I have noticed that I am missing a lot of things on the blog. One thing I've forgotten to blog about is Lumptons. Lumptons are little gumdrop shaped people invented by Leena.
There are Good Lumptons, Bad Lumptons, and Average Lumptons, all with slightly different shapes. When a Bad Lumpton becomes better, they change shape to look more like an Average or Good Lumpton.
This picture is of a Good Lumpton asking for a flame thrower. You may notice that they change shape in many circumstances. This one starts out in her normal shape, is very startled when she isn't given a flamethrower, and then becomes pleadier, and pleadier...
But what do they have to do with Algebra?
Leena finished up the delightful Life of Fred: Pre-Algebra with Biology a while back, and we were trying to decide which Algebra text she wanted to use next. Of all the Life of Fred books I own, the only one I dislike is Algebra I. I find it confusing and quite different from the other books in the series. Math U See is very good, but she hasn't enjoyed it in the past. The world is full of Algebra programs... but the world is not full of math that Leena will have fun doing.
"Could you teach me Algebra using Lumptons?" Leena finally asked.
Well, why not? This is my fourth time teaching Algebra, it would be fun to try it with Lumptons!
I decided to use the Math U See program as my schema for scope and sequence (what to teach and the order of presentation), but to explain it all with Lumptons.
Here, I told Leena that Sally is going into the jelly making business. She has two jars in her pantry and can make 6 more jars of jelly and hour. If J is the number of jars, and H is the number of hours, we can say J = 6H + 2
If you've done a lot of algebra, you might say, "Hey! That's the slope intercept formula!" And it is.
At this point, usually Leena starts coming up with her own questions to further the story. She wanted to know how long it would take to make enough jelly to feed Sulky for an entire day. Bad Lumptons eat more jelly than Good Lumptons and Sulky is a very bad Lumpton. She eats 20 jars a day!
Well if J=20 then 20=6H+2 When she worked it out algebraically, that would be 3 hours.
I find it really interesting that when I teach half the lesson, Leena usually comes up with the other half on her own. I think that, in school, Leena would be written off as "not good at math." But the fact is that she is very good at math whenever she sees the slightest reason to use it. She just finds math in abstraction tedious.
The joy of being a fourth child! My first few tries at algebra, I probably couldn't have done it with Lumptons. I was written off as "not good at math" in school, and didn't know the subject well enough. One of the fun things about home schooling is that I actually understand math, and now I really enjoy it!