Mental addition without going mental
Q How would you teach pupils to add columns of figures mentally?
A The best way to explain is with an example, below left.
First, add the column on the left instead of the right. Count either up or down the column, but don't jump around the sum making groups of 10.
Although this may sound easier it is also easier to lose one's place. Also, it provides practice in using different number bonds. Holding a finger on the position is always useful so you don't lose your place.
In this case the left-hand column is the 10s column and add as 30 + 20 + 60 + 50 + 10, to get 170. Hold this in your head or write it down. Now add the units. I have added from the top down: 4, 12, 15, 20, 22. Then add the 170 together with the 22 to make 192.
A great way to practise this is to set two pupils against each other, one with a calculator and one adding mentally. Prepare a sheet of examples and see who's fastest. Then swap over.
The other three maths groups in Year 11 are going on day courses in the next month but there was nothing suitable for my set (set 2 of 4) who are aiming for Bs (the other courses were for people trying to get A*s and struggling to get Cs).
I therefore got permission to have a maths morning in school with them.
They are all quite enthusiastic and so am I. I know I can occupy them for a morning but I want to make it fun as well as informative. I have to plan it this week and am looking for some good ideas. I have my classroom and access to a room with enough computers for all to have one each plus a large hall if I need it. Any ideas?
I have 18 in the class so if they all turn up, I can have teams of 2, 3, 6 or 9. My aim is for them to learn something (or lots of things) that will improve their GCSE results.
The one thing that I have difficulty with is limits (What is the smallest and largest possible value of x if x is 23.6 to 1 decimal place?). Any ideas?
You could set up a maths mission and split them into teams. The idea would be to complete activities about different concepts over the morning.
This would take a great deal of preparation, but you could use the activities again the following year.
Look at their mock papers and identify weaker areas; use these in the challenge. Having identified the concepts you wish to be covered, a search of the internet will reveal some interesting activities. I would also base some of the activities on past exam papers.
Base the activities on questions but make the activity more interesting by making manipulatives that the pupils use in solving the problems. They would pick up pointers on how to solve such problems, but in a more interesting context.
You have already picked out upper and lower bounds. I can remember having great difficulty when I first had to teach these. Now I find it best to draw a diagram in the first instance. For this example the diagram shows that 23.6 lies between 23.5 and 23.7. Students quite often have difficulty at this stage. In this case we are looking at an approximation to one decimal place so I get them to cover the 23 with their fingers and look at 0.6 asking them what number with one decimal place comes before and after.
So really just counting 0.5, 0.6, 0.7. (If the problem was say 5.63 to two decimal places, then they would be looking at 0.62, 0.63, 0.64 as the sequence.) The boundaries, if you like, are half way between 23.5 and 23.6 (23.55, (23.5 + 23.6) V 2) and 23.6 and 23.7 (23.65).
You know that 23.65 will round to 23.7 to one decimal place, so the highest limit will have to be less than 23.65. You also know that 23.55 will round to 23.6 so the lower bound is greater than or equal to 23.55. The bounds are written as 23.55. LESS THAN LESS THAN 23.6 LESS THAN LESS THAN 23.65; this is usually the best way to record them.
LESS THAN T0
I have created a short worksheet available as a pdf at www.mathagonyaunt.co.uk which you could use as one of the activities.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.
Email your questions to Mathagony Aunt at firstname.lastname@example.org Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX