AMC 10 · 2022 · #1
Grade 6 arithmeticPick an answer.
The expression has two separate halves joined by a minus sign, and each half has an inner ◆ that must be done first. Tool #7 (Subproblems) says: compute the left half on its own, compute the right half on its own, then subtract. The order-of-operations rule plus the absolute-value definition do all the work — no algebra needed. Tool #3 (Eliminate) is the multiple-choice safety net: once we have a numerical value, we read off the matching letter.
Inside the left grouping
Start inside the parentheses.
Absolute value is just the distance between two numbers — Grade 6 "ordering and absolute value" on a number line.
An absolute value is just the distance between two numbers on the number line.
▸ Why?
A difference measures the gap between two numbers, and the bars throw away which way it points.
▸ Why?
Which number is larger decides the sign, and dropping the sign is exactly what leaves the distance.
Finish the left grouping
The left side comes out zero.
Substitute the inner result back in, then evaluate — Grade 5 "use parentheses and evaluate numerical expressions".
5.OA.A.1Identify SubproblemsInside the right grouping
Start inside on the right too.
Same distance idea — 1 and 2 are 1 apart.
6.NS.C.7Identify SubproblemsFinish the right grouping
The right side gives a different value.
Plug the inner result back in and evaluate the outer ◆ — the parentheses tell us this is the last step.
5.OA.A.1Identify SubproblemsSubtract the two
Subtracting gives negative two.
Going from 0 down by 2 lands at -2 — Grade 6 "positive and negative numbers describe quantities".
6.NS.C.5Eliminate PossibilitiesThis AMC 12 problem only needs Grade 6 "absolute value is just the distance between two numbers" — once you read the parentheses carefully, the two halves come out to 0 and 2, and the difference is -2.