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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Board Block Challenge for Two

**Notes for adults**

This game helps reinforce the properties of different 2D shapes and encourages thinking about strategies.

**Easier version:** play the game on a print-out of the pegboard so that the child can keep a record of the moves they've made.

**Harder version:** encourage the child to change the number of pegs on the board or the amount of shapes which are allowed, and discuss how the winning strategy changes.

After playing the game, try to find a winning strategy and talk together about how this was found. How does this change if you play to lose?

There's a classroom version of this game here.## You may also like

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Age 7 to 11

Challenge Level

- Problem

This is a game to play with an adult!

Before playing this game, you might like to have a go at the simpler version, Board Block for Two.

**How do you play?**

You'll need an adult to play with.

You'll also need a circular pegboard, or the interactivity below:

You can also print off some pegboards from this page.

Firstly, choose the number of pegs on your board.

Decide what shapes you will be allowed to make.

You could allow:

- triangles and quadrilaterals

- triangles, quadrilaterals and pentagons

- triangles, quadrilaterals, pentagons and hexagons

- triangles, quadrilaterals, pentagons, hexagons and...

Take it in turns with the adult to add a band to the board to make any of the shapes you are allowing.

A band can share a peg with other bands, but the shapes must not overlap (except along the edges and pegs).

A player loses when they cannot make a shape on their turn.

For your choice of shapes, how does the winning strategy change as you increase the number of pegs on the board?

If you keep the number of pegs fixed, how does the winning strategy alter as you change the shapes you are permitted to make?

How is the game affected if you play to lose?

This game helps reinforce the properties of different 2D shapes and encourages thinking about strategies.

After playing the game, try to find a winning strategy and talk together about how this was found. How does this change if you play to lose?

There's a classroom version of this game here.

The game uses a 3x3 square board. 2 players take turns to play, either placing a red on an empty square, or changing a red to orange, or orange to green. The player who forms 3 of 1 colour in a line wins.

In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?