Teaching mathematics
Teaching mathematics

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

Teaching mathematics

2.4 Looking at structure in a sequence

We now return to the second main approach, where the focus is on looking for structure in a sequence. This is similar to looking at shape, rather than number, but it uses only one term from the sequence. A typical term is chosen – usually the third or the fourth, since the first term is often too simple to show the structure.

Activity 6 Looking for structure

Timing: Allow 10 minutes
shape C pattern
Figure 9 shape C pattern

An activity based on this approach will have two phases of exploration.

In the first short period, learners decide on their ‘shape four’. They can be supported by asking ‘Where do you see the “threes” in shape three?’. This phase ends with collecting several examples of ‘shape fours’, displaying them for comparison and asking ‘If this is shape four, do we know how to make shape five?’

For this problem, you might allow the class to divide into two groups: those who want to extend only the ‘arms’ of the C (so that the fourth shape has 9 squares) and those who have also extended its ‘spine’ (so it has 10). Either method can be justified but they lead to different expressions.

The task for the second phase is for pairs to explain in their books using a labelled diagram what ‘shape one million’ would look like, and find how many squares would be used for any shape.

Isometric dotty paper is a good resource for creating more patterns to practise this approach (Figure 10). Ask ‘If these are shape 3, what is shape 4?’

Figure 10 More shape threes
TM_1

Take your learning further

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses.

If you are new to University-level study, we offer two introductory routes to our qualifications. You could either choose to start with an Access module, or a module which allows you to count your previous learning towards an Open University qualification. Read our guide on Where to take your learning next for more information.

Not ready for formal University study? Then browse over 1000 free courses on OpenLearn and sign up to our newsletter to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371