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This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.


This activity investigates how you might make squares and pentominoes from Polydron.

Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

Prompt Cards

Age 7 to 11
Challenge Level

Prompt Cards

Can you work out what Charlie's number is from these clues?

  • C1: Charlie's number is palindromic, the second and third numbers are different.
  • C2: Charlie's number is greater than 100 and is prime.
  • C3: Charlie's number is odd. The difference between the largest and smallest digits is 5.
  • C4: Charlie's number is less than 1000. The sum of the digits is 14.
  • C5: Charlie's number is not divisible by 3. It is less than 500.
  • C6: Charlie's number is a whole number with only two divisors.

Now can you make this tower from coloured cubes? Or, if you don't have any cubes, you could draw it.

  • C1: There are six blocks in the tower, a yellow one is at the top.
  • C2: The red block is above the green block.
  • C3: One of the yellow blocks is above the green block, the other is below it.
  • C4: Each of the blue blocks shares a face with the green block.
  • C5: No two blocks of the same colour touch each other.
  • C6: There are no brown blocks in the tower.

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. 

Possible approach

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 (wordpdf). 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.

Key questions

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?

Possible extension

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.

Possible support

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.