Sunday, January 29, 2012
Problem Solving Concepts Made Easy
Note that depending on age the emphasis changes...for the older girls it's about the concepts and seeing the rules they have been taught, for the younger students it's about finding same and building addends.
The basic concepts are hero zero and no fun get back to one...but it's all about using those to find same and SEE what x is...the equals sign tells us what x is...and x can be anything depending on the problem.
For all of them it's about making it easy and fun. Let's start with older students:
Now as is typical of many high school math students, they have yet to master multiplication and resort to fingers when adding. I will get them off their fingers and they will have to master multiplication on their own...
Then Watch a six year old doing basically the same thing, CONCEPTS are the same. (BTW it's a piece of organic all natural endangered species chocolate which he picked out from the health food store.)
And the older kids (begin to) SEE the rules:
They are hampered by a mental paradigm that math is hard even when it's this easy...it takes a while for them to realize really math is easy; but when that shift happens the math becomes easy and with or without me A's can be achieved. In the vid we did not evaluate for x = 6 but I did so with them and with Dboyz who figured out that 30 plus 3 is the same as 18 plus 15...and they were quite proud of their skip counting skills...counting by 6's all the way to 30 with the younger boy in the lead. When doing 18 plus 15 they knew five wants to be ten so it takes a five from the 8 leaving 3 tens and three...they also did 8 takes the 2 from the five and again we get 3 tens and 3...lots of DO-able math for kids of all ages. 10 years from now this will be old hat for some students. More to come on the problem solving page at the house of math...the question will come up, how do you do a problem like this?
3x - 2 = 2x + 5...there's no -2 in five. True. You need hero zero again, none of this balancing stuff...you just see same on both sides.
5x + 3 = 2x - 12 again many people can't see same on both sides...that's because of hero zero again. Want a detailed explanation? You need a password. PPPSP = The Password Protected Problem Solving Page.
There are tons of different problems on the PPPS and vid that make them ALL super easy. Remember those boat and current problems? Or how about constant rate problems? AND of course the ones you see here where you might think it's not same on both sides because things got negative...just a few minutes and you will see your way clear...
I have heard from a student that has since moved to the mainland that she is getting A's for the first time in math...all I did was adjust her thinking and hand her some concepts she can use no matter what the topic...beliefs are powerful things. She now believes math is easy...she knows it...so of course she's getting A's. I don't need to be there. And that's the point of all this.