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.
When there is a first combination … you will find a second combination.
I been thinking that these combinations are ideal ways to introduce a child in primary to various terminologies, words, language. One can apply terminologies found in algebra, explain the concept of variables with the pictures you see on the board. In that case the word sum could be brought to the child’s attention, that this word is linked to an addition, introducing the word quotient and product. For visual children this can be a good tool to give them these words. By experience a 10, 11 and 12 year old can by times struggle with word problems hence to a non-understanding of the terminologies they have in front of them.
These important words are often neglected because of the drive of having the right result or answer.
Of course there are millions of ways to give ‘the words’ to a student, yet within the Montessori material is so much that can be used for things, topics, facts and ideas but one doesn’t dare to do.
I can explain (within the chapter of equations) what it means to maintain balance. It is visual, clear and attractive. ‘whatever is done on one side of the equal sign must also be done on the other side’;This board could be my introduction. Later one also can use a scale to let the children explore.
I will continue my investigation of the vabulous variety within the Montessori material, wher and how to apply the given in different topics of mathematics.
Where to start in Geometry? What age is the right one? How much does one need to pay attention to language? Again I think that children can and need to be trained in their visual understanding and additionally one can add the right words to what they see and obsreve. The earlier they learn to be able to express what is in front of them the better it is.
I see it now in the last year of elementry and in the first years of secondary how hard it is ti express properly and clearly what they see and most of all, what they have to do or are doing. SO language is essential and will help them to describe and explain…
If you can explain it, you know how to do it…
THINK INTERDISCIPLINARY 🙂