Visual Sequences

'Get out the multilink cubes and literally build an understanding of arithmetic sequences'

Build a visual representation of the sequence 1, 5, 9, 13. What does it look like? What have your colleagues build? Do all of them make sense? In this activity the aim is to explore arithmetic sequences by building them physically and relating them to objects made of a different number of parts. See how may different ways there are to make different sequences and play with the idea of systematic increase!


The main aim is to introduce the idea of arithmetic sequences and systematic changes from one term to the next. Within this there is an aim to see a link between physical objects and abstract numbers. Students should practise generating particular and general terms of a sequence and work towards the derivation of some general formulae.


You will definitely need some multilink cubes or similar items for this activity. Then the structure and tasks are given by the  Visual Sequences activity sheet. Teachers can read more on  Visual Sequences TN.

Below is a small gallery of responses to building the sequence 1, 5, 9, 13 ! Some require a little more conversation than others and I think they all need 'Classifying' into different groups, but they are all valid answers, one way or another! Enjoy

Syllabus links

New - Section 1.7 Arithmetic sequences and series and their applications.

Previous - Section 2.5 Arithmetic sequences and series and their applications.


Here follows an outline of what the task is. If students are not reading this page then the teacher will need to show and give this overview.

  • Students are given multi-link cubes or similar nd asked to build a visual representation of the sequence 1, 5, 9, 13.
  • Students may make more than one model either by using more cubes or by taking a photograph before dismantling the first and reusing the cubes.
  • There follows a small classroom exhibition of the models. Students look at each others and the class debates the different types.
  • Students record the work and views on the work sheet and follow the tasks thereafter.
  • The exercise may be repeated with a different sequence.
  • Students answer questions different terms of the sequences.
  • Students work on the tasks aimed at generalising their conclusions.

I did it my way!

As a practising maths teacher I know that most of us like to give activities our own little twist and do them 'our way'. It would be great to add a little collection of 'twists' from users. You can either add your twist to the comments section below or e-mail them directly to me at In time some of these twists may appear here....

All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. Any unauthorised copying or posting of materials on other websites is an infringement of our copyright and could result in your account being blocked and legal action being taken against you.