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I'm studying to be a secondary math teacher and will be starting student teaching next month (an algebra 2 class). It's difficult to find activities and projects that are actually informative and time efficient. Any ideas?

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See my discussion of "left brain" and "right brain" approaches to polynomial multiplication in this 3 May 2010 math-teach post at Math Forum for one idea. –  Dave L. Renfro Mar 3 at 22:42
    
Before I go (I have to leave where I'm at in about 2 minutes), here's something else, what I call coping strategies, that might be of use to you. –  Dave L. Renfro Mar 3 at 22:54
    
Thanks! Any similar geometric proofs for algebra 2 topics like quadratics, systems of linear equations, or logarithms? Also, great coping strategies! I think having students create coping strategies for a specific lesson would be a neat project. –  Melissa Mar 3 at 22:57
    
@Melissa: What is the content of algebra 2? What do the students know? –  moose Mar 4 at 12:13
    
• Exponents • Rational Expressions • Scientific Notation • Combining Like Terms • Radicals: Basic Operations and Simplifying • Factoring Polynomials • Fractional Exponents • Solving Equations with Rational Expressions • Imaginary and Complex Numbers • Conjugate Numbers –  Melissa Mar 5 at 16:17

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