What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

You can now explore this further. Click on the picture to get started.

When you've explored what you can do with $3 \times 4 - 5$ then it's time to explore further.

You could change just one part of the number plumber, for example the $-5$ bit.

You might try $3 \times 4 - 6$ or $3 \times 4 + 5$ or $3 \times 3 - 5$ and compare the results.

You'll have lots of your own ideas about things to explore too.

Mathematicians like to ask themselves questions about what they notice.

What possible questions could you ask?

These questions may lead you to come to some decisions about what can happen.

Why work on this project?

Working on this activity can encourage learners to work together, discuss ideas, test things out and explore further. This is how it is to be a mathematician, working alongside other mathematicians, and children can experience this within their own classrooms. The activity can engage pupils in exploring orginal patterns, in contrast to number
patterns that the teacher or books suggest.

Possible approach

After the pupils have seen and written down the numbers as they appear at the bottom of the screen it is time for them to be Maths Detectives.

Ask them what they notice about the numbers. Encourage them to articulate anything at all - any pattern. You could ask them to talk about what is the same and what is different about the numbers in the list to get them started.

It could be that someone notices the number of digits in each of the numbers and how they increase. It may be that they notice a pattern in the units numbers or the tens or ... This sheet shows some possible patterns learners might explore. (It is intended to show you
the possibilities rather than being a sheet to share with children.) It can sometimes be useful in number patterns to explore the digital roots too.This articleexplains what digital roots are. By working in this exploratory way the pupils can be looking at number
patterns that NO-ONE has ever explored before. WOW!

Key questions

So, you've noticed ... what could we do with that?

So, you've got the idea that ... could we explore this further?

What slight change could you make to the set-up so that we explore something similar?

What possible questions could we ask?

Can you make any predictions about what might happen when we change the set-up?

What is the same? What is different?

Can you explain?

Possible extension

When the pupils explore further by changing just one part of the $5$ bits that make up the first number pattern. i.e. $3\times4-6$ or $3\times4+5$ or $3\times3-5$ etc new results wll be found and can be compared.

Possible support

Some pupils may find it easier to explore one step patterns first before they move on to more complicated patterns.