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'Exploring Number Patterns You Make' printed from http://nrich.maths.org/
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.
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 article
explains 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!
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?
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.
Some pupils may find it easier to explore one step patterns first before they move on to more complicated patterns.