*On the third week of maths club my teachers gave to me, three prime rocks! Two logical puzzles! And information on a dead genius...*

Yesterday, the program on offer in Maths Club was a set of interesting word problems about decimals, fractions, and ratios which we deemed too advanced for the Class 5 students. Since all of the Class 5's are my math students during regular class time, I took them aside for a rockin' enrichment activity based on the introduction to division that we did in class.

In class, I had every student gather a handful of stones. (“Handful” is a wonderful ambiguous quantity that guarantees that some students will bring in many tiny pebbles while others will choose a few good-sized rocks.) Each table group counted the total number of stones they’d collected and then made as many piles of seven stones from it as they could. It is the simplest, cheapest division demonstration ever.

In maths club, they took twelve stones and found all of the possible ways to divide them into even piles without getting stuck with a remainder, which is to say, they found the factors of twelve:

When they tried it with seven, though, they found that the only fair arrangements were all-of-the-rocks-together or all-of-the-rocks-alone. I told them that that means that seven is a "prime number." I asked them to use the stones to find more prime numbers. They found all the first ten! I then helped them derive the divisibility rules for 2, 3, and 5 so they could check if a given big number like 5026041 could possibly be prime. (It can't. 3 is a factor.):

That lesson was a great success. I had some trouble in math club, though, too. One of the other groups asked me to check their work converting fractions to decimals. They had written 1/4 as 0.4 and 1/3 as 0.3. I was able to prove to them that their answers were wrong because 1/4 plus 1/4 plus 1/4 plus 1/4 should be equal to 1 but 0.4 plus 0.4 plus 0.4 plus 0.4 is equal to 1.6. I had an awful time, though, trying to explain why the decimal form of 1/4 is 0.25. In Canada, it is the easiest conversion of all to explain because one fourth is a quarter and everyone knows that a quarter of a dollar is ¢25, aka. 0.25 dollars. Technically, the Bhutanese ngultrum is divided into 100 chhertum just as the Canadian dollar is divided into 100 cents and technically there is a 25 chhertum coin. The problem is that coins are never actually used here because everything costs a whole number of ngultrum. 25 chhertum is worth less than one tenth of a penny. There is just no point in anyone carrying around or caring about that much money. I've been in Bhutan two months now and the only time I've seen coins was in the collection of a numismatist half way up the climb to Tiger's Nest. Explaining why 1/4 is 0.25, then, was my first experience of the universal language of mathematics not seeming universal at all because my go-to teaching strategy is tied up in a specific cultural phenomenon.

I'll leave you on a positive note, though, with some comments on maths club written by the students:

How about a century - 100 years. Quarter century - 25 years. Do they celebrate silver anniversary--quarter of a century?

ReplyDeleteLove Mom & Dad M

What a great division and prime-number game!

ReplyDeleteJust the other day I was talking about math with a schoolmate, and we commented how much easier it was when we have ways to see what it all means. I bet your methods are really helping the visual learners in your class.

For the decimal thing, maybe you could use a ruler to put notches on a 10cm candle- When it is half-burned, your kids could check the measurement and see that it is down to 5cm, or to any other fraction/decimal combination