This video from Aljazeera explains the origins of Algebra and how important it is for us today.

This is one in a large series of short videos from NCETM showing how people use maths at work. See the others here.

Use these links to research optical illusions.

What are your  favourite illusions? Make them into a Powerpoint presentation.

Can you use what you have learnt to design your own illusion?

Wikipedia

illusions.org

123opticalillusions.com

echalk

nih.gov

video-best optical illusions

A search engine will find many more!

This cube has 6 faces, 8 vertices (corners) and 12 edges.

This square based pyramid has 5 faces, 5 vertices and 8 edges.

See how quickly you can do this quiz from Purpose Games. Click start, then the computer will give you a number for either F (faces), V (Vertices) or E (Edges). You just have to click on the letter next to the right shape.

Do you know your prisms from your pyramids? See how quickly you can do this quiz from Purpose Games. Click start, then click on the shape whose name appears at the top.

Here is a great site to discover all about three dimensional shapes. Find some scissors and glue, print off some of these nets and see what you can make! http://www.korthalsaltes.com/cuadros.php?type=p

Inspirations
A mathematical masterpiece, imagining the workshop of M C Escher

Here are my hands. Calculate the ratio of the length of the rectangle to the height by dividing 12 by 7.5.

Now work with a friend. One of you make the same shape with your hands, the other measures the length and width. Again calculate the ratio. Swop roles and do this again. You now have three ratios. What do you notice?

Here is the beginning of the Fibonacci Sequence. It is made by adding the two previous numbers together.

1, 1, 2, 3, 5, 8, 13, 21.

Work out the next 10 terms of the sequence and write them down.

Now calculate the ratio of each number compared to the number before it, like this. Round your answers to 4 decimal places.

1÷ 1 = 1

2÷ 1= 2

3÷ 2= 1.5

5÷ 3 = 1.6

8÷ 5 =1.6

13÷ 8 = 1.625

You continue for the next 10 terms. (Use a calculator!)

What do you notice?

You have discovered a very special number, called phi. Find out more about phi and the Golden Ratio here.

Here is a fascinating site to find out about the Golden Ratio and the human face.

http://www.intmath.com/numbers/math-of-beauty.php

Don’t miss the flash application where you can fit a mask to some famous faces to see if their facial proportions match the golden ratio.

You will find the Golden Ratio appears not just in the human body, but in architechture, design nature, cosmology, photo composition, art and much more.

This is a great investigation from N-Rich which combines geometry with simple algebra. Your task is to find a rule that will calculate how many lines there are in any mystic rose. To construct a Mystic Rose draw a circle then use your protractor to place equally spaced dots around the circle. You then join each dot to every other dot with a straight line.

Useful Interactive White Board tool for introducing students to the concept of Line Symmetry.

I chose a Penrose Triangle to be the logo for Maths with Graham. Look closely- it’s impossible! Lots of people think maths is impossible because they had such a hard time with it at school. But usually when they get the help and attention they need they are able to learn, make good progress and even pass exams! The impossible is possible!

If you visit this website you can make your own 3-dimensional Penrose triangle and see photographs of them.  You can read more about the Penrose Trianglee here.