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Round and Round the Circle

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.

Making Cuboids

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?


How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Become Maths Detectives

Age 7 to 11 Challenge Level:

Become Maths Detectives

Have a go at becoming a detective.

Click on the picture to get started.

Alex's Number Plumber

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 make conjectures.  A conjecture is something which you believe to be true but need to investigate further in order to convince yourself.

Why work on this project?

This month's NRICH site has been inspired by the way teachers at Kingsfield School in Bristol work with their students. Following an introduction to a potentially rich starting point, a considerable proportion of the lesson time at Kingsfield is dedicated to working on questions and ideas generated by children.

Working on this project 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 our own classrooms. 

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, which might 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 interesting to explore the digital roots too, see this article. By working in this exploratory way the pupils can be looking at number patterns that NO-ONE has ever explored before. WOW!

You can read more about the approach at Kingsfield School in the article Kingsfield School - Building on Rich Starting Points. Although written from a secondary perspective, it is just as applicable to primary settings.

For teachers who want to create their own alternatives to Become a Maths Detective for use in the classroom, Mike's blog Grumplet describes some instructions and rationale.

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 $5$ parts 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. The operations being explored can be changed in many different ways.

Possible support

Some pupils may find a calculator useful or they may want to use practical resources to support their calculation skills.