# NRICH Mathematics Games to Promote Conditional Knowledge

Here are a few simple mathematics games that can be played at home or in class to improve students’ mathematical thinking and reasoning strategies.

These two games come from a website called NRICH.

NRICH believe that successful mathematicians understand curriculum concepts and are fluent in mathematical skills and procedures.  They also believe that they can solve problems, explain and justify their thinking, and have a positive attitude towards mathematics and to themselves as learners of mathematics.

With this in mind, NRICH mathematical activities aim to nurture curious, resourceful and confident learners of mathematics.

Game 1: You will need seven counters.

Nim-7

1. Place seven counters in a line and decide who will go first. (In the next game, the other player will have the first turn.)
2. Each player takes it in turns to take away either one counter or two counters.
3. The player who takes the last counter (or counters) wins.
4. Play several times so that you get a good ‘feel’ for the game.

Are there any points in the game, before the end, when you know who the winner is going to be? How do you know?

Can you find a way to play so that you are sure you will win right from the start?

Does it matter who has the first turn? Why or why not?

Once you are an expert at this game, you may like to try playing Daisy, which is another Nim-like game.

Game 2:

Got-it

Got It is an adding game for two players. You can play against the computer or with a friend. It is a version of a well-known game called Nim.

1. The first player chooses a whole number from 1 to 4.
2. Players take turns to add a whole number from 1 to 4 to the running total.
3. The player who hits the target of 23 wins the game.

Play the game several times.
Can you find a winning strategy?
Can you always win?

Does your strategy depend on whether or not you go first?

This can also be played on-line.

https://nrich.maths.org/1272

To change the game, choose a new Got It target or a new range of numbers to add on.

Test out the strategy you found earlier. Does it need adapting?

Can you work out a winning strategy for any target?
Can you work out a winning strategy for any range of numbers?

Is it best to start the game? Always?

Away from the computer, challenge your friends:
One of you names the target and range and lets the other player start.

Extensions:
Can you play without writing anything down?

Consider playing the game where a player CANNOT add the same number as that used previously by the opponent.

Mrs Bennett
Mathematics Department

Share!