Challenge Level

This game offers an engaging context for practising addition and subtraction, but it also requires some strategic thinking. The collaborative version provides a fantastic opportunity for learners to reason mathematically, and to experience proof.

The game also offers the chance to focus on any of the five key ingredients that characterise successful mathematicians. The collaborative version lends itself particularly to fostering a positive attitude to mathematics as learners' resilience may be tested!

Show the video to the group, explaining that there is no sound as such and inviting them to think about what they notice and what they want to ask. (You could click through this powerpoint presentation one 'go' at a time if you cannot access the video.) Having watched it once, give them an opportunity to talk to a partner and then
collect some of their questions and 'noticings' on the board. Encourage other members of the class to respond rather than you. Before playing the video a second time, explain that as they're watching, you'd like them to consider what the rules of the game might be. Mediate a discussion following the second viewing so that the class comes to an agreement about the rules of the game and
how a player wins.

Give children time to play several games in pairs so they get a feel for it. A set of printable number lines can be found here. Share some of their strategies and then ask them whether they think it might be possible to cross off all the numbers in a game. Give them time to work co-operatively with their partner
on this challenge before bringing them together again to see what they have found out. You could find out whether, for example, any pairs have used more than half the numbers. More than fifteen numbers? Given enough time, do they think they could find a way to use all the numbers? Some will have realised that it is impossible to cross off zero - encourage them to explain why this is the
case. To give them an example of the kind of reasoning that constitutes a proof, you could share this proof sorter with them. It includes all the steps to create a watertight chain of reasoning, but muddled up. The challenge is to put the statements in the correct order. (If you would prefer learners to be working away
from a screen, you could print off and cut up copies of this sheet, which contains three copies of the statements.)

Learners could then investigate whether it is possible to use all the numbers if the number line goes from 1 to 20 instead. Give them chance to explore this new scenario in pairs. Many will be able to reason that it is still not possible due to there being an even number of numbers in total. Again, you could work on this proof sorter as a class, ordering the statements to help learners get to grips with the idea of proof. (Alternatively, you could print off this sheet, which contains two copies of the proof sorter statements.)

Have you found any good ways to beat your opponent?

Can you cross out all the numbers in one game? How do you know?

What is the biggest number of numbers you can cross out?

If children are struggling with the calculations, a shorter number line may be appropriate so focusing on a number line to 10 still elicits many of the same ideas about possibilities and outcomes as well as the way in which the operations of addition and subtraction work on a limited set of numbers.

Can children reason whether it would be possible to use all the numbers on any number line of consecutive numbers? (They may like to unscramble this proof sorter, or use a printed copy of the statements.)

Children can suggest their own 'what if ...?' questions, for example:

What if we could use multiplication/division?

What if we drew a longer number line?

What would happen if we included decimal numbers in our number line?

What if the number line extended beyond zero to negative numbers?

The possibilities are endless but do make sure they try out their new version of the game to check it is a 'good' game.