Time to Win

This island involves a game that requires children to add time. Essentially, they begin at a certain time and have to select (multiple choice) a time to advance the clock by. Once that time has been added it is crossed off. Once they are all crossed off, they all become available again. If someone makes a time that can be said as ‘quarter to…’, they win.

The key thing for them to be able to play the game successfully is realising that they cross off the times until they are all crossed off and then they are revealed again. A Landing Spot into this is starting with just two times and rather than playing as a game looking at the patterns that are made.

Start at 9am. You can only add 15 minutes or 30 minutes (with the principles of above, cross off one and then cross off the other and then have the choice of both again). What different times can you make before reaching 11am? This is deliberately very confined. We are simplifying how it works in a short problem solving activity to build towards the game.

Time to win rich task, game and island with the Isles of What If...?

Whether the children record the time as digital or analogue (or both) is up to you but it helps to have each step visible with the amount they are advancing by next to each clock. With both this stage and the game later, dry erase pockets are handy to be able to have multiple attempts/games.

5 minutes10 minutesQuarter of an hour20 minutesHalf an hour

Moving onto the game, it essentially works the same way but the children can advance the time by any of the 5 possibilities above. If anyone makes a time that can be read as ‘quarter to…’, they win.

The exploration of the island will mainly be done through exploring the initial game and coming up with a strategy to win. A good starting point for thinking about this is looking at what moves can’t be made as the first go.

I deliberately made it so that if the first player selects 10 minutes as their first go, they can always win no matter what player two chooses (see below).

10 minutes (9:10)5 minutes (9:15)Half an hour (9:45)
10 minutes (9:10)Quarter of an hour (9:25)20 minutes (9:45)
10 minutes (9:10)20 minutes (9:30)Quarter of an hour (9:45)
10 minutes (9:10)Half an hour (9:40)5 minutes (9:45)

As a class, you could then look at changing the game to make it fairer.

What if we used different times?

I’d not allow absolute freedom of their choice of times as obviously it needs to be possible to make a quarter to something. Although you could allow it and ask them to investigate whether the game is possible to win as a line of inquiry.

What if we added a sixth time?

This could be a nice next step as you can select a time to complement the other times. I’d ensure that the time you add is a multiple of five minutes to not make it too difficult to win.

What if we changed the winning time?

You could have this as either a number of minutes or like the Landing Spot, have it as a time they can’t go past. It ensures that games are finished more quickly.

What if we subtracted time instead?

This is a nice variation as it is potentially a little more complex for them to do and not something they might regularly practise.

Children’s possible use of reasoning skills (click on each heading):

Search
Search inquiry reasoning skill in maths

We want the children to ultimately be thoughtful in the times they are selecting. They need to try and think two steps ahead by considering whether the time they select will allow the other player to win.

Organise

Whilst Organising isn’t going to be as explicit compared with other islands, you could collect data on which player wins.

Discover

This game is more about the arguing of strategies more than conjecturing about unseen data. However, explicit mentioning of conjectures when they try and make the game fairer can emphasise the point that conjecturing is about data that we haven’t made yet. They haven’t tried the new version of the rules but can conjecture on what they think will happen.

Investigate
Investigate inquiry reasoning skill in maths

If someone has a strategy, can they Expand the limits of it by finding moves that the strategy doesn’t work for?

Argue

This is the main focus of the island. Once children have come up with a strategy, they need to be able to explain it and convince others that it will work. You can always use beat the teacher as a way of doing this. Play against an individual or the whole class. Can they beat you?

Explore

The ‘What if…?’ questions can definitely come from them. The difficulty they might have though is making a game that still works. If they select a series of times that make the target time impossible, the game no longer works. They can still go down that avenue and talk about why it doesn’t work – just don’t let them go at it for too long!

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