Reasoning · Grade 2-1 Large and Small Shapes
Problem
The two X squares give 8 and the single diagonal 2, so the smallest pieces number 10.
Composing and decomposing a square with its diagonals is exactly the 'put shapes together / take them apart' idea from early geometry.
K.G.B.6Make A Systematic ListJoining two pieces gives 4 per X square, so 8.
Recognizing when two right triangles combine into a larger triangle (vs. a square) is reading the shape's attributes.
2.G.A.1Make A Systematic ListUsing the top-left diagonal as a side, two triangles span squares: 2.
Breaking a medium triangle into the small pieces it covers (a subproblem) lets me count its 'size' reliably.
2.G.A.1Identify SubproblemsBelow the big diagonal is one 4-piece triangle, above it one of 6, and none uses 5.
Tracing the longest drawn diagonal shows the two largest triangles and lets me count the pieces inside each.
K.G.B.6Make A Systematic ListAdding every group: 10 + 8 + 2 + 1 + 0 + 1 = 22.
Adding the counts from each size group is a quick within-20-style sum; organizing first means nothing is missed or counted twice.
2.OA.B.2Make A Systematic ListGrouping the triangles by how many smallest pieces each covers counts every triangle exactly once.
Each triangle covers one definite number of the smallest pieces, so it belongs to exactly one size group.
A bigger triangle is exactly the smallest pieces inside it put together, which is what makes counting those pieces a fair measure of its size.
Sort the triangles by how many tiny pieces each one uses, count one group at a time, then add. That careful list keeps you from missing any or counting the same one twice!