L3 · Comparing unit fractions
“I can compare unit fractions of the same whole: more equal parts means each part is smaller. I can compare the same fraction of different wholes.”
Two pies are the same size. One pie is split into 2 equal parts. The other is split into 4 equal parts. Which is bigger: 1/2 or 1/4? Step 1: The wholes are the same size, so the comparison is fair. Step 2: The 2-part pie shares the whole between fewer parts - each part gets more. Step 3: 1/2 is bigger than 1/4. More equal parts in the whole means each part is smaller.
A whole split into more equal parts makes each part smaller because:
Two cakes are the same size. One is split into 3 equal parts, one into 6. Which is smaller: 1/3 or 1/6? -> 1/6
"Same-size wholes: 1/5 and 1/9. The whole in ___ parts makes smaller parts, so ___ is smaller." -> 9; 1/9
10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.