Flipped Friday – Imaginary Numbers?

Flipped Friday – Imaginary Numbers?

In my Intermediate Algebra course, we finished our work with rational equations and their applications this Wednesday. On Monday I plan to get through solving quadratic equations by factoring, by extracting square roots, by completing the square, and by the quadratic formula. I thought I’d walk you through my thoughts for setting up the Flip assignment for that day.

Flip Topic 1: Factoring Trinomials and Differences of Squares

These are review topics from Elementary Algebra, and students have been factoring trinomials while solving radical equations. I feel comfortable that students can handle this before class. I included two short concept videos on (1) factoring trinomials and (2) factoring a difference of squares. I included two example videos as well. After watching those videos students will work through a few exercises that get submitted through MyLab Math.

Flip Topic 2: Solving Quadratic Equations by Factoring

Again, this is a review topic from Elementary Algebra and my students have been solving quadratic equations by factoring while solving radical equations. There are a few short concept/example videos to watch and a few exercises to submit.

By the way, even though this is review, my main message in the next class meeting will be that solving by factoring will be option 1 for us when solving quadratic equations.

Flip Topic 3: Imaginary Numbers

This is a brand new topic, and I thought for a while about whether students can introduce themselves to the topic. I finally decided that it is similar enough to simplifying square roots and students should be able to handle it with proper guidance. There are a few short concept and example videos, and a few exercises for students to work through and submit. I imagine this topic might take some discussing when we meet in class.

Flip Topic 4: Solving Equations by Extracting Square Roots

This topic is also new, but is made up of several ideas that have already been addressed while working with radicals (simplifying radicals, solving radical equations, …). Again, there are a few short videos followed by a few exercises to turn in.

On the Flip assignment, the combined running time of the videos is just under 14 minutes, and there are 13 exercises to submit.

In-Class Plan

I’ll begin by having students solve a few quadratic equations by factoring, perhaps at the board.

We’ll then have a brief discussion of imaginary numbers, allowing me to clear up any misconceptions and get students to offer their advice to their classmates. Students will then work through a few of these problems.

Extracting square roots will be handled the same way – a brief discussion followed by a handful of problems to work on in groups. There will be more problems to solve for this type than the previous types.

I’m shooting for approximately 30 minutes total devoted to the above. I do teach a 2-hour block class.

Since students will then have solving by extracting square roots under control, solving by completing the square will focus on getting the equation into the correct form by completing the square. I plan to debrief this topic by discussing when this technique should be used.

Finally, we will finish up with a mini-lecture on the quadratic formula. After 2-3 examples together, students will work in groups to solve a few equations using this technique.

I plan to finish with a short group quiz where students will use the various techniques to solve quadratic equations. I will limit them to only using each technique one time, forcing them to think about when it is most efficient to use each technique.

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