19
Dec 16

## Questions to Santa about Multiplication

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Dear Santa

I have been good, so I have some questions about how to play a game. Is multiplaycation possible with natural numbers of things or units?

When something is multiplayed, its number may become more than one and the thing becomes thingS. It may also become less than one thing and become one or more of an equal number of parts of the original thing or unit.

Scaling is about magnitudes of a single unit or dimensions of that single unit. When something is scaled, it may get bigger or smaller, yet there is still one thing, like my dolls' house, giant rubber ant and model planes.

Santa I want to focus on the one thing (or group) and put aside the scaling operation for a moment to ask...

Is it REALLY possible to do positive natural number multiplaycation without ANY form of repeated addition?

If so, how do the elves multiplay toys? Did you also teach the elves the distributive law for Christmas Eve? Or is that handled by Rudolph and you on the sleigh? Do you use GPS satnav too?

Just as I believe in you, I believe many people use their times tables to 'DO' multiplaycation. In fact I believe most mathemagicians learnt their times tables to save time summing identical addends.

Instead of the mathemagicians skip counting slowly from an initial augend to the first addend and then subsequent addends like me, they embed this repeated addition process into their memory to save time and do more painting or free reading in college!

Last term we did peanut axyums and it was the same as kinder. Instead of counting on using our fingers we just did it in our heads. This term we learn about counting on from zero without ANY fingers to start with!

Last year we lernt about the transport rule of multiplaycation. Two fingers shown 3 times is the same as three fingers shown 2 times. Also we got the distribution rule about three fingers shown two times is the same as three fingers shown one time AND three fingers shown one time.

Are these the transport and distribution rules the elves use at Christmas?

If multiplaycation NEVER leverages repeated addition, then to actually DO multiplaycation means it should be capable of being done without knowledge of the times tables.

If multiplaycation is NEVER repeated addition, then was multiplaycation ever DONE before it became CALCULATION via knowledge of the times tables and/or the application of mental algorithms or became a button on the calculator I was taught to use at kinder?

Can multiplaycation ever be operational on the natural numbers without repeated addition somewhere being played as part of the game?

Maybe multiplaycation without leveraging 'repeats' only exists in its own right once you leave the concrete stage or rational numbers and start thinking abstractly.

So Santa, does multiplaycation without ANY reference to repeated addition only exist as an ontology in the book of secret spells and tricks of mathemagicians?

I would like some maths toys but only if the rules of how to play are simple and make sense.

Please remember I have been good!

Love Jonathan

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OK, so my letter to Santa was never sent. Yet I was confused by multiplication as a young boy and have discovered why. The western world has been teaching the wrong model of multiplication since 1570!