# Networks Years 4 - 8

A game for two (2) players and art to create.

### Preparation

• Print this Playing Board.
• Print this set of tiles.
On thin card is best, but paper will do.
• Cut out the separate tiles for one set.
• Find a ruler and pencil for later.
• Markers or pencils for colouring.
• A compass or other method of drawing circles or part circles (optional).

### Networks: The Game

This is a game for two players. To start you need six (6) of each type of tile spread out face up where you can both reach them.
• The rules are on this Networks Starter.
You can read it on screen or print it.
• Play the game as many times as you want just for fun.
You are trying to make a network from Start to Finish.
• Do Challenge 1 when you are ready.
Come back here before you start Challenge 2.
Have fun exploring Networks.

Watch her You Tube video.
She was only five years old, but she was working like a mathematician.
Perhaps she will give you some ideas about playing the game.

Preparing for Challenge 2
Challenge 2 asks you to write a paragraph and use diagrams to help a new player become good at the game.
• What is the smallest number of moves to get from Start to Finish?
• If a player makes a move up the board, or to the left of the last tile, what does that do to the total number of moves in the game?
• There are two types of tiles. What is different about the way they can affect your position on the board?
• How many networks can you make from Start to Finish which use the smallest number of tiles?
How do you know when you have found them all?
• Viv and Vin had a hypothesis that the first player should always win. Test their hypothesis. You will have to work together to make sure each person plays the best possible move each time. Remember to think about what could happen an extra move ahead each time.

What happens if...?

• What happens if ... the start position is the curved tile instead of the straight tile?
• What happens if ... Player A uses only one type of tile and Player B uses the other?
• What happens if ... both players start with six cards (three of each type), shuffle them, stack them face down and have to play with their top card?
• What happens if ... all twelve (12) cards are shuffled and spread face down?
Players have to play with the tile they pick up.
If you can play, you must play, even if you lose.
If you can't play you miss a turn.
• What happens if ... you design one more tile?
Lines and curves can only touch the corners and midpoints of the square.
For example:

Use this template to design your own tile.

• What happens if ... you play a new version of Networks with four of your new tiles and four each of the other two?
Still a total of twelve tiles.

### Networks: Tiling Patterns

Networks in mathematics are simply lines that join at points.
The lines and the points have special names, but that doesn't matter - they're still just lines that join at points.
• In the Networks game, when the lines were joined our interest was in the pathway that led from Start to Finish.
• In tiling patterns we think of the networks as boundaries and look at the shapes between them.
Square tiles have been used for thousands of years to decorate floors, walls and ceilings with mathematical patterns.
• For this part you will need to cut out the rest of the straight and the curved tiles.
• Later you might want to include more of the tile you designed.

Patterns with half-sides
These tiling patterns have been made using the same tile but repeating it using a different rule. The rule usually involves sliding (also called translation), rotation or reflection.

 Starting top left, what's my rule? Starting top left, what's my rule?

 What happens if you add shading? What happens if you use two different tiles? How was I made?

• Experiment with the straight and curved tiles to make tiling patterns.
• When you get one you love, photograph it.
• Then make another one ... and another one ... and ...
• Make a slide show of your best tiling patterns.
Patterns with third-sides
• Explore this slide show of tiles and tiling patterns that start from a square with the sides marked in thirds.
• The ones with the brown background were designed by teachers in training.
• The other ones were designed by Year 6 students at Camberwell Primary School.
Use this guide sheet to experiment, then create your own tile pattern with at least nine (9) tiles.
• We would love photographs of your creations for the gallery below.

### Just Before You Finish

• Add a speech bubble that tells what you learnt.
• Read your Working Like A Mathematician page again and write two or more sentences explaining how you worked like a mathematician in this activity.