An example of this might be where factorising $x^2 + x - 6$ is followed by $x^2 - x - 6$. Throughout the booklet, $x$ has been substituted for other letters, so that students don’t say things like “I can do it with $x$ but not with $a$.” and other similar gripes. The letters have been made the same if a pattern point is being made, as above. The answers are given after each exercise (or each pair in some cases) so that students can quickly check their answers after each attempt. This is to avoid the unwelcome outcome where a student will practise the same error over and over again, and become extremely adept at making that error. (Unlearning is much harder than learning!) There are as many different ways of laying out mathematical calculations as there are teachers, so I have intentionally not suggested methods, though I may add these later in the teacher notes and lesson plans, so that you can encourage your students to do it “the right way”. It is important to note that these exercises are but one resource and it is probable that you will want to use other resources in addition, or turn some of the examples into Tarsia jigsaws. The idea behind these exercises is to give a lot of examples to use, as most text book don’t provide enough and many online exercises are created randomly using some algorithm or other and so do not point up the patterns. How you use these exercises is entirely up to you. In addition, the mixed exercises make very good consolidation or assessment materials. Most of the exercises are fairly self-explanatory, but I have added a few notes below on some of them.