At homework club, a pupil was having difficulty with algebra. The question was: "simplify 7t + 3s + 2t + 5s". I told him it was just a case of putting all the t's together and then all the s's but I don't think he really understood. When I gave him the example 3b - 2a + b + 4a he wrote:2b + 6a.
I couldn't understand his reasoning. Pupils think that because you are a teacher you should know it all. Being able to do something yourself doesn't mean you can immediately pick up what a pupil doesn't understand.
Children seem to think that because you are a teacher you should be able to help them when they get stuck. I am sure I am not alone when I say that some cover-lessons are difficult because of this perceived inability to help. (It is a long time since I did French and I never did the other languages.) I know as a maths teacher I am still trying to find out why someone doesn't understand something. You know you have given this fantastic exposition, feel really pleased with yourself, think "of course I covered everything" and you begin the questions and answers only to find there are some who are still not sure.
We all have different ways of learning. For some, five different explanations won't work, it is only when you try the sixth that they say:
"Well, why didn't you explain it that way in the first place."
I suggest the following as a way to help a pupil who is having difficulty with collecting like terms. I have assumed that the pupils have understood that the "a" terms are different from the "b" terms. I have taken the example you gave. Write it on a strip of coloured paper.
One of the common mistakes made by pupils is that they don't realise the sign of the term is in front of the number not after, so in this expression "2a" is "-2a". I think this is where your pupil was confused, thinking the first term was "3b - " and the second "2a +". This confusion was quite common in the days when some calculators had the negative sign after the number (not now though).
To help them learn this, first explain that when there is no sign in front it means "+" but we don't bother to write it. Write this in front of the first term as I have shown below.
Next, tell your pupils to tear the expression into separate terms, making sure the sign is in front of each term, and place the pieces on the table in front of them.
Now ask them to move the terms that are alike next to each other. This is what they would be doing in their head if they didn't have the paper in front of them.
They can now simplify each term. Ask them if this can be made simpler. The expression they should have is that below.
For those who might have missed a session on collecting like terms, you might need to demonstrate 3b + b by writing each b in the expression as an expansion: Similarly demonstrate 4a - 2a by writing four lots of "+a", circle two of them to demonstrate "-2a". Tear them off to leave 2a.
All my class are trying to find out what a 16-sided shape is called.
A 16-sided polygon is called a hexakaidecagon. Greek prefixes for all the shapes can be found at www.georgehart.comvirtual-polyhedragreek-prefixes.html
This leads you to a site about polygons and polyhedra.
Here's a thought about symmetry: Poetic symmetry
Line symmetry Line
This is symmetry is This
Match a fold a Match
Match a perfect fold perfect a Match
This could be read as:
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.
www.nesta.org.ukEmail questions to Mathagony Aunt at teacher@ tes.co.uk or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX