Monthly Archives: February 2013

18. Similar triangles

This quick activity shows that although the sides change in similar triangles, the angles stay the same. It can also be used with enlargement.

Two pieces of different coloured card (A5 or A6 is fine)
Sticky tape

Step by step instructions
Two Lines
Draw a line parallel to the long sides of one piece of card (min 2cm from the edge)


Place the two pieces of card at 90 degrees to make a cross.


Wrap the lined card around the unlined card


Mark out a triangle using the pencil lines as a guide.
Cut along two sides as shown. It’s okay to tidy up a messy cut, so long as the line remains straight.


Turn over the card and refold in the opposite direction. Stick the bottom edge of the folded card in place, as shown.


Slot the second piece in place.


Turn over.


As the slider moves up and down a contrasting triangle appears and disappears.


You can measure the sides & angles of every triangle you make.

This can be stuck into books by gluing along the folded edges, which still allows the slider to move.

16. Library Fines (Sequences)


County Library
The first day a book is overdue, you are charged 4p. Each day incurs another 4p.
What are the charges for the first week?
(4, 8, 12, 16, 20, 24, 28)
What is the Nth term?
How much would you be charged for being 25 days late?

Village library
The village library charges 10p for the first day and 3p for every subsequent day.
What are the charges for the first week?
(10, 13, 16, 19, 22, 25, 28)
What is the Nth term?
What is the charge for 30 days?
How many days late is one book if the fine is more than £2?
(Solve 3N+7>200)

Look back at both libraries. Under what conditions do the libraries have the cheapest fines?
(1-6 days: County Library
7 days: same
8+: Village library)

Why do the libraries have the same charge on the 7th day?
Prove it algebraically.
(Solve 3N+7=4N)

You can also extend this investigation to looking at calendar dates, with one library open 5 days a week and the other being open 6 days with fines only applying when libraries are open. How would this affect the ‘cheapness’ of fines when days are included?

This method can be used for car hire, mobile phone comparisons, energy bills because sequences link so well with graphs of real life problems.

15. Algebra bingo


When you are teaching simplifying, most published worksheets and textbooks contain pages of themed or mixed questions. It’s not exactly thrilling stuff.

How about a bit of friendly competition?

You just need a set of simplifying questions with answers. Any textbook with the answers in the back would do or project the answers on the board.

Set Up
Ask each student to pick eight answers from a specified set.

The teacher reads out a question. The students simplify it and circle if they have it. First player to get all eight wins.

You could repeat this, increasing the difficulty or change to a different theme eg substitution.

The nice thing about this activity is you are in control of the level of difficulty and you can adapt it as you go on. The game element is engaging and the sneaky thing is that everyone has to do every question to have a chance to win.

14. JDs Tree Diagram

My friend JD came up with this visual way of explaining tree diagrams. I’m reproducing it here with permission (Thanks!). It helps if you have a school uniform with a tie and jumper, however this could easily be done with coats and hats.

Set Up
You need 6 volunteers, dressed as listed:
1. (No jumper, no tie) x 2
2. (No jumper, tie) x 2
3. Jumper, tie
4. Jumper, no tie

(This can be adapted for listing multiple outcomes too)

Draw a V shape on the ground.
Explain that in the morning you have choices when you get dressed. Each branch represents a choice.
Choice 1: Do you put your tie on or not?
Get a student wearing a tie to stand at the end of one branch and one without a tie to stand at the end of the other

Draw a V from each student.
Choice 2: Do you put your jumper on or not?
Get the class to decide who stands where

If all the choices are equally likely, what is the probability of getting in trouble with your teacher over uniform?
Can you prove this by looking at the probabilities of the individual events?
What would happen if the outcomes were not equally likely?

It’s a good idea to try and take a picture of what this looks like to display in class. You could also annotate it with fractions and overall probabilities.

13. Trigonometry Snapdragon

I wanted to boost my students’  level of understanding of trigonometry without switching off their enthusiasm. We’d investigated the tan ratio practically and introduced sin and cos.

Now the tricky bit – how to make picking and rearranging trig rules interesting!

Introducing the Trigonometry snapdragon:


Pinch together the two things in the question eg opposite and hypotenuse.


Look inside the snapdragon at the pinched portions. Follow the instructions eg Sin rule: know hyp, find opp or know opp, find hyp


Unfold the appropriate section for your problem.


You now have the correct rule, rearranged for your problem.


Student Feedback
‘That is amazing’ and ‘Can I make one in the exam?’.

Download a digital version here: Trigonometry snapdragon v2

Also visit the updated snapdragon page for a blank template: Snapdragon fun