AMC 8 · 2010 · #5
Grade 6 arithmeticPick an answer.
AMC 8 2010 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
Every length in this problem is a vertical distance, so the entire problem is a single one-dimensional sum: stool + Alice + overhead reach = floor-to-bulb height. Tool #8 (Analyze the Units) is the gating move because the data is mixed in meters and centimeters; converting everything to cm first makes the arithmetic trivial. Tool #7 (Identify Subproblems) then splits the calculation into two small targets — (a) the bulb's height above the floor, and (b) Alice's reach without the stool — so the final equation reduces to one subtraction.
Put everything in one unit: the 2.4 m ceiling is 240 cm and Alice's 1.5 m height is 150 cm; 10 cm and 46 cm already fit.
Converting m to cm inside the metric system is exactly the Grade 5 "convert standard measurement units" standard.
5.MD.A.1Analyze The UnitsSubproblem (a): the bulb hangs 10 cm below the 240 cm ceiling, so its height above the floor is 230 cm.
Reading "10 cm below the ceiling" as a subtraction is the standard Grade 4 distance word-problem move.
4.MD.A.2Identify SubproblemsSubproblem (b): Alice's floor reach is height plus overhead, 150 cm + 46 cm = 196 cm.
Stacking two vertical lengths (her body, then her arm above her head) is a Grade 4 length word-problem skill.
4.MD.A.2Identify Subproblems"Just reaches" means stool + reach = bulb height, so s + 196 = 230.
Translating "just reaches" into a one-variable equation is Grade 6 expression-and-equation work.
6.EE.B.7Identify SubproblemsSubtract 196 from both sides: s = 230 - 196 = 34 cm, choice (B).
Inverse operations on a one-step equation give the stool height directly.
6.EE.B.7Analyze The UnitsOnce every length is in the same unit, this AMC 8 problem is just one Grade 6 equation: s + 196 = 230.