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GOT IT

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

GOT IT


GOT IT is an adding game for two. You can play against the computer or with a friend.

Start with the GOT IT target $23$.

The first player chooses a whole number from $1$ to $4$.

Players take turns to add a whole number from $1$ to $4$ to the running total.

The player who hits the target of $23$ wins the game.

To change the game, choose a new GOT IT! target or a new range of numbers to add on.

Full screen version


This text is usually replaced by the Flash movie.

Play the game several times.
Can you find a winning strategy?
Does your strategy depend on whether or not you go first?

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.

Are you good at mental arithmetic? Can you play without writing anything down?



 

Why play this game?

Got It is a motivating context in which learners can apply simple addition and subtraction. However, the real challenge here is to find a winning strategy that always works and this involves working systematically, conjecturing, refining ideas, generalising and using knowledge of factors and multiples.

Possible approach

All the notes that follow assume that the game's default setting is a target of $23$ using the numbers $1$ to $4$.

Introduce the game to the class by inviting a volunteer to play against the computer. Do this a couple of times, giving them the option of going first or second each time (you can use the "Change settings" button to do this).

Ask the students to play the game in pairs, either at computers or on paper. Challenge them to find a strategy for beating the computer. As they play, circulate around the classroom and ask them what they think is important so far. Some might suggest that in order to win, they must be on $18$. Others may have thought further back and have ideas about how they can make sure they get to $18$, and therefore $23$.

After a suitable length of time bring the whole class together and invite one pair to demonstrate their strategy, explaining their decisions as they go along. Use other ideas to refine the strategy.

Demonstrate how you can vary the game by choosing different targets and different ranges of numbers. Ask the students to play the game in pairs, either at computers or on paper, using settings of their own choice. Challenge them to find a winning strategy that will ensure they will always win, whatever the setting.


Key questions

How can I work out the 'stepping stones' that I must 'hit' on my way to the target?
Is there an efficient way of finding the first 'stepping stone'?
When is it better to go first and when is it better to let the computer go first?
If the computer says $1$, I say...?
If the computer says $2$, I say...?
If the computer says $3$, I say...?
...


Possible extension

Two more demanding games, requiring similar strategic thinking, are
Got a Strategy for Last Biscuit?
Nim-interactive


Possible support

You could demonstrate the game a few more times at the start. Alter the settings on the game to have a lower target and a shorter range of numbers (for example a target of $10$ using the numbers $1$ and $2$). As you play, note down the running totals to refer back to later.
 
Handouts for teachers are available here (word document, pdf document), with the problem on one side and the notes on the other.  

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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