Competition · AMC preparation · step 4 of 4
AMC 8 · 2012 · #2
Grade 4 arithmeticPick an answer.
AMC 8 2012 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The rates are in mixed units — births per 8 hours, deaths per day — and the answer wants people per year. Tool #8 (Analyze the Units) lines them up: convert the birth rate into births per day, then per year. Tool #7 (Identify Subproblems) splits the task into three clean pieces — births per day, net change per day, and net change per year — so each step is just one arithmetic move.
Find births per day
A birth every 8 hours means 24 ÷ 8 = 3 births per day.
Dividing hours per day by hours per birth cancels "hours" and leaves "births per day" — a Grade 4 distance/time-style word-problem move.
A birth every 8 hours works out to 3 births in a single day.
▸ Why?
The births keep the same 8-hour spacing all day, so the number born in a day is just how many 8-hour stretches fit into the length of one day.
▸ Why?
One day is a fixed 24 hours — the same bundle of hours every time — so 24 hours is the length we are filling with 8-hour stretches.
▸ Why?
Finding how many equal 8-hour stretches fill 24 hours is exactly 24 divided by 8, because division reverses the multiplication that would stack those equal stretches back up to 24.
Subtract deaths from births
Now both rates are per day, so subtract: 3 - 1 = 2 people per day.
Once both rates share the same time unit (per day), the change is a simple subtraction — Tool #7's subproblem move.
4.OA.A.3Identify SubproblemsScale up to one year
Scale the daily gain to a year: 2 × 365 = 730 people per year.
Multiplying (people/day) by (days/year) cancels "day" and leaves "people/year" — multi-digit multiplication is Grade 4.
4.NBT.B.5Analyze The UnitsRound to the nearest hundred
The tens digit of 730 is 3, below 5, so 730 rounds down to 700.
Rounding multi-digit whole numbers to any place is a Grade 4 number-and-operations standard.
4.NBT.A.3Analyze The UnitsThis AMC 8 problem only needs Grade 4 skills: convert a rate, subtract, multiply, and round!
- Find births per day
- Subtract deaths from births
- Scale up to one year
- Round to the nearest hundred
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