# A Miquon question

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I have spent what seems to be an endless amount of time trying to explain communicative property to my 8yo. You know, a group of 8 can always be broken into a group of 3 and a group of 5, whether you write that as 8 - 5 = 3 or 8 - 3 = 5 or 3 + 5 = 8 and so on. So today, doing Math Mammoth, she got it. You could almost see the light bulb go on. But I don't think it was my explaining that did it. I think she finally just spent enough time playing with the blocks that we use, moving them around, and writing the problems out on her own. This all brings me to my Miquon question. I've been told (or read, whatever) that Miquon is discovery based math. But I'm not sure exactly what that means. What does a lesson actually *look* like? Maybe I don't understand because when I learned math, I just memorized the facts and the steps in the process. I didn't spend much time playing or enjoying math. Would Miquon be a good fit for an 8yo who needs to SEE and TOUCH in order to understand? And would I want to start at the beginning? I would be doing it in addition to Math Mammoth, because there really isn't enough practice in MM for us and I've been making my own worksheets anyway.

I know there have been a ton of threads about Miquon in the past, but right now I really don't have time to read them all. So any input would be appreciated.

Thanks.

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So the way it went at my house is my (then) 4 year old preschooler would play with the rods (whose "values" he had very quickly picked up). And I would ask him, "what are all the ways you can make 7?"

He would take a 7 rod, and stack all the different combinations of numbers he could think of on top of that 7 rod. This is called (for whatever reason) making "trains."

One day he said: 3 plus 4 is the same as 4 plus 3.

And I said that's right, you have just "discovered" the Commutitive Law. Then we tried other numbers to see if the Commutivive Law worked there too. Yes, it did. He had "proved" the concept (one he'd "discovered" himself) and he had a name for it.

Then either Miquon Lab-sheets or self-made Lab-sheets in the Miquon style would follow up with 3+4 and 4+3 type questions back to back, and I would ask, "how do we know they are the same?"

Commutitive Law.

Then Lab-sheets would have questions like 3+[ ] =7.

And a child puts a 3 Rod on top of a 7 Rods and "discovers" the difference is 4.

Then it might be [ ]+3=7? Or 3+4=[ ]?

And the idea of what Singapore calls "number bonds" emerges. First as a "discovery" (proved by using Rods) and then followed up with a discussion of wholes and parts and how one can find "differences." The thing that really works is that the child "proves" concepts in their own minds first. This "discovery" is (often) directed, but they prove things to themselves. Then the laws they are learning are made explicitly known, and played around with.

It is an extremely effective and rich way of learning and teaching mathematics.

Bill

Edited by Spy Car
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I can't add much to what Bill has explained but just wanted to answer this question:

Would Miquon be a good fit for an 8yo who needs to SEE and TOUCH in order to understand?

YES, absolutely. My dd is the same and she loves the c-rods. She has understood the commutative property well.

...because there really isn't enough practice in MM for us and I've been making my own worksheets anyway.

Have you tried to use the worksheets software that comes with MM?

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It sounds like Miquon would be a great supplement for your dd. Take a look at the scope and sequence, but from your description I think Red might be a good place to start.

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Yep... we do similar to what Bill described. Take a "7" rod and figure out how many different ways she can make 7 with the other rods. Then she sees 3+4 and 4+3 very clearly. I think the rod play really helps her to see things. We've been doing skip counting for classical conversations and she lines the rods out to skip count them. Then she figures out five "2" rods are ten.

It's weird because we initially tried to do singapore 1a and she got frustrated very quickly. But she does the same problems in Miquon and thinks it's a game... and an OBVIOUS game at that. We shelved singapore for now and decided to just "play" with Miquon. There is some Miquon voodoo magic somewhere that makes things click. I'm a fan.

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Yep... we do similar to what Bill described. Take a "7" rod and figure out how many different ways she can make 7 with the other rods. Then she sees 3+4 and 4+3 very clearly. I think the rod play really helps her to see things. We've been doing skip counting for classical conversations and she lines the rods out to skip count them. Then she figures out five "2" rods are ten.

It's weird because we initially tried to do singapore 1a and she got frustrated very quickly. But she does the same problems in Miquon and thinks it's a game... and an OBVIOUS game at that. We shelved singapore for now and decided to just "play" with Miquon. There is some Miquon voodoo magic somewhere that makes things click. I'm a fan.

The thing is the Rod play is exactly the same thing thing that Singapore is trying to teach in a slightly different form. Singapore even has a concrete>pictorial>abstract sequencing as part of their educational philosophy. They just largely forget the "concrete" part and move directly to "pictorial".

So Miquon is a boon for young kids. It gives them the "concrete" stage for all 4 math operations. It is fun, it is play, and it is age appropriate. Win, win, win.

Singapore is still great for giving structure for a whole-parts math model, but Miquon gets the children comprehending that model concretely, and the Lab Annotations provides on-going ways to the the mathematical laws (that are often implicit in Singapore) explicit using concrete exapmles with manipulatives.

They are a very strong combo. As I suspect would be the same with MM.

Bill

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Thank you all. Where is the cheapest place to buy Miquon and a set of rods?

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I got my books in a set from Rainbow Resource. It was cheaper to buy as a set. There is an inexpensive set of rods (155 pieces) there as well.

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