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My son is working on some LCM word problems on Khanacademy.  LCM is short for “Least Common Multiple”, this KA vid explains it pretty well.

Basically the idea is to take two different measuring rods of two different lengths, start at the same place and keep measuring out lengths of each until the ends match up exactly : the first time this happens is at the LCM.

Easier to see than explain, especially if you get kids to experiment by putting rulers end to end, its kind of a nice little discovery, and the kind of open exploration that gives you the cool math-buzz when you discover something yourself.

I had fun doing a couple of these in GridMaths…

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One nice thing is you can go step by step and see the rulers being added as they chase each other, with the ends not matching.. each team trying to win the race, each one getting ahead for a while..until the grand finale when…  ahh, its a dead heat !  :]

I guess the potential with a software tool, rather than paper, is that you could potentially have Cuisenaire measuring rods of any length [ a set of the first 50 primes would be a nice grab bag of tricks ] … and you could get LCM for larger numbers by just laying down more grid and scrolling to the right.  Its early days, so GridMaths doesn’t have this feature yet.. but I really like the fact that its open to doing things like this.

Prime Cuisenaire Rods anyone ?

When I was a kid there was this class where each student prepared their very own ice-cream container full of counting items – marbles, colored buttons, hexagonal Meccano nuts, etc. Somehow the teacher sold us on ‘owning’ and preparing our own stash, and I was very proud of sneaking in two tiny model mini cars and a couple of cool shells I picked up from the beach.

I also remember those lengths of wood in various colors used for counting/measuring things. These “Cuisenaire Rods” are magic, you can pick up a set on eBay from $10 to $15, or improvise with flat Lego units of different lengths and colors if you have those.

It would be unconscionable of me to not include this staple of Western math diet, so I give you a peak at Cuisinaire Rods in GridMaths.  I hope you like the spicy Mexican color scheme :

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Simple things, but these can be a very tactile way of developing a feel for fractions and division.   They lead into strange discoveries, like the fact that some numbers can’t be made exactly from repeats of smaller lengths… prime numbers !

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A special note to those of you who have taken time to read my experiments, and egg me on with your comments and feedback – your support is so important to me and my son, we heart you !