AMC 10 · 2013 · #2
Grade 4 geometry-2dPick an answer.
AMC 10 2013 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The units carry the whole problem: steps become feet, feet by feet become square feet, and pounds-per-square-foot times square feet becomes pounds. Tool #8 (Analyze the Units) keeps that chain straight so no conversion is skipped. Tool #7 (Identify Subproblems) splits the work into three clean steps — convert, find area, apply the rate. Tool #3 (Eliminate Possibilities) flags the built-in trap: stopping at the area 1200 (choice (D)) means forgetting the half-pound rate.
Convert steps to feet
Each step is 2 feet, so 15×2 and 20×2 make the sides 30 feet by 40 feet.
Multiplying the number of steps by the feet in one step turns a step-count into a real length.
4.NBT.B.5Analyze The UnitsFind the garden's area
A rectangle's area is length times width, so 30×40 gives 1200 square feet.
Length times width tiles the rectangle with unit squares, and each square foot is one unit of yield.
Length times width tiles the rectangle with unit squares, and each square is one unit of yield.
▸ Why?
Multiplying is exactly counting equal rows of squares, so the tiling count falls out at once.
▸ Why?
Each square foot yields the same fixed amount, so the yield attaches to the square itself.
Apply the yield rate
Half a pound per square foot halves the area: 600 pounds, choice (A) — 1200 is the trap.
Half a pound for each square foot means the total pounds is just half the number of square feet.
4.NF.B.4Eliminate PossibilitiesMatch your units before you multiply: turn steps into feet, then feet into square feet, and only then apply the pounds-per-square-foot rate.
- Convert steps to feet
- Find the garden's area
- Apply the yield rate