AMC 8 · 2011 · #5
Grade 4 arithmeticPick an answer.
AMC 8 2011 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The given quantity is in minutes but the answer mixes days, hours, and minutes, so the work is a unit-conversion cascade — exactly Tool #8 (Analyze the Units). Tool #7 (Identify Subproblems) splits the single "add 2011 minutes" task into three clean subproblems: (a) convert 2011 minutes into hours plus leftover minutes, (b) convert the resulting hours into days plus leftover hours, (c) place the leftover hours and minutes on the clock starting at midnight. Each subproblem is just division with remainder.
1 hour = 60 minutes, so divide 2011 by 60: quotient = hours, remainder = leftover minutes, giving 2011 min = 33 hr 31 min.
Trading 60 minutes for 1 hour is the standard minutes-to-hours conversion taught in Grade 4.
4.MD.A.1Analyze The Units1 day = 24 hours, so divide 33 by 24: quotient = days, remainder = leftover hours, giving 33 hr = 1 day 9 hr.
Finding a whole-number quotient and remainder when dividing 33 by 24 is the Grade 4 division-with-remainder skill.
4.NBT.B.6Analyze The UnitsAssemble the three pieces into one total elapsed time: 1 day 9 hr 31 min, ready to add to the start in a single move.
Splitting the trip into "days", "hours", and "minutes" subproblems is the Tool #7 subproblems move, and assembling the parts is the Grade 4 multi-step word-problem skill.
4.OA.A.3Identify SubproblemsAdd to the start: Jan 1, 12{:}00 AM + 1 day = Jan 2, 12{:}00 AM; then + 9 hr 31 min = Jan 2, 9{:}31 AM → (D).
Adding elapsed time to a clock and rolling the date over at midnight is the Grade 3 elapsed-time skill.
3.MD.A.1Identify SubproblemsThis AMC 8 problem is just two Grade 4 divisions (2011 ÷ 60, then 33 ÷ 24) and adding the leftovers to a clock — you can already do it!
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