### Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

### Seven Sticks

Explore the triangles that can be made with seven sticks of the same length.

### Three Fingers and a Loop of String

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

# Board Block

## Board Block

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.

#### 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 pageHere 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?