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Reasoning based on this Japanese activity.

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Line of Four

A game somewhat similar to 'noughts and crosses' on a much larger space.


Stage: 1 and 2 Challenge Level: Challenge Level:1


This is a game for two players.  You will need a copy of the game board.

If you are unable to view the video, here are the rules of the game:

The first player names a 'score' and this is the total that both players try to reach.

The second player places a counter on the board over one of the numbers and says that number.

The first player moves the same counter in any direction along a line segment to a neighbouring number and announces the total of the two numbers.

The second player moves the same counter to cover a neighbouring number, adds on that number, and announces the total of the three numbers.

The players take it in turns to slide the counter to cover a neighbouring number and to add that number to the total. The players must move when it is their turn and no 'jumping' is allowed.

The winner is the player who makes the total to be exactly equal to the 'score' declared at the start. Making the total go above the 'score' loses the game.

Why play this game?

Totality is a very accessible game which offers the opportunity for children to become more fluent with number bonds and addition.  At a higher level, learners can begin to think strategically by considering several moves in advance.

Possible approach

In the video below, you can see the game being played in silence.  Show this to the group, simply saying that you'd like them to watch carefully to see whether they can work out the rules of the game.  

Give them chance to talk in pairs about the possible rules.  Emphasise that they may not be completely sure and that is alright.  They may even have some questions to seek clarity. After a suitable length of time, show the video again so that learners can check their initial thoughts.  Then bring everyone together and agree on the rules of the game together.  You may have to decide whether you can use each number more than once.

Alternatively, you could show this video which does have sound and so explains how to play:

Once everyone is clear about the rules, give pairs a copy of the game board each and a counter.  Allow them time to play the game several times without saying much more yourself.  It is important that learners are able to 'get into' the game before being expected to analyse it in detail.

You could then invite the group to begin to think about good ways of winning (if they haven't done so already).  At this point, you could put them in groups of four so that they play two against two.  This gives them the opportunity to discuss strategy with their partner.

The session could culminate in the creation of a list of 'top tips' for anyone playing this game and wanting to win.

Key questions

What do you need to make your target?
Where could you go next? 
What might your opponent do then?

Possible extension

Some children might enjoy an individual challenge based on this game.  For example:
- What is the shortest 'string' of numbers that adds to their chosen total? 
- How many different 'strings' of numbers that add to their chosen total can they find?
- Could they design a different grid to make the game harder/easier?  (Here are blank boards which may be useful: Word document, pdf.)
- What if the grid contained decimal numbers/fractions?
You could introduce the game Play to 37 as a follow-on to this one.

Martin Shaw who teaches at Seal Primary Academy in Selsey suggested the following:
- Play the game cooperatively i.e. both players work together to try to reach 20.
- Start at 20 and subtract the numbers on the grid to try to get to 0.

Possible support

You could put some children together in pairs straight away so that they have chance to talk to someone else as they play the game.