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Just made a couple of videos explaining multiplication in a visual way, using the ‘Box Method’
I’m working on adding nicer text and math symbol support in GridMaths, so formulas will look like they should.
LaTex is the ‘gold standard’ but I’m thinking of using a simpler alternative which gives most of the benefit, namely ASCIIMathML. I think its quite a nice format, something that covers most of the things a highschool Maths student will encounter, with a reasonably predictable and short syntax.
I’m experimenting with the best way for GridMath UI to enter math expressions, so it may be that you don’t normally see the text representation, but it may be exposed when you need to edit. I’ll use MathJax to render this, so it may be that you can edit and enter LaTex directly if you are a power user and know it well.
In my googling, I happened upon this video ahowing how to do long-multiplication of polynomials.. and thought I’d try the same problem using the Grid or Box method :
For some students it might bridge the gap and give them a helpful intermediate step so they see it as the same kind of thing as multiplying integers. I would also try out the box approach to introduce multiplying mixed numbers with fraction parts, and numbers with decimals, and so on – as it relates back to the earlier understanding of multiplication as area of a rectangle.
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 :
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 !
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 !
Just added a color palette to GridMaths, so it now has rectangles, lines, ellipses in few simple colors and weights. The idea is to help make diagrams clearer, and help with Venn diagrams and other cases where you want to group things together.
Heres a grid sheet comparing fractions : 2/3 and 4/5 … then we show the product and sum using the same visual representation.
If you look carefully, you may notice that I ‘abuse’ the grid in that each grid square is 1/5 high and 1/6 wide – so a 1 unit x 1 unit square is actually 6×5 grid squares. I think this is a legal abuse, in that we often graph things with different x and y axis scales.
The alternative is to have a resizeable non-square grid.. which I think creates too much complexity for not much gain. The philosophy of GridMaths is “keep it simple”, so you can do the basics quickly and easily. I used to think more features = more power = better, but after my son showed me the Minecraft game, and all the cool things people have built with it, I changed my mind about this. I kept thinking.. why is Minecraft so popular, when you can do all that and more in Blender ? Blender is a superb free 3D modelling package, which like all powerful modelling packages takes a while to become proficient at. So, it dawned on me that Minecraft is so brilliant because it brings down the barrier to entry, and makes the 80% of things you need to do to make a world, really easy and quick for everyone.
So I’m adding the most useful things to GridMaths in a way that keeps it really simple. Its not an algebra system, it most likely wont have handwriting recognition… but it should be a really fast way for math teachers to make Math diagrams and for students to do a wide range of worked Math problems, replacing grid paper for that 80% of tasks and adding some nice features. Its kind of like an infinite supply of grid paper, that weights nothing and can be erased and replayed, and saved for later use And.. you can step forward and back thru your edits and change stuff, and students can step thru a worked problem. And you have counting beans and … :-]