The power of visualising

The abstraction of numbers is a fascinating topic for debate and discussion and the root of much confusion in secondary school mathematics students, not to mention many of the worlds adults! As teachers, our challenge is to keep developing successful activities that help people to develop their powers of abstraction and understand ideas in different ways. Visualisation is a key tool in this process and, as such, I am always on the look out for new, and successful old ways of building activities around the idea. In the digital age, it is easy to forget the value of physical manipulatives and practical activity. Here are five number based activities that invite students to create their own visualisations using manipulatives and practical activity!

	Multiple Factors  Age 9+ Time: 1h. Students form interesting groups using their bodies to get a physical appreciation for factors and multiples. They then create a wide range of imaginative designs using counters, beads, collage etc. to represent numbers in terms of their factors for other groups to decipher. Finish with the multiple factors game. Be prepared for a lot of fun!
	Recreating Ratios  This lesson requires students to produce a range of images for a given ratio. The aim is to draw out the equivalence of different ratios and how, and why, they can be simplified. The more creative and imaginative students are in creating different images to fit a given ratio, the clearer the true concept of ratio becomes (great opportunity for display work). It also provides a good lead in to sequences and graphs. Age: 11+  Time: 1h+
	The Art of Fractions  Create some great art and display work whilst practising calculating fractions of different quantities. This activity involves the repeated splitting of rectangles into carefully chosen proportions defined by a single fraction and can lead to some lovely 'Mondrian inspired' pictures! Age: 11+ Time: 1 hr
	Visualising Indices  'Squared' and 'Cubed' can be explained by using 2 and 3 dimensions. The area of a square with length 5 is 52, volume explains cubed, so how can we represent 54? This activity explores visual representations of indices and draws on a little creativity! Age: 14+ Time: 1 hr
	The Rice Show  This activity is inspired by 'Of All The People in All the World' from 'Stan's Cafe'. Use grains of rice to represent different numbers of people! How can we make a pile of rice with 1,000,000 grains in it? Do the estimation then use some statistics to make a powerful display! Age: 10+   Time: 1 - 3hrs