Competition · AMC preparation · step 4 of 4
AMC 8 · 2014 · #10
Grade 4 arithmeticPick an answer.
AMC 8 2014 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The years 1985, 1986, 1987, … form a simple pattern — one contest per year, going up by 1 each time. Tool #5 (Look for a Pattern) turns "the seventh AMC 8" into a year by counting six steps forward from 1985. Tool #7 (Identify Subproblems) keeps the work tidy by splitting the question into two clean pieces: (a) find the year of the seventh contest, then (b) subtract Samantha's age to get her birth year. Algebra (tool #13) is overkill here — a Grade 4 pattern + subtraction is enough.
List the contest years
List the contest years — each goes up by 1, so the n-th AMC 8 lands in 1985 + (n - 1).
Writing out the first few terms makes the rule obvious: add 1 each step. This is the Grade 4 "generate and analyze patterns" move.
The seventh AMC 8 was held in 1991, six years after the first one in 1985.
▸ Why?
The contest years form the unbroken run 1985, 1986, 1987, …, and the seventh year in that run is 1991.
▸ Why?
The contest is held once every year with no year skipped, so each year pairs with exactly one contest and each next contest sits exactly one year later.
▸ Why?
The seventh year of the run is six years past 1985, because seven years standing in a row have six one-year gaps between them.
▸ Why?
Adding those six years to 1985 gives 1991, where the ones 5 and 6 make eleven and ten of those ones bundle up into the next place.
Check with the year formula
Put n = 7: the seventh contest is 6 years after the first, so it falls in 1991.
Adding 6 to a four-digit year is the Grade 4 "fluently add multi-digit whole numbers" skill.
4.NBT.B.4Look For A PatternSubtract her age
Samantha turned 12 in 1991, so subtract her age: 1991 - 12 gives her birth year.
Splitting the question into "find the year, then find the age" is the Tool #7 subproblems move; the subtraction itself is standard Grade 4 arithmetic.
4.NBT.B.4Identify SubproblemsMatch against the choices
Match the birth year to the answer choices.
Reading the choice list is the final "close the subproblem" check.
4.NBT.B.4Identify SubproblemsThis AMC 8 problem only needs Grade 4 skills — counting up by 1 to spot a year pattern, then a single subtraction — that you already know!
- List the contest years
- Check with the year formula
- Subtract her age
- Match against the choices
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