Teach 180: Multiple Ways (Day 145)

One of the big takeaways I hope my students get after being in my class is there are multiple ways to solve a problem.  Depending on what information you have or what you need to figure out, some ways are more efficient than others.  This is true in life and it is true in math.  In math, we can tell that the methods are valid when they give us a similar solution.

We began Precalculus today by reviewing how to find the area of an equilateral triangle with a side of x.  We used three different methods. The formulas for these methods are shown below. Half the class was assigned to use the second method and the other half of the class was assigned to use the third method. We confirmed the solutions by finding the area with the traditional (bh)/2 formula.

Although I had students work together, they were all using the same formula in their small groups.  This meant that they didn't get to fully experience the fact that there are multiple ways to solve this problem.  Next time, I plan to have students work in trios with each person being assigned a different method.  If they don't get the same same solution, they would need to help each other to diagnose what went wrong.  In addition to seeing multiple methods and possibly determining which method they like best, they would be relying on each other to evaluate their solutions and correct their errors.  A math teaching win!

P.S. I may even introduce Pick's Rule next year.  A fourth method that gives an approximation for the area based on lattice points!