Points of view (changing the subject of an equation)

This post is practicing simple equations. In 3 days there will be another one to change the subject of more simple equations. If you write your answers in the box at the bottom I will check them and reply to you. I won’t publish them on the page though!

  • “I am forty-one years older than you” is my point of view. In algebra language I would write R=C+41
  • What’s your point of view?
  • C=R-41

Looking at some of the people in my family then,

  • R=D+26 (I am 26 years older than D, my oldest daughter)
  • What’s her point of view?
  • D=R-26

Now let’s look at another relationship in my family,

  • R=G+28
  • Who is older? R or G?
  • R is older than G, by 28 years.
  • so how would G see it?
  • G=R-28

Now here’s something you can work out,  given I am 54 at the moment,

  1. How old is C?
  2. How old is D?
  3. How old is G?
  4. One more person in my family is T. R=T (that’s my point of view) How old is T?
  5. What is T’s point of view, in other words write T=…



Dear H,

We have just spent 2 lessons on Trigonometry and here is the writeup as promised. You were getting everything right but these notes are in case you forget a small step and need to revise.

Sorry you couldn’t remember SOH CAH TOA, but it’s really quite complicated, what with labelling the triangle, writing out SOH CAH TOA, remembering which way round they go, what they mean and how to use them…

So anyway we were just using the SINE RULE and CROSS SUMS to find the missing side or the missing angle.

Before you start, make sure you have revised

  • Cross Sums
  • Pythagoras’ Theorem

Finding an unknown side, given a right angled triangle, with one known side and one known angle.

      1. Work out the value of the missing angle and write it into the correct corner. (For example, the 3rd angle in a 90/42/? triangle would be found by doing 180-90-42=)
      2. Draw a cross sum. In the top line, write the KNOWN SIDE and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)
      3. Underneath the KNOWN SIDE write down the sin of its opposite angle
      4. Underneath the “?” side, write the sine of its angle. That’s sin(?)
      5. Write down the sum you plan to type into your calculator
      6. And do it!
      7. Write the answer back on the diagram and check it looks sensible

Finding an unknown angle given a right angled triangle, with two known sides.

  1. If the Hypotenuse is unknown you will have to use PYTHAGORAS’ Theorem to find it, first.
  2. Draw a cross sum. In the top line, write the KNOWN SIDES and an x (or ?, or whatever the exam is calling the side you are looking for. In the images below we labelled it “?”)
  3. underneath the known sides, write sin(of their opposite angle), one should be sin(90), the other will be sin(?)
  4. Write down the sum you plan to type into your calculator
  5. This time the cross sum’s answer will be weird (0.67834 in the example below) and you need to write sin(?)= 0.67834 or whatever.
  6. You found the sine of the angle – to find the angle itself, press Shift, Sin, ANS, =
  7. Write the answer onto the diagram and check it looks reasonable.

If the hypotenuse and one other side is given, then you wont need Pythagoras. So its easier.

Recommending mathsbot.com

I am grateful to Mr. Holding who teaches locally for this link. So simple! Lots of GCSE questions presented one at a time. A couple of examples are reproduced below.


The Proof Questions on this site are invaluable – the best collection I have seen.

This slideshow requires JavaScript.

Game – Prime Number Recognition

You will need:

2 dice and a pen and paper.

Take in turns to:

  • Throw the dice
  • From the dice, construct 2 or perhaps 3 numbers. For example, if you throw a two and a three, you can make 5, 23 and 32 (3+2=5, two followed by three is 23 and three followed by two is 32)
  • Score one point for each prime number you have made (so this example scores one for the 5 and one for the 23, scoring two points in total).
  • If you need to use a calculator, then a Casio fx-83GT PLUS can tell you whether a number is prime. This is *not* cheating – students will soon start to recognise the primes they need, rather than having to check using the calculator!

The Winner Is:

The person who has the most points.

Things to discuss:

  • Why are two even numbers always such bad news? (even+even=even and the only even prime number is two)
  • Is it possible to score three points with one throw?
  • If there is a six in your throw, what happens?

This sample space diagram may help:

Sample Space Diagram for 2 Dice




















































How to Factorise a Number (Or Check that is Prime) using a CASIO fx-83GT PLUS calculator

On the CASIO fx-83gt PLUS factorising is done like this:

  • Entering the number,
  • press equals,
  • SHIFT and ., ,,, (this has “FACT” written above it in yellow).
  • The Prime Factor Form is displayed as the answer.
  • If the number is Prime, then the number itself is displayed.

This is a natural way to introduce what indices mean, because the CASIO gives the answers in index form eg 34 rather than 3x3x3x3

Understanding Mean and Median

For a collection of questions that encourages students to *think* about mean and median rather than just crunch numbers, there’s no resource to beat this one that is available free to download from the TES site. (You will need to create a TES login account – that’s free too).


Recommended Resources from JustMaths

For Pupils in Years 7 to 11, I find the “bread and butter” cards on JustMaths really useful – entertaining, and a broad range of revision topics.

Easier (basic skills) stuff is on this page:


and harder stuff (Grade C+, I use these in Years 10 and 11) is:


Thanks Mel!