Tile and Cut Figures with Congruent Pieces
A region is cut into, or built from, congruent pieces; the piece count, a side length, or the total area follows from how the copies fit. Learners recover a side from the number of cut pieces, count grid cards, identify tiling pieces and area, and read a base shape from solid views. It links multiplication and division to spatial structure.
grade 2–4 GeometryMeasurement & dataOperations Draw a DiagramVisualize Spatial Relationships
Progression (5)
g3 1. Cut a rectangle into a grid of cards GeometryMeasurement & data
g4 2. Base perimeter from multiple views Measurement & dataGeometry
g3 3. Recover side length from number of cut pieces OperationsMeasurement & data
g4 4. Count distinct shapes built by adding congruent tiles Geometry
g4 5. Identify tiling pieces and total area GeometryMeasurement & data
Bridges to competition (7)
Reasoning problems that extend this idea toward competition:
Rectangle side and perimeter from equal squares Invariant
Side length of a square from fitted figures Logic
Count ways to tile with one piece Shape enumeration
Tile a rectangle with distinct pieces Shape enumeration
Count distinct shapes from joined pieces Shape enumeration
Divide a shape with straight cuts Shape enumeration
Split a rectangle into product tiles Shape enumeration