← Sensim Lab Sensim Math

AMC 8 · 2015 · #1

Easy mode Grade 5
📗 View original problem →

Problem

Picture a rectangular room. The floor is 1212 feet long and 99 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: 11 yard is the same as 33 feet.

How many square yards of red carpet does Onkon need?

(A) 12(B) 36(C) 108(D) 324(E) 972\textbf{(A) }12\qquad\textbf{(B) }36\qquad\textbf{(C) }108\qquad\textbf{(D) }324\qquad \textbf{(E) }972

Pick an answer.

(A)
12
(B)
36
(C)
108
(D)
324
(E)
972
View mode:

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

#8 Analyze the Units 5.MD.A.1 Step 1
  • Convert each side from feet to yards using $3$ feet $= 1$ yard.
  • Divide each length by $3$.
$$12 \text{ ft} \div 3 \tfrac{\text{ft}}{\text{yd}} = 4 \text{ yd}, \quad 9 \text{ ft} \div 3 \tfrac{\text{ft}}{\text{yd}} = 3 \text{ yd}$$

💡 Dividing feet by (feet per yard) cancels the "feet" unit and leaves "yards" — a Grade 5 measurement conversion.

#1 Draw a Diagram 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.
$$4 \text{ columns} \times 3 \text{ rows} = 12 \text{ unit squares}$$

💡 Tiling a rectangle with unit squares and counting them is the Grade 3 visual definition of area.

#8 Analyze the Units 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.
$$\text{Area} = 4 \text{ yd} \times 3 \text{ yd} = 12 \text{ yd}^2 \;\Rightarrow\; \textbf{(A)}$$

💡 Multiplying yards by yards produces square yards — the units track the geometry exactly.

[1] #8 5.MD.A.1 Convert each side from feet to yards using $3$ feet $= 1$ yard. Divide each leng
[2] #1 3.MD.C.7 Sketch the floor as a $4 \text{ yd} \times 3 \text{ yd}$ rectangle and split it
[3] #8 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.7 Relate 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.3 Apply 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.1 Convert 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!

More like this

Same archetype — closest grade level first.