AMC 8 · 2015 · #1
Easy mode Grade 5Problem
Picture a rectangular room. The floor is 12 feet long and 9 feet wide.
Onkon wants to cover the whole floor with red carpet. Carpet stores sell carpet by the square yard, not the square foot.
Remember: 1 yard is the same as 3 feet.
How many square yards of red carpet does Onkon need?
Pick an answer.
AMC 8 2015 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Try it yourself first — the explanation is most useful after you’ve attempted it.
Toolkit + CCSS Solution
Understand
Restated: Onkon's room floor is a rectangle that measures $12$ feet long and $9$ feet wide. He wants to cover the whole floor with red carpet, but carpet is sold in square yards, not square feet. Using the fact that $3$ feet $= 1$ yard, how many square yards of carpet does he need?
Givens: Floor is a rectangle: $12$ feet long, $9$ feet wide; Unit conversion: $3$ feet $= 1$ yard; Answer choices: (A) $12$, (B) $36$, (C) $108$, (D) $324$, (E) $972$ (square yards)
Unknowns: The floor's area in square yards
Understand
Restated: Onkon's room floor is a rectangle that measures $12$ feet long and $9$ feet wide. He wants to cover the whole floor with red carpet, but carpet is sold in square yards, not square feet. Using the fact that $3$ feet $= 1$ yard, how many square yards of carpet does he need?
Givens: Floor is a rectangle: $12$ feet long, $9$ feet wide; Unit conversion: $3$ feet $= 1$ yard; Answer choices: (A) $12$, (B) $36$, (C) $108$, (D) $324$, (E) $972$ (square yards)
Plan
Primary tool: #8 Analyze the Units
Secondary: #1 Draw a Diagram
The trap of this problem is units: the dimensions come in feet but the answer must be in square yards. Tool #8 (Analyze the Units) keeps the bookkeeping honest — convert each side from feet to yards first ($12$ ft $= 4$ yd, $9$ ft $= 3$ yd), then multiply to get area in square yards. Tool #1 (Draw a Diagram) helps younger solvers see why the answer is $12$ and not $108$: sketching the $4$-yd by $3$-yd rectangle and tiling it with $1$-yd squares shows exactly $12$ tiles, making the unit conversion concrete instead of abstract.
Execute — Answer: A
5.MD.A.1 Step 1 - Convert each side from feet to yards using $3$ feet $= 1$ yard.
- Divide each length by $3$.
💡 Dividing feet by (feet per yard) cancels the "feet" unit and leaves "yards" — a Grade 5 measurement conversion.
3.MD.C.7 Step 2 - Sketch the floor as a $4 \text{ yd} \times 3 \text{ yd}$ rectangle and split it into $1 \text{ yd} \times 1 \text{ yd}$ squares.
- The grid has $4$ columns and $3$ rows of unit squares.
💡 Tiling a rectangle with unit squares and counting them is the Grade 3 visual definition of area.
4.MD.A.3 Step 3 - Apply the rectangle area formula with both sides already in yards.
- The product gives area directly in square yards.
💡 Multiplying yards by yards produces square yards — the units track the geometry exactly.
5.MD.A.1 Convert each side from feet to yards using $3$ feet $= 1$ yard. Divide each leng 3.MD.C.7 Sketch the floor as a $4 \text{ yd} \times 3 \text{ yd}$ rectangle and split it 4.MD.A.3 Apply the rectangle area formula with both sides already in yards. The product g Review
Reasonableness: Cross-check by computing in square feet first: $12 \times 9 = 108$ square feet. Since $1$ square yard $= 3 \text{ ft} \times 3 \text{ ft} = 9$ square feet, the floor is $108 \div 9 = 12$ square yards. Same answer, $\textbf{(A)}$. The trap answer $108$ appears as choice (C), which is the result if a solver forgets to convert. The other choices ($36$, $324$, $972$) come from dividing or multiplying by $3$ instead of $9$ — clear sign that the units must be tracked carefully.
Alternative: Tool #1 (Draw a Diagram) alone solves the problem: draw the $4 \text{ yd} \times 3 \text{ yd} = 12$ feet by $9$ feet rectangle, slice it into $3 \text{ ft} \times 3 \text{ ft}$ squares (each $= 1$ square yard). The grid has $4 \times 3 = 12$ such squares, so the answer is $12$ square yards. No formula needed beyond "count the tiles."
CCSS standards used (min grade 5)
3.MD.C.7Relate area to the operations of multiplication and addition (Visualizing the floor as a grid of $1$-yard unit squares and counting $4 \times 3 = 12$ tiles to get the area.)4.MD.A.3Apply the area and perimeter formulas for rectangles in real-world and mathematical problems (Using $\text{Area} = \text{length} \times \text{width}$ to compute $4 \text{ yd} \times 3 \text{ yd} = 12$ square yards.)5.MD.A.1Convert among different-sized standard measurement units within a given system (Converting $12$ ft to $4$ yd and $9$ ft to $3$ yd using the given relationship $3$ ft $= 1$ yd before computing the area.)
⭐ This AMC 8 problem only needs Grade 5 unit conversion plus the Grade 4 rectangle area formula you already know!
⭐ This AMC 8 problem only needs Grade 5 unit conversion plus the Grade 4 rectangle area formula you already know!
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