1. Learning outcomes ALL MUST be able to find at least 5 octagon loops (level 3 – 4) MOST SHOULD begin to find simple relationships from their patterns (level 4 – 5) SOME COULD explore relationships set in general terms using algebra. Level (5 – 6)

2. Octagon FLOWER BEDS! Alan Titchmaths (famous celebrity gardener) is designing a new flowerbed for his TV show. Use octagon tiles to make this flowerbed. Paving stones

3. Flower beds – the rules! Edges must touch like this… NOT like this… or this…

4. Flowerbeds – the rules! Each tile must touch two others like this….. NOT like this…

5. Flower beds Use up to 10 tiles. Make different Octagon loops. Display your patterns clearly.

6. Flower beds

7. Not all flower beds have line symmetry. …this one has rotational symmetry. Flower beds

8. Investigation. This pattern uses 6 tiles. It has 10 free edges on the inside. It has 26 free edges on the outside. 26 outside edges 10 inside edges Flower beds

9. Investigation. Count the edges on all your patterns Record all your results in a table. 26 outside edges 10 inside edges Flower beds

10. PatternNo. of tiles Inside edges Outside edges Total edges 14 26 38 410 512 Always even? 4 2024 2610 36 32 48 7244 38 60 16 22 28 n6n 3n + 8 3n - 8 Flower beds

11. Flower beds Alan Titchmaths wants to know how many free edges there will be altogether if he uses 100 tiles! Use your findings to help him. “For 100 tiles you will have have….” 292 + 308 600 free edges