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montessorisbev
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| Posted: July 13 2011 at 1:43pm | IP Logged
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Hi All ,
I have a question.. My ds 9 is ready for 2 x multi digit multiplication. The thing is I don;t know how to teach it except for giving him the formula or the set of statements for going about doing it. I don;t know if that will help his understanding of it.
What did you use for your children?
I am considering buying the math mammoth worktext for mult/ div. We have used montessori for the introduction to these concepts in the past,and while I think these have been wonderful, I don't have the checkerboard material or the test tubes for these higher concepts.
Any reccomendations?
thanks
Bev
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Mackfam
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| Posted: July 13 2011 at 2:24pm | IP Logged
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Bev,
I didn't use the checkerboard or the test tube materials to teach multiplication or division as I didn't have those materials either, but the more I use Montessori manipulatives, the more I find that a good set of decanomial beads and a basic set of golden beads works great for conveying many basic concepts. Some of these Montessori math presentations may give you a few ideas.
To teach multiplication, I first introduced the 100 chain and the 1000 chain and used the counting chain arrows. One day I would ask my son to mark the chain with the arrows counting by 10's...then 5's...and so on. He really enjoyed this. Then, I brought out the decanomial beads and had him line up the beads of 2s and we'd count....1 group of 2 is = 2....2 groups of 2 is = 4....and so on. Sometimes he'd write things down, but I didn't require that. My goal was to convey in concrete, hands-on and visual ways what was going on mathematically when we multiply. Once he had the concept of a number family of multiplication and could visualize it (so for example, once we had finished the [2x] family or the [5x] family....) - we moved on to just finishing up by using flash cards to help reinforce the multiplication facts.
Once a child understands multiplication, it was easy for me to explain that division was just undoing. We used the decanomial beads (or you can use ANY counter for this) in groups again for this....so for example, 16 divided by 4....I would set out 16 of the (#1) decanomial beads and show my son how to read the problem....16 total divided into 4 groups.....so he would divide the big group of 16 into 4 equal groups...and then he *sees* what division is. Then, I might set out 4 groups of 4 and see if he can show me the division problem from there -- he makes a CONNECTION!! From there, I just used flash cards to reinforce the math facts again, but only once my son could *see* the concept in front of him, interact with it with his hands, and then visualize it in his head --> then we move on to memorization techniques.
Here are some resources to consider:
Decanomial beads - I wouldn't part with my set because I use it to convey so many mathematical concepts to all my children (though I'm sure I didn't pay that much for my set...I'll link more sources for you at the bottom of this post). You don't have to use beads though, any manipulative that shows clear *groups* of a number and offers enough of those *manipulative-things* for the child to interact with would work here!!! If there is one *thing* that I love from my Montessori collection of materials, one tool that gets used over and over and over again....it is this decanomial bead box.
100 and 1000 chains - again, these are an expense and I'm sure there have got to be diy ways to accomplish this concept without the chains, but I do really like the visual these chains present. I have a set of both chains and find them valuable for skip counting and beginning to visualize multiplication concepts through skip counting on the chain.
Counting chain arrows - free printable here :: inexpensive quality printable here :: chains already printed on a thick plastic here at Alison's Montessori -- these are a bit of a pain to keep organized, but they've been a very useful tool. Personally, the idea of printing and cutting all those arrows makes my head spin...but it could be done easily especially if one had older children to help. I didn't at the time, so I purchased the ones from Alison's and I like them. An alternative to the counting arrows is to use small counters or flat glass marbles (a little fat, but they would do), or something else and just tell the child to mark by 2's or 3's. The drawback is that you wouldn't have the number printed on the arrow to help the child with skip counting - 3-6-9-12 - and so on. I had another idea to roll the chain of golden beads out on a roll(s) of dry erase paper and have the child use a dry erase marker to indicate the skip counting numbers...but you'd need SEVERAL rolls for the 1000 chain!!!
For affordable Montessori materials:
Kid Advance
Montessori Concepts
Montessori Outlet
Montessori For Everyone
You probably know about a lot of these resources, Bev, but I thought I'd list them for the benefit of others reading that might want to look into them, too.
I do like the Math Mammoth books a lot, too, but I also find great value in how the Montessori math presentations convey concrete --> allow for interaction and for the child to make connections --> and begin to assist a student in visualizing a concept. This lays fantastic groundwork for more abstract upper level math work! Thought I'd mention these ideas since it's clear you enjoy some Montessori work!  Hope that was ok!!
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Jen Mackintosh
Wife to Rob, mom to dd 19 , ds 16, ds 11, dd 8, and dd 3
Wildflowers and Marbles
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Mackfam
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| Posted: July 13 2011 at 2:28pm | IP Logged
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montessorisbev wrote:
Hi All ,
I have a question.. My ds 9 is ready for 2 x multi digit multiplication. |
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montessorisbev wrote:
We have used montessori for the introduction to these concepts in the past,and while I think these have been wonderful, I don't have the checkerboard material or the test tubes for these higher concepts.
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Oh good grief, Bev!! Forgive me! This is a case of me not reading your post close enough the first time! 
I realize my entire post doesn't answer your question about multi digit multiplication and higher concept division, but I'll leave it anyway in case it's helpful to someone else. Ugh. Sorry!!
Yes - do check out the math mammoth books!! I just ordered and downloaded a few earlier this spring and I like the series a lot!!
Back to the regularly scheduled answer.... 
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Jen Mackintosh
Wife to Rob, mom to dd 19, ds 16, ds 11, dd 8, and dd 3
Wildflowers and Marbles
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AmandaV
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| Posted: July 13 2011 at 3:13pm | IP Logged
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I haven't taught this yet to my child, but math was my favorite subject and I temporarily majored in it before teaching.. so here's a thought that makes sense to me, and I used a bit with my 6th graders who came in without understanding 2 digit multiplication: you could could teach with rectangles using tens and ones separated for an area model. Hard to draw on here so I found this video - looks pretty well explained. I don't recall calling it a house, but that makes sense:
2x2 multiplication area model
Oh, and I found this NCTM explanation and lesson: Illuminations:Multiply and Conquer
I'll think on division...
I hope that helps some!
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Amanda
wife since 6/03, Mom to son 7/04, daughter 2/06, twin sons 6/08 and son 7/11, son 1/2014
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Angel
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| Posted: July 13 2011 at 3:59pm | IP Logged
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My dd had a tough time with this. I used Making Math Meaningful 4, which takes a much more hands-on approach to show that you are really multiplying the UNITS first, then the TENS, so that 25 x 31 is really 25 x 1 + 25 x 30. It demonstrates with diagrams of squares. The division got a little unwieldy, but by that time, she was ready to make the shift back to Saxon for the not-hands-on explanation.
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Angela
Mom to 9, 7 boys and 2 girls
Three Plus Two
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montessorisbev
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| Posted: July 14 2011 at 1:42am | IP Logged
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Thanks for the replies - all of them are helpful :) I will check out the links postedd.
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4Real Forums : Living and Loving Numbers
Topic: How did you teach 2 digit mult and div
