Teaching the Quadratic Formula

Because my school is a SIG (School Improvement Grant) school we are periodically observed by the Illinois State Board of Ed. A couple weeks ago, they came in to observe the math and English departments. I was observed on Wednesday and the English teachers were scheduled to be observed on Thursday. Due to a freak break in our water main, the school had no water and was shut down on Thursday. So ISBE's only impression of our teachers was based on my classroom...and I rocked it. Apparently they bragged all over me and were impressed at how rigorous my lesson was considering I am only a third year teacher. Plus, they missed the first half of my class! They were in a meeting and someone interrupted them to tell them they were supposed to be in my class. They said they shouldn't tell teachers when to expect them and then not show up! lol

Anyway, they had asked me ahead of time to prepare lesson objectives, how my lesson connected to the Common Core, sample student work, and any formative or summative assessments that would follow the lesson. I will say that I went overboard in creating a lesson plan with a fancy template and I decorated the folder I put everything in. I also had a student greeter who welcomed them in the room and escorted them to their seats. I think these were the things they were most impressed by.

As far as my actual lesson, I feel confident that it was not posed or over the top but included things I normally do. I didn't prep my kids other than to tell who would be there and I felt that the classroom environment was essentially unchanged after they took their seats.

So let me preface: we had just learned the square root method to solving quadratic functions. The day before I had quite a few students out so we did some board work and review. I wanted to briefly introduce the formula to get the following day's lesson off to a good start. I decided to try a 3D puzzle, which is something we had tried in our grad class. What I did was create an 'empty' quadratic formula and overlay that with a 5 x 5 grid (I have 5 students) in Powerpoint.
I cut them apart into 5 strips of 5. Each student had a strip and two crayons. No students could have the same two shades of crayons. They had to use both colors in each square on their strip and no space could be left white. Then we cut them all apart, mixed them up, and they had to put them together.

I thought it would be easy but it did take longer than expected and it required them to work together. I ended class by showing them this classic video- if you watch it, you have to watch the whole thing.

So the next day, we started class as usual with a bell ringer. I asked them to write the standard form of a quadratic and the formula for finding the AOS of an unfactorable quadratic. I asked the students to explain what we did the say before with the puzzle and then we all watched the video again. Now, everyone has seen the formula. We started our notes by writing down the quadratic formula and the AOS formula and comparing. They notice that both formulas have -b/2a. Here's where I transition into the discriminant. I tell them we are going to ignore the part of the formula we are familiar with and work with the b^2 - 4ac. I send them to the board and they do three example problems, just finding the discriminant. Then it's back to their seats. I give them a baggy with six different equations.
I tell them to find the discriminant of each (which they have already shown me they know how to do at the board) and then I ask them to sort. I love sorting! I don't give them any information. Some students sorted them into 2 piles of three, based on the equations set equal to y or 0. Some looked at where the 3's and 4's were and sorted by their positions. Then I told them they had to have three piles. They re-sorted. I asked each of them to describe how they sorted in one sentence. They shared and we decided who had the best idea. They agreed that one pile had negative answers, one was positive, and the others equaled zero. That led us into a discussion about real and imaginary roots and visualizing what roots mean and whatnot.
Next I said that we would put the old part of the formula and this new part together and practice using the entire formula. We consulted our sorting cards to tell us how many roots the first equation should have and students set off to solving. This was the first time so all the problems worked out to be nice whole numbers and no negative discriminants. I ran out of time before finishing all of the examples, but like a good girl, I stopped early to do the exit slip, which was asking them to answer the lesson's essential question: "How does the quadratic formula help you find the roots of a quadratic equation?" I thought it tied in nicely with the unit's essential question: "How can we find the roots of any type of quadratic equation?", both of which I made up myself. My observers came in late, after the video and board work but right during the sorting. I love sorting! Luckily, I got to talk to them afterwards and explain my cool 3D puzzle and show them the Crank Dat Quadratic Formula video. One of them is a former math teacher and was familiar with the Pop Goes the Weasel tune but liked the new video. She even said, "Isn't that that Superman song?" which earned her brownie points with me. They asked me if I created the lesson template myself, which I did, but was inspired by one I found from Microsoft Word. They thought that it looked very much like backwards design which made me happy inside because that's where I'm trying to go. Since then we have solved quadratics with like terms on both sides, with discriminants that need to be simplified, finding exact and approximate answers, quadratic applications and word problems. I feel that they have handled it all really well and that this was a great start. I'm no Dan Meyer but I'm proud of my lesson and it's results and I wanted to share that all with you! While I'm sharing, here are all my resources that I mentioned above: Lesson Plan Template Unit Plan Template (I did not create) Quadratic Formula 3D Puzzle Discriminant Sort (I love sorting!) The Quadratic Formula PPT The Quadratic Formula Notes Bell Ringer and Exit Slip Thanks for reading my extra long post and for cheering me on.

I love sorting!


  1. Wow! Thanks for sharing, this looks really neat. We are doing quadratics in 2 weeks.

  2. The way you structure your class periods sounds similar to mine. Thanks for a thorough description and this lesson is heading into my virtual filing cabinet. I'm not teaching Algebra 1 this year, but I'll definitely keep this in mind next year when I'll surely be at it again!

  3. Lisa and Allison,
    Thanks so much for reading. If you ever use any of this, please come back and comment on how it went!

  4. I'm late to respond. We will be getting to the quadratic formula in a couple of weeks. This is the youtube video/song that I show in class. It is not too easy to find, but the kids love it (even if some of the celebrities are out of date!)


    Thanks for all of your ideas!

  5. Nice blog.Quadratic is all about splitting middle term problems because the problems are generally of discriminant is greater than zero.So, a teacher has to teach firstly the splitting problems.And he also has to teach What is Standard Deviation?This is also very important topic of maths.

  6. Nice post. I found some interactive videos on you tube specially targeted for quadratic equations. Check this out: http://www.youtube.com/letslearnmathematics

  7. Thanks for this post! I sing the "Pop Goes the Weasel" tune for the formula and have a hard time getting my kids to sing along (high schoolers are soooo cool, haha), so I think my kids will get a kick out of the new one and be more apt to join me! I'm also going to try your sorting activity. Thanks again!

    1. I couldn't get them to sing at all but I just played it a couple of days in a row to get it stuck in their heads. I heard them sing a little of it or even mouth it so I know it stuck even though they were too cool to admit it. =)

  8. This is a great lesson. As you stated, it does take the students a longer time than expected to color and cut the puzzle. However, it is definitely worth the effort. I had my students piece the puzzle together the following class period as a warmup. Some did it with ease while others were really challenged. The discriminant portion is so valuable and I was intrigued that my students also sorted the equations into two piles at first. Only 2 groups in each class saw that there were really 3 groupings. This lesson brought about great discussions! LOVED IT!!!!

    1. Thanks so much! I don't think I've ever received such specific feedback on a lesson. I'm glad that you had great discussions and a great experience. =)