How To Master Quadratic Equations

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feature photo above by Junya Ogura via flickr (CC BY 2.0)

A couple of weeks ago, James Tanton launched a wonderful resource: a free online course devoted to quadratic equations. (And he promises more topics to come.)

Kitten and I have been working through the lessons, and she loves it!

We’re skimming through pre-algebra in our regular lessons, but she has enjoyed playing around with simple algebra since she was in kindergarten. She has a strong track record of thinking her way through math problems, and earlier this year she invented her own method for solving systems of equations with two unknowns. I would guess her background is approximately equal to an above-average algebra 1 student near the end of the first semester.

After few lessons of Tanton’s course, she proved — within the limits of experimental error — that a catenary (the curve formed by a hanging chain) cannot be described by a quadratic equation. Last Friday, she easily solved the following equations:

\left ( x+4 \right )^2 -1=80


w^2 + 90 = 22 w - 31

and (though it took a bit more thought):

4x^2 + 4x + 4 = 172

We’ve spent less than half an hour a day on the course, as a supplement to our AoPS Pre-Algebra textbook. We watch each video together, pausing occasionally so she can try her hand at an equation before listening to Tanton’s explanation. Then (usually the next day) she reads the lesson and does the exercises on her own. So far, she hasn’t needed the answers in the Companion Guide to Quadratics, but she did use the “Dots on a Circle” activity — and knowing that she has the answers available helps her feel more independent.

Introduction to the Quadratics Course

Life Lessons from James Tanton

This is Kitten’s favorite James Tanton quote so far, from the video we watched on Friday:

… And I am going to panic, because we got 16, but the problem doesn’t want 16. It wants 15. So I have two choices right now: Give up, and cry, and just go home.

Or use my common sense. What would I like this to be?

A good piece of advice: If you want something in life to work out the way you want it to work, just make it happen.

I want that to be 16. How can I make that happen? Just add one. Bingo! It becomes 16. However, if you make changes in your life, you’ve got to deal with the consequences …

— James Tanton
Quadratics 2: The Algebra of Quadratics

2 thoughts on “How To Master Quadratic Equations

  1. This is such a lovely commentary! Thank you so much to you and Kitty for sharing your thoughts about the course I have here. I can’t wait to get all my other ideas for more courses up and running.
    Cheers, James.

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