Multiples Grid

Why do this problem?

This problem is an interesting way of reinforcing understanding of factors and multiples.

Possible approach

To start with, ask children to talk in pairs about why the numbers in the first 100 square are shaded blue, pink and purple. Invite them to share their ideas and encourage correct use of vocabulary.

Learners could continue to work in pairs, perhaps using the second page of the printable sheet, which shows the four parts of differently-shaded 100 squares. As they work on the problem, trying to find out which factors have been chosen in order to produce the shading, encourage them to justify their solutions to their partners, and perhaps then to the whole class. How are they going about the task? It might be useful to discuss ways of working systematically so that no solutions are omitted.

This spreadsheet, which shades the squares according to the chosen factors, can be used to check their hypotheses. In a plenary session, you could use the second sheet of the spreadsheet to pre-prepare some shaded sections of the 100 grid without numbers. If you tell them which multiples have been shaded, can the class work out where the small part of the 100 grid is, i.e. which numbers it contains?

Key questions

Possible extension

Learners could explore the spreadsheet for themselves at a computer. Challenge them to make up their own questions to ask a friend.

Possible support

A multiplication square may be useful for those children who find instant recall of multiplication facts difficult.