I recently worked with the children in my class on BASE 5. I say BASE 5 because that was what I introduced the base work on. I was, once again, surprised how well this abstract concept, of using a different base, became something rather simple and logic for the children. How come?
I think it was the link to their well-known ‘base’ they work on- Base 10.
The sheer knowledge of how to do an exchange (carry over, what they all do on a daily-basis, is implanted in them, therefore, the act of using a different base is a simple logical frame-work.
I need to add that I do, meanwhile, work in 6th grade (elementary) yet 1st grade of the IBMYP programme. These two do overlap yet regarding heir age, 11 to 13, their reasoning mind is well developed (at least on an analytical side) therefore their wider understanding of the concept at hand is given and the time is right o confront them with this kind of lessons.
So I introduced the topic by readdressing the decimal system, making the link to the wooden hierarchical material, the families (simple, thousand, million) and directed them to the all known place values in the decimal system. A nice brief recap of what they know, bringing them back to where they come from. All felt secure and confident, that they remember all of this.
After the introduction was done, we went to the lace vales of base 5. Since the concept was understood within the decimal system, it was logic for them that instead of multiplying each number by ten, we multiply by 5;
1 – 5 – 25 – 125 – 625 = place values of base 5
All that was clear and the links were made.
The concet was understood and hence we established that in base 5, we only have 5 numbers. Vice versa, in base 10 we have 10.
Base 5 = 01234
Base 10 = 0123456789
All that was clear, and the addition exercise in base five presented no difficulty; Instead of exchanging at ten, we exchange at 5. Keeping in mind that five is an illegal number such as 6 7 8 9.
With some we went onto transforming base 5 to base 10.
There, all the knowledge of multiplication and division comes in action and need to be applied.
All in all, I need to say that this lesson was/is a fantastic manner o introduce something new yet all the known need to be applied and repeated; I can recommend to not wait too long to introduce to 11/12 year old children. It wraps it up very nice with something exciting and new.