AMC 10 · 2024 · #1
Grade 4 arithmeticPick an answer.
AMC 10 2024 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The problem is a position-on-a-line picture: one fixed person, some people to the left, some people to the right. Tool #1 (Draw a Diagram) makes that picture explicit — sketch L L L ... L | P | R R R ... R and the count becomes visible. Tool #7 (Identify Subproblems) cleanly splits the line into three independent pieces — left of the person, the person themselves, right of the person — so we can count each piece and add.
Sketch the line in three labeled pieces — people on the left, the named person, people on the right — so the total is just their sum.
Kindergarten position words — left of, beside, right of — are exactly what the problem describes, and a quick sketch turns the words into something countable.
K.G.A.1Draw A DiagramCount the left side — being 1013th from the left leaves 1012 people before this person.
If you are number 1013 in a counted-from-1 line, 1012 people came before you — a one-step word-problem subtraction within Grade 2 reach.
2.OA.A.1Identify SubproblemsCount the right side — being 1010th from the right leaves 1009 people after this person.
Same idea on the other side: the 1010th-from-right has 1009 people to their right.
2.OA.A.1Identify SubproblemsAdd the three pieces — 1012 + 1 + 1009 — to reach 2022, the whole line.
Combining three disjoint groups is the addition principle of counting; the four-digit sum is exactly the Grade 4 multi-digit addition fluency.
4.NBT.B.4Identify SubproblemsThis AMC 10 problem only needs Grade 4 multi-digit addition (and one careful subtract-1 from position counting) that you already know!