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I’ll deal with that number later

Today we are looking at a 2nd/3rd grade subtraction problem.

Let’s get started!

Quick question:  What is 120 really Do you know?  Can your child explain it to you?

Can they make that 120 friendlier?

I think that 100 + 20 is a lot friendlier than 120. It will be easier to take 38 away from 100, than it would have been to take it away from 120.

Since I don’t really need that 20 right now, I’m going to stick it on my forehead.

I’m holding that 20 in my brain and I’m going to come back to it later.

Sweet!  Now I can just deal with taking 38 away from 100.  That’s way easier.

100-38 on an abacus is super easy.  Don’t have an abacus?  Try a blank hundreds chart.

I like the Abacus because with enough practice kids start to visualize what 100 really is and know answers intuitively.

Ooops!  Is there still a number on my forehead?  I better deal with that 20 now.  62 + 20 = 82  I’m using adding (which I’m really good at) to help me do subtraction.

That means that 120 – 38 = 82!

But wait!  Did I really need a paper and pencil or could I have just done that problem in my head?  Hmm…

Math Boot Camp for Moms, Day 4

Don’t use an algorithm when mental math would be faster

I’m your coach Jenny and I like to think about numbers.

No really, tell that to your kids. Clearly express to them that you are their coach and that you like math (whether that’s true or not).

Let’s start by warming up!

What’s wrong with this picture?

A third grader who draws all of those lines and junk on a simple problem like 1,000-344 = is telling you a lot. They are showing you that they are clinging to a traditional algorithm instead of using their brain.

We need to teach our kids to think.

There are LOTS of better ways to solve this problem. Today we are looking at one possible method.

I’m using number cards from my Right Start kit, but you could just use paper and pencil.

Notice that I’m laying out the problem in a horizontal fashion. This encourages children to let go of their algorithm life-raft and start using their brain instead.

Let’s start by thinking about the number 344. What do I need to do to 344 to make it a friendly number?

No wait! I’m going to make this even easier. I’m just going to think about the 44. What do I need to do to 44 to make it a friendly number?

I know. I could add 6 to it and get 50. 50 is a friendly number.

That means that 44 + 56 = 100. 100 is a really friendly number.

That makes me think that 344 + 56 must equal 400.

And you know what? I know that 600 + 400 = 1,000.

That means that 654 + 344 = 1,000. I’m using adding (which I’m really good at) to help me solve a big subtraction problem.

What do you know? I can do that problem in my head!!!

The real art in teaching math comes from asking questions.

How would you solve this problem? Do you have a way that you like better?  Feel free to leave a comment and tell us about your stratgey.  Or, you can just mock me for having numbers on my forehead.  Whatever…

Math Boot Camp will be back in session tomorrow!

Math Boot Camp for Moms, Day 1

Subtraction

Bruce finished off his major chapter on subtraction last month, and he wasn’t too keen on it at first.  I teach math from a Constructivist perspective, which means enabling children to develop their own meaningful strategies for solving problems, instead of just blindly teaching traditional algorithms.  Here’s a nice website that explains more about the Constructivist philosophy: http://mathforum.org/mathed/constructivism.html

Bruce, myself, his classroom teacher, and my husband were all in the trenches there for a few weeks as Bruce explored different strategies for solving triple digit, minus double digit problems with and without regrouping.  In normal classroom situations, Bruce would have been exposed to his classmate’s strategies and thinking, which would spur his own ideas, creativity (and showmanship).  But since he is working independently through the second grade book, I had to introduce some ideas to get him started.

The first strategy I introduced was solving equations on two abacuses, flipped over on side A, so that they represented 200.  (We were starting with problems no greater than 200.)  This went on for about a week, and Bruce was not impressed.  He does not like using an abacus at all, and so I never got to teach him the side B methods.  I was really bummed about this, because my husband worked with an engineer from China, who was just brilliant at math, and Chang said that when he solved problems in his head he could picture the little beads on the abacus sliding.  I wanted this for Bruce, but maybe I didn’t introduce the abacus early enough.  I’ll know better next time for Jenna. 

The second strategy I introduced to Bruce was thinking about the problems in terms of money, and then counting out the equations in pretend change.  236-89 would become $2.36- .89.  Bruce was not too thrilled with this strategy either.  He could easily solve problems this way, but under protest.

Finally I broke down and taught him one of the methods the book demonstrated, ungrouping, which uses pictorial representations of hundreds tens and ones.  I had resisted showing him this method, because Houghton Mifflin uses it as a precursor to borrowing, which I do not want Bruce to learn until later.  But I’m eating a big slice of humble pie right now because this is the method Bruce absolutely loved.

All of a sudden Bruce started tearing through his subtraction work at top speed.  He called this strategy “Busting open the hundreds”.  I’d usually draw out the squares, lines and dots for him on the white board, and he would erase them and then redraw things as he started working.  Pretty soon, he was solving problems in his head, by just looking a the picture and not even erasing anything.  Then he didn’t even need the pictures at all. 

The way Bruce would solve the above problem is that he would think: “100-89 = 11.    11+36=47  100+47=147”  He doesn’t need to do any carrying or traditional algorithms at all, which is a testament to the Constructivist method.  Constructivism encourages children to think and understand what numbers really mean, instead of just blinding computing an algorithm, which can stunt their development of number sense.  Bruce’s accuracy isn’t 100% yet, but it is on par with your typical second grader.  I’ll teach him the traditional methods of borrowing and carrying someday, but not until Bruce can do even harder problems intuitively, in his head.