Reasoning · Grade 3-1 Meaning of Fractions
Problem
The quarters grid makes four small triangles, the thirds grid three parts.
Carefully drawing the overlay shows the green is a tall four-sided region, not a single grid cell, so I must not stop at the first small piece.
3.G.A.2Draw A DiagramThe smallest piece holding both is 1/24.
Using one tiny shared unit turns a messy overlapped picture into simple counting of equal tiny pieces.
3.NF.A.1Identify SubproblemsChoosing one tiny piece that both grids agree on turns the messy overlap into plain counting of equal pieces.
A fraction names how many equal pieces of one whole you have, so a shared piece size is what lets both grids be read as fractions at once.
The green region is exactly the tiny pieces inside it put together, so counting those pieces measures it with nothing lost.
The shading takes 3 units above and 2 below — 5 units.
Adding the upper half-quarter and the lower sliver counts the whole green shape instead of only its top piece.
3.NF.A.1Make A Systematic ListFive out of twenty-four is 5/24.
If every piece I name adds up to exactly one whole, I can trust I read the overlapped picture correctly.
3.NF.A.1Make A Systematic ListMeasure both grids in tiny 1/24 pieces, then count: the green covers 5 of them, so it is 5/24 - all Grade 3 equal-share thinking!