Helping kids learn algebra

In the math study groups we organize at home, we’ve moved past fractions and percentages into the wild and wonderful world of algebra. Translating a problem into an algebraic equations is somewhat familiar to J-, but the process of solving algebraic equations confuses all the kids. I have a feeling that we’re either taking up the topic before the teachers have had a chance to adequately explain things, or the real-life situation (“Town”) leaves the students little time to focus on other lessons. Well, it is what it is (this is becoming one of my mantras these days), so we just have to do our best.

The small-group format is still working well. We’re going to try it with four kids to see if pairing them up to help each other will help the kids learn more effectively and build more confidence. W- has also checked out an armful of books from the library. I’ve been paging through “Real-World Algebra” and similar books to find some ideas for exercises the kids can relate to.

We try to liven things up with energy and amusing examples. They have to eventually become comfortable with abstract exercises such as 5n + 30 = 180, and it’s difficult to make that more interesting. I don’t want to just repeat the fake word problems of standard algebra textbooks, so I’m keeping an eye out for real-life situations in which I’ve used algebra myself. It can be hard to notice when you take math for granted, but math is everywhere, so I should be able to collect examples.

In the meantime, there are small things we can do to help them keep their attention on math or to remember the concepts more vividly. I tried this example for distribution:

2 * (number of lions + number of tigers + number of bears) = 2 * number of lions + 2 * number of tigers + 2 * number of bears.

I drew a lion, a tiger, and a bear instead of writing the corresponding phrases. =) Then J- said, “Oh my!” and everyone laughed.

The kids often forget that whatever they do to one side of the equation, they need to do to the other. As a result, J- once ended up with the interesting equation 2 = 4. Looks like we need to review how to use the equals sign. ;) We might try the see-saw metaphor. If you have a balanced see-saw, you can keep it balanced by adding or removing the same amount from both sides. You can keep it balanced by multiplying and dividing from both sides. If you add, subtract, multiply, or divide one side without doing the same to the other, you end up with an imbalanced seesaw. We’ll see if that helps them remember.

Because we’re discussing new material for them, we have to walk through the exercises together before they can try things on their own. When they try things out, progress can be slow and frustrating. We’re seeing if we can take advantage of group dynamics by posing a question and encouraging the kids to talk out loud about the strategies they might use. They help each other out, too. The group format definitely pays off – seeing other kids struggle or succeed helps a great deal.

Do you have any favourite middle school group study resources or tips? =)

  • Frank D

    I started teaching my kid algebra (when he was around 6) by having him calculate the number of pennies I had hidden inside of my hand:
    3 x the # of pennies in my hand = 12
    when he got it right, he got the pennies! After doing many little problems, I told him I was tired of repeating \pennies in my hand\ and would just use p
    p / 6 = 1/2
    (he still got the pennies). Slowly, I started incorporating fractions, later squares and square roots, or if we did it in the car, there would be no pennies, but he would still like doing it, as kind of a game. Eventually, the problems became to long to remember, so I would have to write it down, etc.
    Now that I’m reading \Reality Is Broken\, by Jane McGonigal (awesome book), it makes even more sense, since it’s set up as game, has a very fast reward system, I can keep it more and more challenging as time goes on, etc. So I really like teaching this way, set up as a game.
    He’s 14 now and still remembers learning algebra that way, and is still good at doing math in his head. (If only I could continue bribing him learning and doing his homework with just pennies :)
    Frank D.

  • Morgan D

    You might want to check out the Khan Academy . It was recently featured on TED and has videos covering algebra, practice lessons, and an ability to keep track of progress.

  • I make up word problems that revolve around cats. For example, suppose Simba can run 1 meter per second, and Sylvester can run 3 m/s. It’s dinner time, and mom opens the tuna can when Simba is 20m away and Sylvester is 40m away. If they both run toward the tuna at the same time, who will reach the tuna first? How much time will it take the first cat to reach the tuna? If Sylvester reaches the tuna first, at what time will Simba and Sylvester be the same distance away, and what would that distance be?

    One real deficiency in math education in USA is that negative numbers are introduced so late. I don’t recall seeing our daughter learning them until grade 4 or 5. I think they should be introduced a few weeks after subtraction, in grade 1.

  • Raymond: Love that idea! We will work some physics into our exercises.

    J- is in grade 7 and is starting to work with negative numbers in her equations. I’m sure she’s come across them earlier and the concept doesn’t boggle her, but it would certainly be useful to practise all the operations with negative numbers. =)

    You can always introduce concepts earlier than the school does. Good luck and have fun!

  • Sacha – have you seen the nrich site?
    You may be inspired by some os the activities there.


  • A few years ago the school system’s math teachers actually put out a notice that told the parents not to show the students “tricks’ to solving problems. This was a few years ago when they wanted the kids to do division a Certain Way.

    Naturally, I disregarded that notice, and I continue to show her material ahead of time. For example, when she was solving linear equations, I solved a quadratic. “This equation has 2 solutions; x will have two values.” “No way.” Five minutes later, after solving and substituting the solutions back in, she goes, “Oh wow!” :)

    I’ve also introduced imaginary numbers. She thought I was kidding. I can’t wait…. LOL