A. has been working on algebra, and while I really like the VideoText program I have her using, I realized that she was having difficulty with equations because she couldn't picture what was going on. I remembered that I had heard of a manipulative program designed to teach algebraic concepts and went on a search. I came up with the Hands-On Equations program. A. and I have been working through it together, and I really like it. (I can't say the A. 'really likes it'. She is tolerating it and humoring me, but she can do it.) I think the way they have devised for helping students see what is happening when they are solving equations is genius. I know that A. thinks it feels babyish, but once we complete all three levels, I'm pretty confident that her abilities will take a giant leap forward and she will have no more trouble with what she is doing in her other program. Besides, how can you not like a program which allows your child to easily (A. got it the first time) solve a word problem such as this: "John is 6 years older than Keisha. Together, their ages equal four times Keisha's age How old is each?"
Want a brief demonstration? Here is a simple example so you can see how it works. The variable 'x' is represented by the blue pawn and the whole numbers in the equation are the red cubes. (Add the cube numbers together... don't place them together. That number on the right side is 13, not 103.)
The equation for this picture is: 4x + 5 = 2x + 13
One of the rules of the manipulative is that if there is a blue pawn on each side of the balance, you can remove both. So the first thing we did was to remove the two matching pawns on either side. That leaves us with: 2x + 5 = 13
Now, we can also remove the same whole number from both sides. Here we have removed 5 from each side, leaving us with 2x = 8. We haven't learned how to divide yet, but the manipulative assumes that a child can look at this and figure out in their head that x will equal 4.
Here's a slightly more difficult equation.
Notice the pawns and numbers one above the other? This is how to demonstrate: 2(x + 3) = x + 8. Notice there are two sets of x + 3. We then combine them together and remove the matching pawns from each side which leaves us with this:
x + 6 = 8. Then we remove 6 from each side and that gives us an answer of x = 2. Ingenious, isn't it? We are now starting to learn how to work with negative numbers. As we work through this, I have also been writing out how we would demonstrate what we are doing in a more traditional method so A. can see how the two relate. I'm thinking I will always start with this in the future before doing a traditional pre-algebra program with the rest of my children.
My second advertisement is to invite you to come see Thin Ice Theater's newest production, Little Women. It's next weekend and A. is playing Aunt March. Either email me for details or go to Thin Ice's website. Expect more theater posts soon.