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The True Scale Multiplication Grid

I came up with a neat idea for a multiplication grid visual the other day, and stuck it up on Twitter where it has been doing the rounds with unprecedented alacrity:

I’ve loved reading comments and seeing how people are using the grids already, with fellow teachers, students and your own kids (I’m making one on A1 squared paper for my son this weekend – here’s one 3-year-old who will know what multiplication means before he learns his tables, if I can manage it!)  A few of you came up with ideas for variations I could do, including starting the grid from the bottom-left to mimic a Cartesian coordinate grid, and emphasizing square numbers.  I’ve also done one with the prime factorization of numbers on one side of the diagonal, which I quite like.  I’ve put all the images together into a single pdf document to make it easier to access.  It’s on my website at www.thechalkface.net/resources/true_scale_multiplication_grid.pdf:

Please feel free to mess about with these, share them, modify them, distribute or display them.  I’d love to hear what you get up to, and in particular if you come up with any great ideas for investigations please share them in the comments section below or on twitter: @the_chalkface

My plan with the multiplication table was to give learners a clearer intuition for multiplication.  It is my firm belief that most difficulties students encounter with ‘hard’ topics like proportion, fractions and algebra usually stem from an inadequate grasp of, and familiarity with, multiplication.  There’s no point trying to teach expanding brackets until the distributive property makes sense numerically, for example, and the right sort of visual might help students to see not just the what, but the why.

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11 thoughts on “The True Scale Multiplication Grid”

1. Sally Ryan says:

Thanks very much for making this public and not charging for it. I am a support teacher and I think this might just flip the light switch for some of them.

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2. Patricia DeCorsey says:

Sorry dear, but Maria Montessori came up with this grid (she called “The Decanomial”) over 100 years ago. We teach it to the children in Montessori classrooms around the world starting at age about 3 1/2 and all the way to 6th grade.

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• It turns out I probably saw a version featured on Resourceaholic a few years ago, as it happens! I’m pleased to hear that tables are being introduced like this, and only mildly disappointed (though not very surprised) it wasn’t an original idea.

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3. Great ideas resurface throughout the ages. Just goes to show how important a tool this can be! Thank you for helping to bring it back into widespread use.

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4. Amy Hinrichs says:

Montessori idea
Useful on many levels
Several hands on classroom materials reflect the mathematical patterning

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5. These are wonderful, as is your generosity! I am so sad when I see teachers spending their hard earned \$ on TpT products when the MTBoS community is so open and generous.

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6. Cindy Opler says:

I love this! Wondering how to use it with the more advanced students who already know their facts. How can I add a level of complexity to it for them?

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• Looking for patterns within the shapes is always enlightening. Is there a geometric way to see why 7 x 9 is one less than 8 x 8, or why 4 x 8 is four less than 6 x 6? Precursor to quadratics and difference of two squares: (n+1)(n-1) = n^2 – 1 and (n+2)(n-2) = n^2 – 4.

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• Cindy Opler says:

Thanks for this idea!

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7. AJacoby says:

Lovely implementation! One minor issue/suggestion: it’s a little hard to compare the relative sizes of the rectangles — the size of the font dominates the actual size of the rectangle. For instance, since the font for 42 is larger than the font for 50 (since 42 is closer to the diagonal), the rectangle for 42 looks larger to me, though I know logically it isn’t. Could the font size increase linearly with the size of the rectangles? Ie, use 42 pt font for 42 and 50 pt for 50?

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8. Angelo DeMattia says:

It might have not been original to the this world, but it was likely to this last creator!
I wonder if the wheel has been discovered on other planets …

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