I like to have an hour and a half with my GCSE students [14-16 years old]. It's long enough for me to fit in three areas of work for each session.
I like to start each session with a warm up and then we select two further areas from below...
Warm Up
This involves some number work. Familiarisation with the 12 times table really helps here and so we investigate ways of making this 'stick' with the student.I also like to use square numbers and, over time, see how far we can get up to 30². We also bring in cubed numbers and can take them up 10³. It's very rewarding watching a fifteen year old self-declared arithmophobe trot out all the square numbers AND cube numbers in order up to 1000. While this may sound fanciful for most students it really is achievable by learning the most suitable methods.
This knowledge really helps the student recognise numbers that would otherwise appear random and intimidating when they crop up on Exam Papers, e.g. 729 - this is the square of 27. It's also the Cube of 9. From here we can also explore multiplying decimals using these numbers/digits. For example:
0.27 x 0.27 = 0.0729
Or
2.7 x 2.7 = 7.29
Being able to handle fractions is often an assumption we make of our young students and I like to ensure we don't take this ability for granted.
Factorisation of numbers like 12, 24, 36 and 72 can be done methodically so you can know that you have all the factors in front of you. This is very useful in making quadratic equations less intimidating.
Depending on what is discovered about the tutee's ability with these 'nuts and bolts' of GCSE maths we might stretch this into the second part of the session. Otherwise we go on to the two from the following...
1. Specific Topic
The second part of the session is usually given over to an area of Maths with which the student has specific issues.2. Homework
If a student is having trouble with a set homework then this could also direct us to cover a specific topic.3. Exam Paper
We can pull apart exam questions and help our understanding of Exam Craft.4. A4 Revision Sheets
I encourage a student to obtain an A4 folder. Over the course of my tuition we will be creating an A4 revision sheet for each topic - here I guide the student into writing their own Revision Notes for a particular topic. I restrict them by using one A4 sheet per topic, so that it is up to them in how they reduce the notes to fit on one piece of paper.I make it clear that while they may decide to never return to a revision note it is the mere fact that they have actually written the revision note in their own words that makes the subject 'stick'. We only write a revision note once the student has 'Got It' and they are able to write it in their own words. We hope that by the time of their exams we have a healthy looking A4 folder full of their own revision notes.
