AMC 10 · 2018 · #1
Grade 3 arithmeticPick an answer.
AMC 10 2018 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The pan is a physical rectangle sliced into a neat grid of equal squares, so Tool #1 (Draw a Diagram) turns the words into a picture you can count: rows and columns of little squares. Tool #7 (Identify Subproblems) splits the one hard question into two easy ones — how many pieces fit along the 20-inch side, and how many fit along the 18-inch side — and the grid picture shows the total is just rows times columns. This is faster and more honest than reaching for area division, because the array makes the multiplication obvious.
Picture the pan as a grid
Slice the pan into equal 2-inch squares — the cuts form a grid, so the question is just 'how many squares fill the grid?'
Cutting a rectangle into equal squares makes a grid, and counting squares in a grid is something you can see at a glance.
3.MD.C.6Draw A DiagramCount pieces along each side
Line pieces along each side separately: 20 ÷ 2 = 10 along the long side, 18 ÷ 2 = 9 along the short side. The grid is 10 by 9.
Lining up 2-inch squares along a side is the same as asking how many 2s are in that length — a division.
3.OA.A.2Identify SubproblemsMultiply rows by columns
A 10-by-9 grid holds 10 × 9 = 90 squares, since each of the 9 rows has 10 pieces. That's choice (A).
In any rectangular array, the total count is rows times columns — you don't have to count one by one.
3.OA.A.1Draw A DiagramCut a rectangle into equal squares and it becomes a grid — count how many fit across and how many fit down, then multiply.
- Picture the pan as a grid
- Count pieces along each side
- Multiply rows by columns
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