Reasoning · Grade 2-1 Making Shapes
Problem
One cut splits the square into two pieces, and there are three ways to draw it.
Trying the easier one-cut version first shows me exactly which shapes a straight line can carve, so two cuts is just combining two of these.
2.G.A.1Solve An Easier Related ProblemTwo parallel cuts make three strips: 3 quadrilaterals.
Two parallel lines never meet, so every piece keeps 4 right-angle corners just like the original square's edges.
2.G.A.1Draw A DiagramTwo parallel cuts across the square leave three pieces, and every one of them still has four right-angled corners.
Two parallel cuts can never cross each other, so they can only stack the square into strips rather than carving it into corners.
The three strips fill the square with no gap and no overlap, so together they are the whole square cut up and nothing has been lost.
Two cuts crossing like a plus give 4 quadrilaterals.
Two lines that cross divide the square into 4 parts, and because the cuts run side-to-side each part still has square-style corners.
2.G.A.2Make A Systematic ListSnipping two opposite corners leaves 2 triangles and 1 hexagon.
Each corner snip removes a 3-sided triangle; the leftover keeps the square's other two corners plus the four new cut-corners, giving 6 sides.
2.G.A.1Draw A DiagramAll five sets differ, so every new way counts.
Comparing the shape-name-and-count lists side by side is exactly the rule the problem gives for 'same vs different.'
2.G.A.1Make A Systematic ListJust two straight snips on a square can give 3 four-sided pieces, four four-sided pieces, or even two triangles and a six-sided piece -- counting the sides of each piece is all the Grade 2 shape sense you need!