AMC 10 · 2018 · #1
Grade 3 arithmeticPick an answer.
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
See the pan as a grid.
Cutting a rectangle into equal squares makes a grid, and counting squares in a grid is something you can see at a glance.
Cutting a rectangle into equal squares makes a grid, and a grid's count is rows times columns.
▸ Why?
Equal rows repeated down the side is a count of equal groups, which multiplying records.
▸ Why?
How many squares fit along a side is just how many times the square's side goes into that length.
Count pieces along each side
Count the pieces along each side.
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
Rows times columns gives 90.
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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