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Base ten and Cuisenaire for harder problems


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I have been watching the educational Unboxed videos and I finally am understanding better how to use them along with other stuff better. I do not typically like to watch videos to learn but It has been worth it because I see how to use them for all sorts of problems now.

 

She referenced Crewton's House of Math and it gets even into more difficult math then the Educational Unboxed videos but I am having a much harder time with those videos and he seems to have issues with certain ways the problems are set up in the Educational Unboxed videos but I am having a hard time understanding why. I really think it will help my oldest dd and my other two when we get to it.

 

http://craftknife.blogspot.com/2016/03/how-to-model-long-division-with-base.html

This blog post got my closer to understanding this type of long division but I still feel like I am missing a step of how to construct 1122 like that and I do not get the arrow thing.

 

Do you start with 11 100s and then trade one of the hundreds for tens so you can do the 4 across in 34 and then another so they line up?

Edited by MistyMountain
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Well... I read that blog post and found it extremely non-intuitive.  Having the sides of the rectangle not correspond to the number written beside them, all so it would fit the way we write the algorithm... is cumbersome and could be avoided by rotating the rectangle 90 degrees.

 

Figuring out how to lay out the rectangle *is* solving the long division problem.  Everything after that point is just counting.  I wish that were emphasized in that blog post!  

 

I found using base ten cards (right start) to be an easier way to model long division without needing to invest a million dollars in base ten blocks- that is, I found grouping to be a better model-->algorithm demonstration than area and missing side, though I also did area with missing side using cuisinaire and hundred flats using the Education Unboxed method.  For either method, I think there comes a point of diminishing returns with larger and larger numbers.  Once the child is rock solid, conceptually, with long division by a single digit divisor, then modeling it with a 2 digit divisor is pretty cumbersome without really adding much value.  Or at least, having them complete more than a small number of problems with a physical model seems like major overkill to me.    

 

If you want to see how to use the base ten cards to model long division, I could probably either find or make a video pretty easily.  ETA:  

is basically how I do it, I just use physical cards or blocks.  

 

 

 

Edited by Monica_in_Switzerland
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That is a good idea to use the Right Start base ten cards. I have those. The video you linked had a good one suggested in the side with two digit with numbers in the teens that I liked. Maybe working on single digit and then teens until it can be done confidently without a model and just doing a few problems with bigger numbers would be enough to understand.

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I always use base 10s to introduce anything with regrouping. My son especially needs to see concretely why that 100 just became 10 10s.

 

I found it very helpful with long division and multiplication.

For long division, we made the number to divide out of blocks, then tried to divide them into the correct number of groups (usually separate pieces of paper or drawn circles). If you can't physically divide up a block then you need to regroup it.

 

We did it with just blocks for a while, then blocks with me writing the algorithm (painfully slowly, step by step), then blocks with him writing (even slower), then I had him draw representations of the block while he wrote.

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