Teaching Algebra, or Banging Your Head With a Whiteboard

educationrealist here writes up “the five big ideas of first year algebra”, which I likely could have used as guide to the algebra class I plunged into this past term. I’m reblogging as part of my hope to remember this when I teach algebra again.


The Five Big Ideas of First Year Algebra:

  1. Identifying the slope and y-intercept of a line from a linear equation, and graphing a linear equation provided in slope-intercept form.
  2. Solving multistep, single-variable equations that involve distribution and combination of like terms.
  3. Using substitution or elimination to solve a system of equations.
  4. Binomial multiplication
  5. Factoring a quadratic equation (a=1)

(You middle-school algebra teachers are saying “Wait, what about graphing a parabola? What about point-slope and standard form for linear equations? What about….” Stop right there. I teach the kids who didn’t make it through your classes. Some winnowing is necessary. Furthermore, I said the five BIG ideas, not the ONLY ideas.)

I’ve taught some form of algebra every year. From my first year on, I’ve nailed factoring quadratics. I do it with the generic rectangle, which has the added feature of helping out when a > 1. The integrated method I…

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