How might a base 3 or a base 7 number system work?

 Creative, logical, and reasoning maths thinking.......

        (Student-generated questions to investigate our central idea)

As we have already theorised, we have a base 10 number system because we have 10 fingers.  

To help us deepen our understanding of how our base 10 number system works, we imagined we were visiting an alien planet. Instead of 10 fingers, the aliens have either 3 fingers or 7 fingers. 

So we wondered:

To create a new number system, we decided we would need to:

° create symbols for each digit

° think what would happen once we reached '3' or '7'

° find a way to make an odd number number system to work

° make sure there was a logical pattern to how the numbers worked

° be able to make large numbers

° could we make decimal numbers?

° be able to find a way to use those numbers to add, subtract, multiply or divide

To help us, we reexamined what we had already learnt about our base 10 system:

Then in partners, REALLY amazingly creative and logical thinking took place. Our room was abuzz with deep mathematical reasoning skills!!!

Some of our base 3 or base 7 number systems:

       Coming up with different ways to create large place values.....

 

Thinking of ways we could add, subtract, multiply or divide using our new number systems......

These students thought about how 'to the power of' might work in their number system......

Logical, creative, mathematical  pattern-making......

 Still working out how to manipulate the numbers. They had a lot of interesting debate whether they were accidentally creating a base 10 number system or not and then used 'to the power of' to rectify and solve the issue. Amazing thinking!

We haven't had a chance yet to peer-share our new number systems, but based upon conferencing with the partners during their thinking processes, I know they will be beaming with pride when the have the chance- and rightly so - such incredible reasoning and creativity! There was so much excitement and 100% full engagement throughout the entire process.

Below is the peer feedback we will use after sharing: 

After sharing and giving feedback, we will then go back to our central idea to think about what the advantages of our base 10 number system are.....