KS4 Foundation HCF
Before teaching Foundation HCF I teach LCM using times tables as multiples, then I introduce factors using times tables. I start with 12 and show that it is in the 2, 3, 4, 6 and 12 times tables and 2 x 6 = 12 etc.
Then I show that 1, 2, 3, 4, 6 and 12 are the factors of number 12. Then I show that 13 can only be formed from 1 x 13 and define 13 as prime.
For their activity I use the resources shown in this link to get to the highest common factor of 2 numbers.
Normally the differentiation is the main issue as some grasp this very quickly and yet others struggle, especially those that are weak on their times tables. So this list shows the resources for the extension for those who need to be kept busy and stretched.
For further differentiation I use harder numbers and then 3 numbers to solve.
Nuffield
This book - Number and Algebra 1 - by Nuffield, contains a very introduction to factors. Starting on page 23 Unit 3 introduces Multiples and Factors. It starts with a brief definition but then gives a good set of activities for the pupils. This can last for the rest of the lesson and some will complete but I only use C1 to C4. I then continue with D Common Factors on page 24 for their activities.
Number Property
This Flash resource is an 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.
Algebra Core
This book - Algebra Core - has a wonderful chapter - Multiplication Mixtures - that I use as an extension to factors, I only use the sections that I did not use for LCM. Pages 63 to 68 have the key activities.