## Tuesday, January 26, 2016

### A Better Question for Quadratics #MTBoS blog3

This is my 3rd post in the series on the #MTBoS blogging initiative: When teaching quadratics in Accelerated Algebra 1, I teach solving by all the methods.  Sometimes they ask, why so many methods?  I try to show them the advantage of one method over the other.  I want them to analyze the quadratic before they just jump in and try it.  I would say they are 50-50.  50% will try factoring and 50% will try quadratic formula.  However, over the past few years, some kids are turning to completing the square as their first mode.

On my quiz for this unit, I have a favorite question.  I give them three quadratic equations and I ask them to solve them using factoring, completing the square, and the quadratic formula.  They must use each method once and explain why they chose that method.

The first quadratic equation is a factorable quadratic with a = 1.  It is the only one that is factorable.  Kids will mess up by not looking at all of the problems first before deciding on a solving method.  They will do the first with the quadratic formula because they like it.  Then, they try one of the others and it is not factorable and they write - no solution or not factorable.  Okay, well, if it isn't factorable, then use another method to actually solve it!

By this quiz, we have also learned complex numbers.  The second equation has "a" not equal to 1.  I would choose to do this one with the quadratic formula because I think I am more likely to make a mistake doing completing the square when "a" is not 1.  The last equation is not factorable, but "a" is equal to 1, so do completing the square here.  I try to give the kids a hint and have the constant on the other side of the equation.  I do accept either method on the last two as long as they can explain their reasoning.  The second one is a complex solution.

They are allowed to use their calculator on this part of the quiz, so if they really made the connections, they could check these by graphing it on their calculator, but I don't think they do that yet.

1. I really like this idea and will be stealing it :) Thanks for sharing.

2. Cool idea. Are the kids pausing and thinking in the ways that you want them to?

3. I like this idea for your quiz - would work for methods of solving systems of equations too! :) (I teach 8th grade so quadratics are no longer mine - but they used to be!)

I used to do a "4 corners" activity where each corner would represent a method for solving quadratics. I would post a problem, and students would stand in the corner that represented the method they would use. They would have to justify their choice and try to convince others it was the best. Students could move. Then they solve using that method.

I agree - hard to get them out of their "one favorite" method of anything!

4. Yes, this must be an Accelerated class if they're already using complex numbers in Algebra I!

That being said, now that the students have learned complex numbers, they should know that ALL quadratic equations have a solution -- which means that the answer "no solution" that they tried to write is NEVER correct. (This, of course, is the Fundamental Theorem of Algebra.)

But yes, I know that many students often wonder why they must learn more than one method. I was once a long-term sub in an Algebra I class and when we were learning about factoring, this very bright girl had her father show her the Quadratic Formula, so when asked to factor x^2 + 5x + 6 (which is not an equation, just an expression to factor), she'd just write -2 and -3 and didn't want to learn how to factor.

5. Love the idea of getting the students to use all of the methods for solving quadratics. Will definitely use this in the future. Thanks.