Patterns We Can Find With Prime Factorisation

To enquire further into prime and composite numbers, we began by discussing our analogy that the prime factorisation of a number is like that number's DNA.(See this previous link)


What would we like to investigate about this?

Some great suggestions were made.

Last week, we thought we had found a pattern in how many factor trees could be made when we double 6.

A few of us wanted to continue with that investigation so they did.


Someone else suggested we could see if there are patterns when we prime factorise the doubling different numbers.

Another suggested we could see if patterns exist when we prime factorise the multiples of a number.

Should we do this with partners or individually?


Usually as a class we we have a mixture when this is asked, but today we felt we should this individually so that we could

We then chose numbers we wanted to explore. 



As we found the prime factorisation of each number, we looked out for patterns that were emerging.

Some of us thought we identified patterns, but then the pattern would break.

Why?

Some of us found ways to predict the next number sequence and prime factorisation.

Why?


Some of us couldn't find patterns.

Why?


After investigating, we then published and used these to share our pattern discoveries.





Doubling 6 patterns:

Doubling of 9 patterns:

Doubling of 10 patterns:

Multiples of 11 patterns:

Multiples of 8 patterns:

Doubling of 8 patterns:

Multiples of 6 patterns:

Multiples of 3 patterns:

Multiples of 5 patterns:

Multiples of 4 patterns:

Doubling of 11 patterns:

After sharing our discoveries, we wrote a quick reflection about how this has helped deepen our understanding of numbers.




Some samples:

 

 

When orally sharing as a whole class, an interesting debate ignited over whether a pattern is still a pattern if it ends.......

Some interesting reasoning skills and wonderings emerged from this which we added to our wonder wall to investigate.