D. made this film at the end of yesterday’s tutorial. He chose 4 equations that summed up what he had learned during the hour’s lesson. I am indebted to M.F. who originally noticed the easy trick for plotting lines which have a fractional gradient.
D. made this film at the end of yesterday’s tutorial. He chose 4 equations that summed up what he had learned during the hour’s lesson. I am indebted to M.F. who originally noticed the easy trick for plotting lines which have a fractional gradient.
You are making great progress with algebra, I think. The crucial link between the written symbols and what they actually MEAN is not easy to make, but you are putting the hours of practice that you need, in order to become confident.
Here are some more questions. I know we discussed the idea that I could build an interactive game for you that would check each piece of your working, and your answers, but on reflection, I think you are getting sufficiently fluent with algebra now, that this level of feedback would actually be unhelpful, like bolting stabilizers back onto a bicycle after you have begun to balance it by yourself.
You are already in the (excellent) habit of keying the question into your calculator, keying in the answer, and comparing the two, What I would like you to focus on this week, is actually writing down the “easy version” and, if the question and answer DON’T match, then key in these workings out as well to narrow down the problem.
The huge advantage of you and the calculator (rather than the computer) doing the checking, is that you are able to use your calculator throughout the IGCSE exam, so you are practicing really useful skills, not using a tool that will be taken away from you.
After working on the last worksheet with you, we both realised that the sums were too densely packed on the page, and a bit dazzly. I hope this version is easier. I have left gaps for you to write the “easy version” out directly below the sum.
As you work, it may be worth being aware of the commonest errors you were making in the lesson (which are errors most people make, you are not alone 🙂 )
Jargon-wise, what we are doing is called “multiplying out brackets and simplifying”. That’s the terms the examiner would use (instead of “writing down the easy version and writing down the answer”.
So here are three more worksheets:
I set this problem today, during a lesson in which we had been looking at simultaneous equations with 2 unknowns:
A + B = 92
A + c = 57
B + C = 59
M came up with this answer:
POSTSCRIPT –
M then set me this problem:
A-B = 25
B+C = 151
A+C = 176
which turned out to have an unexpected twist in it….. Have fun!
Mathematical Language Covered
You will need:
Creating the Puzzles
Give out 2 pieces of card each. Create your choice of sequence, write it on the coloured side of the card. On the back write F(X)= and the function you used.
Discuss boundries – numbers under 10. (I should have set more – no decimals and no division yet. But it did make life interesting!
As they produce the cards, check the function – if it isn’t in simplest form, then simplify it with them and write that version underneath. Point out that their friends won’t be able to guess any more complicated version of the rule. eg if the rule they used was F(X)= 2X+3X+1 then the friends will guess 5X+1
If you think any of them are quite difficult, give them one or two stars. This will let the pupils self-differentiate.
Solving the puzzles
Put the cards down SEQUENCE SIDE UP and the pupils choose which one they want to do. Try to guess the F(X), key your guess onto the calculator, can you make that exact sequence? Once you have made it, turn over and check the rule on the card. Then initial the front of the card to note that you have done it.
Plenary:
What was easy? What was more challenging? Do we need another lesson on this (My group decided they found the minus ones harder so we pencilled in a lesson on handling negative numbers.