Why do this problem?

This problem is an accessible context in which pupils can apply their knowledge of number properties. It provides a great opportunity for learners to reason logically and to communicate their reasoning with others.

Possible approach

Introduce the first part of the challenge to the whole group and give them time to work individually, then in pairs without saying too much. (It might be useful to print out copies of it from this sheet.) You could bring them together for a mini plenary after a short time, asking whether they can
suggest some clues that are not needed and how they know that they are redundant.

Suggest that pairs continue to work on the problem, recording whatever and however they find useful. Let them know that you will be asking them to explain their reasoning, as opposed to simply focusing on the answer.

As you go round the room, listen out for children who are using logical reasoning to eliminate the redundant clues and to find the number. They might well use vocabulary such as 'because' and/or 'if ... then ...'. You could warn a few pairs that you'd like them to share what they have been saying with the whole group in due course.

Bring everyone together again to share their solution but in particular to share examples of logical reasoning that led to it. You can then set the group off on the follow-up challenge where they could work in pairs to create a similar task for another pair with exactly four clues, none of which are superfluous.

To end the lesson, place learners in groups of four so two pairs can try out each other's new challenges and report back.

Suggest that pairs continue to work on the problem, recording whatever and however they find useful. Let them know that you will be asking them to explain their reasoning, as opposed to simply focusing on the answer.

As you go round the room, listen out for children who are using logical reasoning to eliminate the redundant clues and to find the number. They might well use vocabulary such as 'because' and/or 'if ... then ...'. You could warn a few pairs that you'd like them to share what they have been saying with the whole group in due course.

Bring everyone together again to share their solution but in particular to share examples of logical reasoning that led to it. You can then set the group off on the follow-up challenge where they could work in pairs to create a similar task for another pair with exactly four clues, none of which are superfluous.

To end the lesson, place learners in groups of four so two pairs can try out each other's new challenges and report back.

Which clues do you have to have to find the number?

Which clues don't tell you any more information?

Can you explain why?

Learners could tweak the challenge for themselves. For example, they might like to create a version which requires a different number of clues.

Encouraging children to shade or colour the grid somehow to reflect the information in each clue at a time might be helpful. Having the clues written on individual pieces of paper is a good way for each one to be read individually, and they can be grouped easily according to which are useful and which are not.