# Board Block

## Problem

You can play this game for two players on the interactive pegboard, or on a real circular pegboard if you have one. Or you could print off sheets of circles from this page.**How to play:**

Firstly, choose the number of pegs on your board. Six might be a good choice to start with and you could print off this sheet of pegboards with six pegs if you are not using the interactivity.

Take it in turns to add a band to the board.

Bands must fit round three pegs, in other words, each must make a triangle.

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

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

**Try playing, several times.**

**Did you find any good ways to win, in other words, any winning strategies?** We would love to hear about them.

Once you've mastered this game, why not play to lose?

You might like to extend the game - have a look at this for a more challenging version.

## Student Solutions

As this is a game, there is no solution in the same way that other challenges have solutions.

However if you work out a strategy for winning, or if you work out what might be important to think about when trying to win, it would be good to hear about it.

## Teachers' Resources

#### Why play this game?

This game combines higher-order thinking (in terms of developing a strategy) while reinforcing the properties of a triangle. It is a great context in which to encourage learners to re-think an approach when what they have tried doesn't work. You may like to read our Let's Get Flexible with Geometry article to find out more about developing learners' mathematical
flexibility through geometry.

#### Possible approach

It might be worth simplifying the game to start with so that you have just four pegs on your circular board. Introduce the class to the rules of the game, then challenge them to play against you. Allow time for several games to take place so that everyone really gets to grips with how to play.

Next, invite children to play in pairs. Their aim is to try to beat their partner. You may be able to set this up so that each pair has access to a computer so that they can use the interactivity. If this is not possible, using 'real' circular geoboards would be very helpful. Alternatively, you could print off appropriate sheets from this page.
Here is a sheet of pegboards each with six pegs.

After a suitable length of time, bring everyone together to discuss progress. Has anyone found a good way of winning? Is it better to go first or second in this game? Encourage learners to explore the game more so that they try to come up with a strategy that always works.

In the plenary you could challenge a pair or group to beat you and then articulate how they knew they were going to win.

#### Key questions

What triangle could you make first?

What *could* you do next?

Could you have done something different to start with?

Could you have done something different then?

Is it better to go first or second? Why?

#### Possible extension

Children could be challenged to play the game on a geoboard with more pegs. How does this affect the game?

Board Block Challenge offers more ideas for children to explore.

#### Possible support

Playing the game on a print-out of the geoboard might help children as they will then have a record of the moves they made (see this page). They could then refer back to previous games more easily and refine their strategies.