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As part of a free summer enrichment program for highly-motivated high school students, I need to plan eight hour-long lessons for mini-courses titled as "Algebra 2" and "Calculus" separately. Despite the titles of these mini-courses, they do not give students any actual school credits and they should primarily be seen as somewhat informal (I say "somewhat" because I will have to evaluate their progress) small-group meetings where I help students get ready for their real credit-bearing Algebra 2 and Calculus classes that they will take in the future.

Ideally, these classes would not be designed with the idea that students should achieve mastery. The summer program also requires to be in other kinds of mini-humanities, science, and art courses, so the program and the students are not all exclusively focused on math.

The problem I am having is deciding how to map the course and plan instruction for both classes given that I would want to make sure that I engage every kind of student regardless of prior ability or interest. This objective is important to me because I am not actually teaching a "real-deal" Algebra 2 or Calculus class and so I want to help the students feel confident when they enter high school again in the fall.

  1. What kinds of topics do you think I should cover for our short time together? (If you can't answer this, how do you suggest I go about paring down the list of topics before I even get to see all my students?)

  2. My own Google searches always seem to turn up pacing for standard high school courses, but I won't be able to follow these. If I did, it's possible I wouldn't cover both differentiation and integration in Calculus. Would covering only integration be a good call?

  3. I don't know where to begin in designing my Algebra 2 course. I don't think I would want to risk boring these highly-motivated students with possibly unnecessary Algebra 1 review. Would you suggest giving a diagnostic assessment on our very first class meeting?

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I do not know exactly what the content of courses like Algebra 1 or Algebra 2 is supposed to be. Having said so one possibility is to carefully plan a modelization of some "real life" situation in which problems can be solved by algebraic techniques. An example of an activity I once performed with high school students is the following.

Divide them in groups and make them compete in a sort of city-buliding & war game like the many one you can found in Internet (e.g. Ikariam, ClashofClans, Grepolis...).

Usually this leads to solve some linear optimization problems.

Say: you can build two type of war units, each with its offensive and defensive value and each with maintenance cost. Which is he combination that gives you the best value for money in offence? and in defence?... This sort of problems lead through: - recognizing how to model this situation in a math framework. This is where they'll have more difficulty and you'll have to help them a bit in this. - solve linear equations at first, then system of linear equations. - if you think they can handle this you may enter also some linear inequalities and guide them through geometrical solutions of easy linear programming models.

The approach could be that of having them discover rules and solutions, with you playing the role of "tutor". Competition can be used to engage them more actively (you can consider a prize for the winner group at the last lecture).

So rather than "lecturing" organize some sort of game in which they'll win thorugh understanding mathematically the kind of problems you pose them.

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Start with:

  1. What is student background (grade level, etc.)

  2. What is student ability (very smart? Below average)?

  3. Total hours of classroom?

  4. REASONABLE estimate on out of class time available.

  5. Based on 3 mostly and 4 partially, figure how much you can cover and want to cover.

  6. Keep it light and motivational.

  7. USE CLASS TIME. Assume they do NOTHING outside of class (bullet 4).

  8. Do something fun and non indoor class related. Class outdoors. A demonstration. A physical experiment. Doesn't matter. Just at least one "thing" that is more summer camp and less teacher in a room.

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