Reasoning · Grade 2-2 Rules and Problem Solving
Problem
Each inscribed square cuts 4 corner triangles.
Drawing one square with its midpoint diamond lets a child see and count the 4 little corner triangles directly.
2.G.A.1Draw A DiagramSo the figures run 4, 8, 12.
Looking at the small cases first turns a hard 9th-figure question into easy counting we can actually do.
2.NBT.A.2Solve An Easier Related ProblemSkipping by 4, figure n holds 4 × n.
Adding the same 4 over and over is exactly skip-counting by 4, which is repeated addition (multiplication).
3.OA.A.1Look For A PatternEach new inscribed square adds the same 4 corner triangles, so the totals go up by 4 every time.
Adding the same 4 over and over is counting equal groups of four, which is exactly what multiplying by four does.
Because the step from one figure to the next never changes, any figure is the first total plus that step repeated.
Figure 9 gives 4 × 9 = 36.
Once we know it grows by 4 each time, the 9th total is just nine groups of 4.
3.OA.C.7Look For A PatternEach step quietly adds 4 triangles, so the 9th figure is just 9 groups of 4 -- Grade 3 times tables finish it!