Why do this problem?
This problem is an accessible context in which pupils can apply their knowledge of number properties and the terminology of position. It provides a great opportunity for learners to reason logically and to communicate their reasoning with others, developing their listening skills.
Introduce the first part of the challenge to the whole group and explain any words which the children are unfamiliar with, going through some examples of palindromes on the board. Give pupils time to work on the first part of this task in pairs. It might be useful to print out copies of it from this sheet (word
). 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 explain to a few pairs that you'd like them to share what they have been saying with the whole group in the plenary.
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 make or draw the tower from the second part of the question, focusing on explaining their reasoning to their partner.
Which clues have you used so far?
Which clues do you have left to use?
Are there any clues that don't tell you any more information?
Can you explain why?
Pupils could be asked to write down or draw their answer, along with a written explanation of their reasoning. They could also think of their own number or tower of blocks and write clues for another group to solve.
Using the sheet of clues cut into individual pieces of paper is a good way for each one to be read individually, and they can be grouped according to which children think are the most important and which are giving the same information as another clue.