Factorising Quadratics

Click here for the answers

Skill or no skill? A Game for 2 or 3 players


The winner is the player who has the highest total score at the end of a round

You Need:

  • A set of playing cards
  • A dice (or one each)
  • A spare piece of card or paper you can cut up

Before You start:

  • Agree how many score cards you will have, whether you are playing skill or no skill. Make enough score cards (about 2cm square is fine)

Example of working out your score:

If your dice says “3” and your playing card says “3d+1” then your score is 10, because 3×3+1=10

Playing “No Skill”

  • Suppose you have agreed to 5 score cards each. Deal the players 5 playing cards each, which they put in a line in front of them (no cheating!!)
  • Players take turns to roll the dice, and work out the score from the card, writing that score on the next small score card they own.
  • When everyone has finished using their cards, total up the score cards and see who won.

Playing “Skill”

  • Suppose you have 5 score cards. Agree a higher number of playing cards and deal those out.
  • Each time a player rolls their dice, they can choose which playing card to use this turn, to work out their score. Once a playing card is used it is turned over. You won’t be able to use it again.
  • You will find that some cards work well with large dice scores, some work well with smaller ones. Some cards (we called them “golden cards”) work brilliantly with sixes and can score as much as 49!!!

Making the playing cards:

It’s up to you how hard you make the algebra, but here are some ideas to get you started. You need about 20 cards.

  • 2d+1
  • d²-5
  • 4-d
  • d-3
  • (d-1)²
  • 3d+1

Part 2 – More Revision and Practice, changing the subject of an equation

These examples are a bit more difficult that in my previous post.

  • M=2P  (Who is older, Mo or Polly?)

The easiest way of working this out is to give P an imaginary age, and work out Mo’s age. The equations says Mo is double Polly, so if Polly is 20, Mo would be 40. So Mo is older.

  • M = 2P (What is Polly’s view of the relationship, in other words, write P=…..)

The answer is P=M/2

Try these….

  1. X=2Y. What is Y’s point of view?
  2. C=Y+12.What is Y’s point of view?
  3. D=2Y-1.What is Y’s point of view?

To check your answers, give the person on the right hand side of the equation an age, work out the age of the “subject” person, and then work backwards in your answer to check you get back to where you started.

Here are some more:

  1. X=2Y+4. What is Y’s point of view? If Y is 20, how old is X?
  2. C=3Y+2.What is Y’s point of view? Again, pretend Y is 20.
  3. D=2Y-5.What is Y’s point of view?
  4. A=2Y-6.What is Y’s point of view?



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=…


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.

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