### Counting with coffee Beans on grid paper

When I started teaching my son maths we did a lot of counting coffee beans. We would arrange 12 beans in groups of 3 and groups of 4… The idea was to start building up intuition and then segway into multiplication.

Don’t ask me why coffee beans.. I must be a bad parent! The beans just happened to be handy, being dark they were easily visible when put on 5mm math grid paper and fit nicely in the squares. You can use small buttons or raisins even. Its pretty tactile, so works okay for young kids [ as long as they are old enough not to swallow small things ]

### Abstracting to Multiplication

Later we drew the ‘beans’ in the squares and then just drawing a circle in the box instead of placing a bean. This gradually led to tracing out the rectangle outlines of the groups and let the squares on paper take the place of actual beans.. so it abstracts really well in a fairly natural and unforced way.

There are some nice ‘tricks’ you can do on squared paper that grow out of this approach –

- every rectangle is a multiplication product, so you can use it to figure out any times table question
- you can work out all the times-tables and write them in the top right square before reciting them
- introduce distributive property (a+b)*c = a*c + b*c by showing the rectangles add up
- ask.. are there any numbers that cant be made by a rectangle product? [ yes..prime numbers]
- show square numbers – 1,4,9,16 …
- you can show how to add 2n+1 to n squared to get the next square number
- you can introduce series – 1+3+5+7+ … and show how they sum to make the square numbers
- make a stepped-triangle 1+2+3+4+5+6 and show how two of these can be put together to make a rectangle, which leads to sum 1 to n = n(n+1)/2

So this approach leads very naturally into some really nice mathematics. Along the way it reinforces the rote learning of times tables (auditory repetition) with visual intuition.

### The web app – introducing Doctor X

I thought there was probably an App or web page to do this kind of thing interactively. I googled around and found lots of times table grids, math systems but nothing that seemed to take the grid-paper-rectangles-and-counting-beans approach into an interactive medium.

I made notes on what the app might look like, and then spent some time making a quick prototype in Javascript. I found It needed a way to step through some basic usage notes and examples, so I added a howto box. Then we came up with a silly name for this thing.

Anyway, here is the current version of the visual grid calculator for kids, which I’m calling :

“The Doctor X Amazing Griddable Multiplication Contraption”

When I get time Ill make some more in-depth tutorials and worksheets on some of the concepts I mentioned above. Let me know what you’d like to see,

enjoy!

gord.

## 2 comments

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June 14, 2012 at 18:04

Sue DowningI love it. I recently made, labeled, and laminated a 10×10 grid on a 4 x 6 card to help a 6th grade student who really struggles with multiplication. She draws the rectangle with a dry erase marker and then starts crossing out boxes at the top and marking them at the bottom to make rows of 10. I think she will really like your contraption! If I were to add an option, it would be to allow an X to be placed on colored blocks so they could be “moved” to make rows of 10. Thanks for making and posting this!!!

June 17, 2012 at 08:12

quantblogSue, thanks for your comments.

Id love to hear how your student gets on with DoctorX. If she makes a ‘picture’ she likes, she can now share via email or twitter with her friends.

I have a few features in the pipe when I ‘get a round tuit’ as they say.