Who hasn’t studied mathematics and seen the chart for multiplication from 1×1 to 10×10 on the wall? I had a teacher once who said that that was OK but the chart really gets interesting when you make it 12×12. And we did with chart paper. Adding 11 lets you really explore patterns in multiplication and adding 12 gets you into talking about multiples of dozens.

What more can you do?

Well, if you work it in reverse, the multiplication table can become a guzz-inta table to talk about division.

Over the weekend, I was intrigued by this Twitter message from **@the_chalkface**.

A multiplication grid… to scale! Each entry is the right size (oh, and square numbers are squares!) pic.twitter.com/NbbXB0jpdZ

— TheChalkface (@the_chalkface) April 27, 2017

Now, how about that. It’s your traditional 10×10 multiplication table done in proportion to the numbers represented. The progression of results is presented very visually; it’s a natural for those who are familiar with mathematics blocks.

Mathematics is beautiful and this really shows it. Numbers are done by proportion and things are displayed very visually according to size. What’s neat about the representation is that numbers that are square really are square. For the beginner, they can truly see that 81 is indeed bigger than 36.

Now, this bit of genius invites further investigation and so I hopped over to his **blog**. The latest post at the time that I visited explained how it was done. It was so interesting to read. But, there was a real gem found in that this wasn’t the only grid that visually represents the traditional chart.

A number of alternatives are available **here** in PDF format.

He calls them a true scale multiplication grid. And, it is.

What fun can you have with it?

Just a computer science example, used by everyone, I’m sure. It’s a classic program to demonstrate nested loops. Then, it gets interesting when you have the students right justify the numbers and also display the grid. Mathematics and Computer Science. Does it get any more beautiful than that?

When I was first learning computer science I would occasionally have some bad days when I thought I’d never “get it.” One of my moral boosting exercises was to write a program that would print out the multiplication table up to 12 x 12. Or sometimes to some arbitrary set of values. Trivial of course but somehow I found it satisfying. I probably wrote that program 3 or 4 times in my university days. These days I occasionally use it as an exercise for beginning students.

With calculators so common I don’t know how much tables like these get used in real life. I remember when they were printed in textbooks and on paper book covers (does anyone still use book covers for textbooks?) Are we getting old Doug?

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