Competition · AMC preparation · step 4 of 4
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.
Turn minutes into hours
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.
The 2011 minutes are the same length of time as 33 hours and 31 minutes.
▸ Why?
One hour is always exactly 60 minutes, so every full group of 60 minutes can be renamed as one hour and whatever is left over stays counted in minutes.
▸ Why?
The 2011 minutes hold exactly 33 whole groups of 60 with 31 minutes left over, that is 2011 = 60 × 33 + 31.
▸ Why?
Thirty-three hours is 33 equal groups of 60 minutes, and 33 such groups come to 60 × 33 = 1980 minutes.
▸ Why?
The 1980 minutes packed into those whole hours and the 31 minutes left loose fit together with no gap and no overlap, so they add back to all 2011 minutes.
Turn hours into days
1 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 UnitsCombine the elapsed time
Assemble 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 the time to the start
Add 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!
- Turn minutes into hours
- Turn hours into days
- Combine the elapsed time
- Add the time to the start
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