUNTS when the wholes are different sizes, and I can move one fraction between strips, groups and the number line.”

Representation — a way of showing a fraction: a strip, a shape, a group of objects, or a point on the number line.

Different-sized wholes — wholes that are not the same size, like a small muffin and a large muffin. The same fraction of each is a different amount.

Worked example

A small muffin is ONE whole. Cut it into 2 equal parts: each part is 1/2 of the small muffin. A large muffin is a DIFFERENT whole. Cut it into 2 equal parts: each part is 1/2 of the large muffin. Both parts are named 1/2 - but they are NOT the same amount. The large muffin's half is much more muffin. The lesson: a fraction name describes a share OF ITS WHOLE. Change the whole, and the same name describes a different amount. That is why L5's comparisons always insisted on the same whole.

Check yourself — explain it

Why is 1/2 of the large muffin more than 1/2 of the small muffin?

Paired problem — example still visible

Cake S is small, Cake L is large. Is 1/4 of Cake L more or less than 1/4 of Cake S? -> More (a fourth of the larger whole is a larger amount)

Faded completion — last step is yours

"1/3 of a big pie vs 1/3 of a small pie: the fraction names are ___, but the amounts are ___." -> the same; different

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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