# KS4 Foundation LCM

To teach foundation LCM I always begin with the word 'Multiple' as often I find students do not have a true understanding of this word. I link it to 'Times Tables' and give examples and an activity to ensure they have thoroughly grasped the definition of the word.

The next stage is often the most difficult for pupils, that of finding the common multiples and the lowest one. I get them to write out a list of multiples for two numbers and put a ring around the first common one. Again I find the English is the problem, the understanding of the word 'common'. But once grasped this activity is successful.

The resources below follow this pattern and include some extension work for those who grasp the concept quickly. Because of the teaching of the English words I find the differentiation is critical as some may grasp the whole topic in 15 minutes whilst others will take 2 or even 3 lessons with a homework in between them.

### Mutliples

This book - Numeracy Multiplication makes sense - is the first resource I use for those who initially find multiples difficult. Page 5 contains a student worksheet called missing pieces, these are multiplication grids with missing squares and begin very easily and gradually increase in level but only to an easy start for my pupils.

Page 9 contains a student worksheet - connecting multiples - this increases the level and I find this stretches some pupils to the point they do understand what the word means, adding is the main issue with some finding 36 + 6 difficult so the exercise on page 5 is repeated for those students.

Page 11 - Tens and Fives - can be used for extension work for those who finish early as it stretches them with wordy questions.

### Mutliples Extension 1

This book - Algebra Core - has a wonderful chapter - Multiplication Mixtures - that I use for extension pupils, it covers multiples, factors, prime numbers, prime factors. I miss out the 'power' section on pages 63 and 64 and continue with the factor table on page 65. I continue to page 68 that has sufficient work for any who understand this topic and stretches them sufficiently.

### Mutliples Extension 2

This Flash resource is another extension resource, it contains 10 questions that can be answered - but only for extension pupils and is not applicable for any who find this topic challenging. The questions can be repeated and very good for a smartboard where some pupils can be trusted to come to the board and work on their own. The top questions are tough enough so I allow the students to use calculators and their text books, the prize is to get 10/10.

### Lowest Common Multiple

This book - **Number and Algebra 1** - by Nuffield, contains a very good chapter for those who struggle with this concept. Starting on page 21 Unit 3 introduces Multiples and Factors, as I follow LCM with HCF this chapter is used as a link between them. It starts fast with multiples hence my use of 'Numeracy Multiplication' as the first resource.

The common multiples are introduced and uses Venn diagrams to illustrate the 'common' element. This I have found very good for the majority of pupils. Having found the common multiples the step to finding the lowest one is the simplest step and easily grasped.