Lesson overview
Learning objectives
- Describe a shape using coordinates.
- Apply translation, rotation and reflection.
- Use area constraints to eliminate impossible packing regions.
Resources
- Printable pentomino sheet
- Squared paper
- Scissors and card where permitted
Starter
Display five joined squares and ask how many genuinely different shapes can be made when rotations and reflections are treated as the same.
Main activity
- Generate pentominoes systematically and agree naming conventions.
- Record one piece as five coordinate pairs relative to an origin.
- Transform the coordinates to rotate or reflect the piece.
- Attempt a 6 × 10 packing, recording failed arrangements rather than erasing the evidence.
- Discuss how a computer could represent the board and test placements.
Plenary
Choose one failed placement and explain how it helped reduce the search space.
Differentiation
Use pre-cut pieces and labelled grids for support. Extend by coding a backtracking solver or proving area constraints for possible rectangles.
Assessment evidence
Coordinate lists, transformed shapes, a packing attempt and an explanation of a systematic strategy.