AMC 10 · 2018 · #1
Easy mode Grade 3Kate bakes a pan of cornbread shaped like a rectangle. It is 20 inches long and 18 inches wide. She cuts it into small squares. Each square is 2 inches on every side. How many squares does she get?
Pick an answer.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: A rectangular pan of cornbread is $20$ inches long and $18$ inches wide. It is cut into small square pieces, each $2$ inches on a side. The question asks how many of those square pieces the whole pan is cut into.
Givens: The pan is a $20$-inch by $18$-inch rectangle; Each piece is a $2$-inch by $2$-inch square; The cuts run straight across, so the pieces tile the pan with no gaps or overlaps; Answer choices: (A) $90$, (B) $100$, (C) $180$, (D) $200$, (E) $360$
Unknowns: The total number of $2\times 2$ pieces in the pan
Understand
Restated: A rectangular pan of cornbread is $20$ inches long and $18$ inches wide. It is cut into small square pieces, each $2$ inches on a side. The question asks how many of those square pieces the whole pan is cut into.
Givens: The pan is a $20$-inch by $18$-inch rectangle; Each piece is a $2$-inch by $2$-inch square; The cuts run straight across, so the pieces tile the pan with no gaps or overlaps; Answer choices: (A) $90$, (B) $100$, (C) $180$, (D) $200$, (E) $360$
Plan
Primary tool: #1 Draw a Diagram
Secondary: #7 Identify Subproblems
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.
Execute — Answer: A
3.MD.C.6 Step 1 Picture the pan as a grid
- Draw the pan as a rectangle and slice it into equal $2$-inch squares.
- The cuts make a grid: each little square is exactly one piece, lined up in rows and columns.
- Now the question is just 'how many squares are in this 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.OA.A.2 Step 2 Count pieces along each side
- Find how many $2$-inch pieces fit along each side separately.
- Along the $20$-inch side, the pieces fit $20 \div 2 = 10$ times.
- Along the $18$-inch side, they fit $18 \div 2 = 9$ times.
- So the grid is $10$ columns wide and $9$ rows tall.
💡 Lining up $2$-inch squares along a side is the same as asking how many $2$s are in that length — a division.
3.OA.A.1 Step 3 Multiply rows by columns
- A grid that is $10$ across and $9$ down holds $10 \times 9$ squares in all, because each of the $9$ rows contains $10$ pieces.
- That gives $90$ pieces, which is choice (A).
💡 In any rectangular array, the total count is rows times columns — you don't have to count one by one.
3.MD.C.6 Draw the pan as a rectangle and slice it into equal $2$-inch squares. The cuts m 3.OA.A.2 Find how many $2$-inch pieces fit along each side separately. Along the $20$-inc 3.OA.A.1 A grid that is $10$ across and $9$ down holds $10 \times 9$ squares in all, beca Review
Reasonableness: Cross-check using area. The pan covers $20 \times 18 = 360$ square inches, and each piece covers $2 \times 2 = 4$ square inches, so the number of pieces is $360 \div 4 = 90$. Same answer (A). It also makes sense that $90$ is the smallest choice: the bigger options like $200$ or $360$ would require pieces smaller than $2\times 2$, so they are too large to be right.
Alternative: Tool #3 (Eliminate Possibilities): each piece is $4$ square inches, so the piece count must divide the total area of $360$. Choice (E) $360$ would mean each piece is $1$ square inch, and (D) $200$ doesn't even divide $360$ evenly — both can be ruled out by a quick area sanity check, leaving the small grid count $90$.
CCSS standards used (min grade 3)
3.MD.C.6Measure areas by counting unit squares (Seeing the cut pan as a grid of equal $2$-inch unit squares, where each square is one piece to be counted.)3.OA.A.2Interpret whole-number quotients of whole numbers (Dividing each side length by the piece size, $20 \div 2 = 10$ and $18 \div 2 = 9$, to count pieces along each edge.)3.OA.A.1Interpret products of whole numbers as total number of objects in groups (Multiplying rows by columns, $10 \times 9 = 90$, to get the total number of pieces in the rectangular array.)
⭐ Cut a rectangle into equal squares and it becomes a grid — count how many fit across and how many fit down, then multiply.
⭐ Cut a rectangle into equal squares and it becomes a grid — count how many fit across and how many fit down, then multiply.
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