In the last lesson, students learned what n-th roots are. In this lesson, we explore what happens with positive and negative radicands when we have an even or an odd index. Students need to understand why taking an even root of a negative number yields no real solution, and that this is different than an irrational solution that is real. The estimation exercises in the last lesson were meant to start tackling this misconception: i.e., "you can't take the square root of 12 because no number times itself is 12".

In this lesson, students also learn when to include the plus/minus and when not to - which I think they will tend to confuse with the real/not real question. Additionally, we discuss the difference between exact and approximate solutions. I had originally planned on solving equations like 3x^5 - 40 = 152 in this lesson, but I decided that really focusing on the stuff I described above merits a whole lesson.

By the way, I really wowed the students with the new animations in Keynote - flame, sparkle, etc. I know that it's bad design to rely on animations, and I only typically use dissolve (to make text appear more gently), wipe (when I have arrows), and pop (when I want something eye-catching to appear, like a circle around a group of numbers). But I just couldn't resist having a wrong answer burst into flames. A little showmanship really made lesson 3's presentation more fun. I held the remote behind my back, and clicked as I threw a fireball at the screen with my other hand. Quite a few kids were properly amazed at my magical talents. And later in the class, I used sparkle to make the 2 disappear off the radical sign: I flicked the screen with my finger, and it sparkled away. I told them that Tinkerbell took the 2 away.

Ok, here are the files for tomorrow:

Lesson 4 (real or not, into to power equations)

Keynote for Lesson 4

Keynote Quicktime

A beautiful combinatorics argument

18 hours ago

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