Thursday, May 12, 2011

Simple Equations - Horizons' Style

Basic Equations with Variables, in Horizons Math (starting 2nd or 3rd Grade)


Horizons Math teaches Equations, and I think they start this in 2nd grade.  Many math curriculum teach equations with variables, but not quite like Horizons!  I'll give an example:

Most Math curriculum will teach something like this:
x + 6 = 11;
The next step, according to other Math programs is to turn the addition problem into a subtraction problem:
11 - 6 = x;
Then 6 is subtracted from 11 to get 5
5 = x

Horizons Math shows the algebraic step missing in other programs.  Here is Horizons' method:
x + 6 = 11;
Next step is to subtract 6 on both sides of the equation.  This cancels the 6 on the left side, and gets the 6 onto the other side.  It also gets the variable alone, which is what we want;
x + 6 = 11
    -6    -6
--------------
Here, the 6s cancel on the left, and you can subtract 6 from 11 on the right.
x       =  5

I would suspect that many kids have the same reaction as my child: why do it that way?  It doesn't make sense!  I can do it the first way intuitively, and I get the answer just fine.  Why subtract from both sides?  Today I showed it with blocks, and I think it made more sense.  See the video above to see how I explained it with the blocks.  The example problem is
n + 5 = 9

Hopefully, this is enough to get the pattern.  After I explained it this way, my daughter was able to apply the whole "subtract on both sides" idea to her math problems.  Thankfully, she automatically made the connection that she'd use the opposite sign when confronted with this kind of problem:
y - 2 = 8
It seemed intuitive to her to add 2 to both sides.  Thank goodness, because I was having a hard time figuring out how I'd show that with blocks!  Looking online, the explanations get into some pretty big concepts: negative numbers and making 0.  It's not that my daughter couldn't get those concepts, I just hate to pile on too many new concepts all at once:)
Want more?  Here's a Khan Academy video that shows the same thing (without the blocks):
http://www.khanacademy.org/video/solving-one-step-equations?playlist=Developmental%20Math

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