# 'Create imaginative representations for numbers using factors and multiples'

Take a look at the picture flickr gallery below.

Can you work out what numbers each design represents and what factors were used to build it?

Number theory is all about seeing relationships between numbers and seeing numbers you thought you knew everything about in a new light. Get ready for a lot of fun!

### Resources

The first two activities are explained below (link here for printing):

Think you now understand all about factors and multiples? Pit your wits against a partner in this Multiple Factors game - the embedded spreadsheet below gives you an overview (but you cannot edit it). Play the MultipleFactors game using excel. Click on the yellow reset button next to "Player 2" to start a new game. For an online version try this one from the illuminations website, it keeps score for you or why not play against the computer! The computer's no dope, so think carefully about how many factors each number has to ensure you pick those that will give you the highest score!

### Description

• You may want to start by looking together at the pictures in the above photo gallery to ensure everyone is clear on how a number's factors can be used to create different representations.
• Students need space to move around. Use the school courtyard or a corridor or hall if there isn't enough space in your classroom.
• Ask the class as a whole to get into equal groups of 2, 3, 4, 5 etc. Ask them to be as imaginative as possible as to what forms their group can create! (see flickr gallery at the top of this page). Take photos of their groupings. Using iCloud helps facilitate instant sharing of these photos with the class.
• Which numbers resulted in equal groups and which didn't? What do we call these numbers?
• For the main task, students have to make as many different, imaginative and interesting patterns as they can from 24 beads, 36 beads and, if time, 40 and 48 beads.
• The only condition is that the patterns must be based on groups of equal numbers of beads e.g. they cannot have a pattern made of groups of 3 beads with a left over group of only two or one etc.
• Can they create two or three different patterns for the same grouping?
• If time permits: Ask students to make up some equal group patterns for other numbers. Groups can then take photos, share these via icloud for display on the teachers IWB or in a network area. Other groups have to work out what the number represented is and what factors were used to construct the pattern. It is this instant, published outcome to their work in the form of a shareable picture that really motivates students. Share them via facebook, flickr, upload them to students' mobile devices etc.
• Finish with the multiple factor game above to evaluate students' understanding of factors and multiples and provide a fun context within which to practise.
• This activity can be used with secondary (11-18yr old) classes. It can also be used alongside Money Multiples Investigation and The Prime Cicada as a three part mini transition module from primary to secondary. One way is to have the primary teacher teach the first lesson (money multiples or this lesson) in primary with the secondary teacher observing, the second lesson can again be taught in the primary school, but with their maths teacher for the following year leading the lesson (with their primary teacher in support) and the final lesson in their new secondary maths classroom with only their maths teacher.