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The power of practice

multiply out and simplifyDear M,

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 🙂  )

  • If there was a minus sign in front of the first bracket, you were not always “seeing it” clearly when you keyed expressions into your calculator
  • If there was a minus in front of the bracket as well as one inside it, you sometimes made the wrong decision (although you had pretty much stopped doing that by the end of the lesson, errors have a nasty habit of creeping back in a few days later!)
  • You made more errors when you did everything mentally, and fewer when you jotted the “easy version” as a working step.

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:

multiply out and simplify 1

multiply out and simplify 2

multiply out and simplify 3



Trial and Improvement for George

George was guessing answers today and got it down to a fine art – usually getting it right in 3 or 4 tries. We were working really fast because we had set our calculators up to give the answers exactly the way we wanted to see them, ie to one decimal place, and as a number not as a square root (or Surd). Here’s how:

  • Shift    Mode   6:Fix    1      gives the answers Fixed to 1 decimal place
  • Shift    Mode   1:MathIO    2:LineO     gives you nice mathematical INPUT but just a decimal OUTPUT which is perfect.

With Guessing you can go round in circles and forget what you tried…. so we do Trial and Improvement which sounds really posh but it just means we jot down the guess each time and the answer it gives. It’s nice to see the list getting shorter, as you get better and better at making a good first guess.

*** When you have finished this work, you can put your calculator back into its normal mode by pressing:

  • Shift 9(Clr)  3(All)  =(to confirm) AC(to start again)

Pythagoras trial and improvement with George