Subtraction, counters, & other manipulatives

[FairProspects]

Can someone explain subtraction to me (or how to teach it) using a manipulative other than counters or an abacus?

 

I realize that counters are less than ideal because they do not show the relationship between numbers. Ds really needs some kind of concrete manipulative for subtraction but refuses to use an abacus - he just doesn't like it. He will occasionally use a number line, but frequently balks at that as well.

 

What else can I use to cement the concept for him that is not counters? Ideas?

 

Interestingly enough, he does get that subtraction is the inverse of addition and if the problems are paired together, he can easily solve them without manipulatives, but subtraction alone? Forget it. :glare:

[kristinannie]

I love the way Miquon describes subtraction in the Lab Annotations using C-rods. Is it copyright infringement if I post specifics here? As a former lawyer, I always get worried! :D

[Lily_Grace]

I like the MUS way of overlaying one rod on top of the other. We've also used graph paper in red and blue cut into number strips to achieve the same: a strip of 4 red squares on top of a strip of 5 blue squares shows 5 minus 4 and the 1 left over.

 

Eta: the strips also work very well with the subtraction strip boards found on the righthand side of this page - http://www.montessorimaterials.org/math.htm

They have the red and blue rulers at the top of the page, too, but we used them without the numbers written on them.

Edited August 9, 2011 by Lily_Grace

[raceNzanesmom]

I like the MUS way of overlaying one rod on top of the other. We've also used graph paper in red and blue cut into number strips to achieve the same: a strip of 4 red squares on top of a strip of 5 blue squares shows 5 minus 4 and the 1 left over.

 

Eta: the strips also work very well with the subtraction strip boards found on the righthand side of this page - http://www.montessorimaterials.org/math.htm

They have the red and blue rulers at the top of the page, too, but we used them without the numbers written on them.

 

I like how Steve does this too.

 

I also teach him how to do the inverse for any problem in his head (8-6=? is the same as 6+?=8). With practice he's gotten very good at that, so he may have to pause and think but he can easily get it by switching it. Another thing that helped early on was making up stories- 8 people came to the pizza party, only 6 ate pizza, how many did not eat pizza? You can use any counter for those- pennies, buttons, etc. You make up a story for one problem,, then have him make up a story.

[Spy Car]

I love the way Miquon describes subtraction in the Lab Annotations using C-rods. Is it copyright infringement if I post specifics here? As a former lawyer, I always get worried! :D

 

It is called "fair use."

 

Besides Miquon sales go up when people describe how easily it teaches subtraction.

 

Bill

[MerryAtHope]

I Another thing that helped early on was making up stories- 8 people came to the pizza party, only 6 ate pizza, how many did not eat pizza? You can use any counter for those- pennies, buttons, etc. You make up a story for one problem,, then have him make up a story.

 

Yes, stories involving food--especially if it was a story about my children eating my food (cookies, pieces of pizza, etc...). They thought that was a hoot, and they never had trouble solving a subtraction problem that involved eating my food!

 

We also used Base 10 blocks and money and board games. Base 10 blocks helped the most here for teaching, especially when we got to having to "borrow." It was very easy to demonstrate and for them to see that they had to exchange a ten for ones or a hundred for tens, etc... Money and board games were helpful for reinforcement/drill.

 

Merry :-)

[FairProspects]

I actually bought and sold Miquon because I could not wrap my head around it. I have the C-rods, but is there anything that can tell me an idiot-proof way to use them? Sort of like an "Activities guide for the Abacus" but for C-rods instead?

[Spy Car]

I actually bought and sold Miquon because I could not wrap my head around it. I have the C-rods, but is there anything that can tell me an idiot-proof way to use them? Sort of like an "Activities guide for the Abacus" but for C-rods instead?

 

I have never used it, but Ellie has frequently linked to Mathematics Made Meaningful. It looks extremely straightforward in showing how C Rods can be used in an idiot-proof fashion.

 

Bill

[zoo_keeper]

This is stolen from another poster, but we also use poker chips. The white chips = 1, the red = 10, and the blue = 100. So when ODD is doing, say 92-38, she's got 9 red and 2 white chips. Then she'll hand me 3 red chips and cash in another red chip for 10 white chips, after which she'll return 8 white chips to me, leaving her with 5 red chips and 4 white chips (54). After a while she should learn to give me 4 red chips at once and only ask for her 2 white chips in change back. I hope this is somewhat clear.

[bleeglaser]

We've used the base 10 blocks and it's worked really well. My 6yr old can count up to 100 and I've just found out he is no longer intimidated by subtractions. I laminated the Saxon math flashcards and he's been doing great with those. Anything he can't do in his head he will use the blocks. So 12-4 for example, he will count a stick of blocks(10) and then he will add 2 more. Then he counts all 12 blocks to make sure it's right. Then he will remove 4 and count the blocks remaining. We also have counting animals which we started with too. His brother likes to play with those so we don't use them as much. The blocks stick together which helps with counting I think.

[nansk]

How about part-whole circles? 10-6 would be seen as, 'One part of 10 is 6; what is the other part?'.

With C-rods, we did it the same way; laid the smaller rod over the bigger rod and asked which rod would fit the missing part.

[Alessandra]

These are some things we do, using Singapore Math, which emphasizes number bonds:

 

-- laminated cutouts of apples placed on a page w/ a pix of a tree. There are 6 apples on the tree, two fall off, how many are left? (For addition, 4 apples on the tree, 2 on the ground, how many altogether?)

 

-- plastic balance-type scale w/ objects (we happen to use counting bears). Six objects on one side, move two to other side, how many are left?

 

-- Singapore clown on a page. Clown has a rectangle below and a rectangle above each hand. We put a number card -- say 6 -- below, and then put 6 objects (we use counters) over one hand of the clown, move some counters, ask how many are left.

 

-- using the same clown, we then replace the counters with number cards. The we put the number cards on a ___ - ___ = ___ template.

 

This is what I do for a math-challenged child. Obviously, YMMV.

 

Here is a clown image - if you copy and paste to a doc, you can the add boxes using text box function with a border.

 

http://www.google.com/imgres?q=clown+image&hl=en&client=safari&sa=X&rls=en&biw=1456&bih=844&tbm=isch&tbnid=5_e8qlBFe2ZxfM:&imgrefurl=http://www.kidopo.com/coloring-pages/holidays/purim/purim-clown/&docid=-kcPx_SUPow-mM&w=609&h=677&ei=zGxCTorqD8mXtweosKnDCQ&zoom=1&iact=rc&dur=330&page=2&tbnh=157&tbnw=141&start=30&ndsp=29&ved=1t:429,r:3,s:30&tx=81&ty=44

 

ETA Singapore emphasizes progressing from a 'number story' to a number bond to a number sentence.

Edited August 10, 2011 by Alessandra

[peacefully]

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