AMC 8 · 2025 · #5
Grade 3 geometry-2d
Pick an answer.
AMC 8 2025 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The map is already a diagram, so Tool #1 (Draw a Diagram) just asks us to use it — read the position of each point by counting blocks right and up from the corner. Because the streets form a grid, the shortest path between any two labeled points is simply (horizontal blocks between them) + (vertical blocks between them); there is no benefit to zig-zagging. Tool #7 (Identify Subproblems) then splits the loop into four independent legs F → A, A → B, B → C, C → F. Solve each tiny leg by counting, then add the four numbers.
Read each labeled point off the grid: F = (6, 5), A = (7, 3), B = (0, 0), C = (2, 4).
Describing where something is on the grid using right/up counts is Kindergarten position language.
K.G.A.1Draw A DiagramOn a grid the shortest leg is (horizontal blocks apart) + (vertical blocks apart); split the loop into four legs (Tool #7).
Adding side-distances to get a path length on a grid is the same idea as finding perimeter pieces in Grade 3.
3.MD.D.8Identify SubproblemsLeg F → A: 1 block right and 2 blocks down, so 3 blocks.
Just counting blocks across and down and adding them is a Grade 2 addition word problem.
2.OA.A.1Draw A DiagramLeg A → B: 7 blocks left and 3 blocks down, so 10 blocks.
Counting blocks across and down, then adding, is still Grade 2 arithmetic.
2.OA.A.1Draw A DiagramLeg B → C: 2 blocks right and 4 blocks up, so 6 blocks.
Same idea: count across, count up, add.
2.OA.A.1Draw A DiagramLeg C → F: 4 blocks right and 1 block up, so 5 blocks.
One more across-and-up count, then add.
2.OA.A.1Draw A DiagramAdd the four legs: 3 + 10 + 6 + 5 = 24 blocks, which matches choice (C).
Summing four small numbers fluently is Grade 3 add-within-1000.
3.NBT.A.2Identify SubproblemsThis AMC 8 problem only needs Grade 3 addition and the idea of "path length around a shape" you already know!
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