Grade 5/6 Maths

As thinkers we wondered if there were patterns in numbers. If there were, how could we recognise, describe and symbolise patterns in numbers?

We each had an integer on a card.

We started by dividing our integer by 2 and realised that all integers that could be divided by 2 evenly were even numbers.

Therefore, all even numbers were factors of 2.

We realised we could symbolise that by 2 x integer.

We replaced the word integer with the symbol n

So all even numbers can be symbolised as or take the form: 2xn or 2n

We checked our thinking by everyone multiplying their number by 2. We all ended up with even numbers.

We then wondered how we could symbolise odd numbers and realised that all odd numbers could take the form

 2n +1

or 2n -1

We checked our thinking by multiplying our numbers by two and then adding one. Everyone ended up with an odd number.

Therefore, there are patterns in numbers. We symbolised the patterns of odd and even numbers.

Going Further:

Angus looked at our line and realised that odd numbers could also take the form

2n+3

Archie then realised that you could add ANY odd number to 2n, and the solution would be an odd number.

We checked this as well and it was also true!

Eg: when n=13

2n+1

2x13+1=27

2n+5

2x13+5=31

The simplest way of showing this pattern is

2n + 1