AMC 10 · 2013 · #2
Grade 4 geometry-2dPick an answer.
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
The paces convert to real lengths.
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
Multiplying gives the area.
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?
Rows of equal length repeated down the width is a count of equal groups, which multiplying records.
▸ Why?
Each square foot yields the same fixed amount, so the harvest is a count of squares times that rate.
Apply the yield rate
The rate turns it into 600, choice (A).
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