Notation for solving equations

I just found this via Math Teachers at Play...

 Carolin's Notation for Solving Equations

Carolin is a student from Germany. I just wanted to note that that is exactly how I was taught (in Finland) to note what is done to each side of the equation, and I really like the notation. I don't know if it's used in all Europe...

Basically, you note in "the right side margin" what you're going to do to both sides of the equation in your next step. The "margin" is made by writing a vertical line to the far right of your actual equation solving process.

6x - 5 = 2x      | -2x

4x - 5 = 0       | +5

    4x = 5       | ÷4

     x = 5/4

I just wanted to pass this on in case some of you who are teaching how to solve equations find it useful with students.


Anonymous said…
Thanks - that's how I learned it in Germany when I went to school many years ago, and this is how I am teaching my children to keep track of their algebra steps.
Smartvlearning said…
The equation made mathematics pretty simpler.
Paula Tyroler said…
I am a grandmother of twin girls, age 10. They are not home-schooled, but I have been using your Mammoth series as a supplement to their regular schoolwork. Their Canadian "official" math textbooks (Nelson) are pathetic. I don't understand why they are being used.
The main reason of this short note to you is to tell you that the "European" notation for solving equations was (and perhaps still is) used in Czechoslovakia when I was going to school there in the fifties. It is practical and makes a lot of sense, but I almost forgot it. Thanks for reminding me. I will use it when I teach my granddaughters the art of solving equations.
Paula Tyroler
This notation does for Algebra and Arithmetic what two-column proofs do for Geometry.

I used to tell students to memorize this strategy for solving linear equations in one variable:
a) Distribute (a rule for eliminating brackets)
b) Combine similar terms (reduces linear equations to two terms on each side)
c) Add the opposite (of the smaller variable term, of the smaller constant term) to both sides (reduces a linear equation to two non-zero terms, total)
d) Multiply both sides by the reciprocal of the numerical coefficient of the variable term (solution: x=5, or whatever).

They were to indicate, with curved arrows from line to line (as your student uses "|") to show what they had done (e.g., +(-2x+3)).
Anonymous said…
I wonder if you'd be interested in the math tool I invented. It came from a need to teach my algebra students how to balance equations such as "solve for x in: 22x + 17 = 3x + 5", where the student has to either subtract 3x - 22x or 5 - 17 to get to the answer. My students were having a lot of difficulty with this, answering that "3x - 22x = -25x", and so on. As it turned out, this was the BIGGEST mistake my students were making in algebra, which boils down to simple integer subtraction! The tool is called the ZeroSum Ruler and you can see it here at my blog...

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