Home » Posts tagged 'algebra'
Tag Archives: algebra
Okay Public School families, this is where I introduce you to something from the Homeschooling world that can be useful for families like ours. Have you ever heard of Life of Fred by Stanley F. Schmidt, Ph.D?
The “Life of Fred” series is a very unusual way to teach math, science, history, literature, and plain old common sense, in an integrated format. Half chapter book, half graphic novel, half textbook (hmmmm… those fractions don’t add up); the Life of Fred books teach through story and humor. The hero of the books, Fred, is a five year-old math professor at Kittens University, somewhere in Kansas.
I’ve been a bit harsh on these books in the past because Life of Fred uses a lot of algorithms early on, especially in the Fractions book. I’m much more of a Constructivist teacher, so too many algorithms, too early, makes me nervous. I also don’t think Life of Fred would be good for “mathy ” 1st-3rd graders who were emergent readers. The reading would hold back their math, which would be very frustrating.
But! If you were to take the opposite type of child, let’s say a kid who loved words, stories, pictures and funny jokes but who wasn’t very interested in math, then Life of Fred is absolutely perfect. I was just talking with a teacher friend last week who was dealing with that exact situation. “Have you heard of Life of Fred?” I asked her. “It’s just what you need.”
Another important thing to note about Life of Fred is that it is a spiraling curriculum. This means that Dr. Schmidt introduces a concept and then circles back to it later on. So if your child doesn’t quite understand something in chapter one, don’t worry, it will be reviewed again later.
Right now my son is reading Life of Fred: Pre-algebra 1 with Biology. In terms of Algebra, there’s nothing harder than Hands On Equations or Continental Math League. But there is a lot of other stuff, like fractions, decimals, and conversion factors. Kids with strong fifth grade math skills would do fine with this book.
I’ve been reading Life of Fred : Pre-Algebra 2 with Economics for fun. I’ve also got Hot X: Algebra Exposed! by Danica McKellar on my reading list. It doesn’t hurt for a mom to brush up on math she learned 25 years ago, right? Luckily, Life of Fred makes that pretty fun.
If you’ve read the recent article My Daughter’s Homework is Killing Me, then you know that parents all over our country are scratching their heads, wondering when homework got so dang hard.
I think that part of the reason is that complex concepts (like algebra) are being introduced in earlier grades.
In an ideal world, an early introduction to algebra would help prepare students to master advanced math in middle school and high school. It’s scaffolding for the future.
In the meantime, parents look at their kids’ homework and go “Whoa.”
Here’s a trick that might make homework easier. Add candy to the equation!
To show how this can work, I’m using an example similar to what you would find in the 5th grade Houghton Mifflin Math Expressions textbook, which the Edmonds School District uses.
Problem: Mrs. Garcia’s neighborhood has 28 pets. There are twice as many cats as hamsters and four times as many dogs as hamsters. How many of each pet are there?
You could use guess and check to figure this out, which would take forever. Or you could use algebra. Or you could use algebra and candy…even better!
One piece of candy corn equals the number of hamsters. Two pieces of candy corn equals the number of cats, which is twice the number of hamsters. Four pieces of candy corn equals the number of dogs, which is four times the number of hamsters. In all, the total number of pets is 28. That would mean 4 hamsters, 8 cats, and 16 dogs in the neighborhood.
Once you introduce candy into the equation, math homework becomes more fun. Just don’t forget to have toothbrushes on the ready.
Move over pawns, we have a new way of doing Hands on Equations to help jazz up the last five lessons. Instead of using the blue and white pawns, we are using chocolate and yogurt covered raisins.
My son Bruce started doing Hands On Equations a year and a half ago. (For more info, click here.) We very steadily worked on one lesson a week all through first grade. But in second grade, Bruce’s normal school work was doing a better job of “filling up his brain”, so we moved Hands On Equations to the back burner. This summer we’ve been cooking it up again, and are almost done.
Here’s an example of the problems he is working on now:
3(-x) + 2 = -10 + x
I can’t say enough good things about Hands on Equations. I’m still really impressed. If you’ve got a kid who can handle third grade math, be sure to look into it. The website is: http://www.borenson.com/
(From Lesson 6)
Can you believe a 6.5 year old can do this? Granted, my son Bruce is very bright for his age and is capable of doing third grade math, but this isn’t a case of “My son is so smart!” or, “I’m such a great teacher!” 😉 This is an example of brilliant, Constructivist curriculum at its finest. Can you imagine how easy Algebra 1 is going to be for my son someday if he can already do problems like this in first grade?
I’m not a representative for Hands On Equations and I don’t have any affiliation with the company. I just think this program is awesome. I really want to write a grant and bring HOE to my son’s school, but I haven’t even broached the subject with his teachers.
As a former teacher myself, I know that I really have to watch myself. I don’t want to be pushy, I don’t want to be the problem parent, and I just want to let Bruce’s wonderful teachers continue doing a wonderful job as they see fit. I know as well as anyone that public school teachers can sometimes be under enormous pressure to strictly implement district-approved curriculum, without any room for creativity. So for now, HOE is just a fun activity that we are doing at home. But oh my goodness! The teacher in me sooooo wants to run a HOE small group during centers time. I know those first and second graders and they would eat this up.
Bruce(6.5) and I are now on lesson 3 of Hands On Equations, the incredible hands-on approach to learning algebra at a young age. I sound like an advertisement, but I don’t have any affiliation with the company, I promise! 🙂 From the above picture you can see what type of problems Bruce is currently working on.
As his mother, I have to point out that his handwriting is a lot better than this example shows. It was 8pm last night when we “played” this, and since it was “a game” I let him be sloppy. Bruce was also eating a peanut butter and jelly sandwich at the same time.
Here is how you set up the board for problem #3: x + 3x = x + x + 10
Two of the x’s cancel each other out. So the leagal move is to take them away.
At this point, it is really easy to see that x = 5. Then you put the pieces back on the board so that you can manualy verify that 20 = 20.
I was talking with my friend Ari of Discipuli Speak fame, who was a math whiz himself at a very young age and who is now a teacher, and he was telling me how important it is for kids to understand that what’s on the left side of “=” has to balance what’s on the right side. It’s important that kids don’t just think of “=” as a signal to write the answer afterwards. Well, we are only on lesson #3 of Hands On Equations, and I’m pretty sure Bruce understands this concept pretty well now, and he’s only six and a half. That’s pretty darn cool!
For those of you who have not heard of Hands On Equations before, this is going to be one of those posts that is going to make you think Man, I wish I had learned math that way! for the rest of the day. I first heard about HOE on the blog Homeschool Ninjas. I have no affiliation with HOE whatsoever, and have dutifully shelled out my money like everyone else. Bruce(6.5) and I have only done one lesson so far, but I’m definitely thinking this was money well spent.
When our box of materials arrived from UPS, Bruce was of course curious about what was in the box. When he found out it was a math game, he immediately lost interest. Later that night when my husband was putting Jenna to bed, I told Bruce that he could eat a bowl of ice cream if he played the math game with me. He immediately agreed. Then, when we were getting the game set up I told him: “There’s good news, and bad news. The good news is that this game is really fun. The bad news is that we only get to play it for 27 nights.” That instantly peaked his interest! (I said 27 nights because there are initially just 27 lessons. Later on we will do the verbal problem solving book, but by then hopefully Bruce will be hooked.)
As soon as we started playing Bruce became super excited, because this is actually really fun. There is a lot of logic involved, as well as adding, subtracting, and basic division. Bruce kept hooting and hollering every time he got a problem right, and my husband had to come down and tell us to be quiet because we kept waking Jenna up!
I don’t know if you can tell from the ice cream picture, but the one mistake I made is that I did not have Bruce right down his answers correctly. We’ll have to fix that in the next lesson. I also should have been using the red die instead of the green die. It would have been better if I had the lesson plans in front of me, but I chose not to this time because I wanted Bruce to think of this as a game and not a math activity.
All through the activity I kept thinking to myself, I can’t believe I’m teaching algebra. The highest math level I have ever taught before was fight grade math in my 3rd/4th grade classroom. Although I got through college level Calculus in the 12th grade, I’m not a natural “mathy” person. But HOE seems really easy to teach and understand. It is the kind of math instruction that makes you think: Gee, if had learned algebra this way when I was little maybe I would be “mathy” person!
On a final note, I chose to purchase the basic kit and the verbal problems book. Beth from Homeschool Ninjas bought the package with the video instructions. I’m not sure if I chose the best combination of materials or not, but will keep you updated.