A Geometric Valentine's Day

We're just digging into geometric mean in Geometry and the inevitable question of "Why are there 2 types of means?" always arises. 

Here's a timely explanation of one way math & geometric mean are used in real life....just in time for Valentine's Day!

Happy Valentine's Day to all of you!

Update: Discussed this with my class last period...they immediately wanted to know if I used eHarmony or Match.com (despite the fact that they know I'm in a long term relationship) and which was better. They decided they should probably test both to figure out which one worked better.  I guess I'm glad they're trying to test their conjectures? Scientific thinking at its finest. 

Mathematical Bakery

Working with generalized proofs today, we ran into a problem that said (a+b)(a+b)...we were using the distance formula. Oh the crazy answers I heard from my Geometry students!! Sure, we haven't done a lot of multiplying of binomials this year, but still....I was a bit frightened. I explained to them that at the end of this year we're going to do a pretty hefty Algebra review to make sure they're in shape to take Algebra 2 next year. I told them "factoring is cake compared to what you'll see there!" The following conversation ensued:

Student 1: "So....you're saying Algebra 2 is like a scone?"

Me: "What??"

Student 1:" Well if factoring is cake, Algebra 2 is a scone....it's a little harder."

Student 2: "Pre-Calculus must be like a stale scone!"

Student 3 (from across the room): "And Calculus is like a really hard loaf of bread!"

Student 1: "Good thing we have studying...that's our coffee! We can dip our scones into it and it will soften them and make them taste better."

Student 3: "I don't think I'm going to study in Calculus."

Me: "Why not?"

Student 3: "Because....old bread dipped in coffee? Gross."

Groups of kids like that remind me why I love my job, especially on the days when you're ready to hide under your desk.

Just a normal Monday night....

Most people spend their evenings catching up on HBO shows, eating leftovers from the Super Bowl, & doing recreational proofs, right? 

That's what I thought.

What do Hercules, Kings, and Exponents all have in common?

Just introduced exponential functions in Algebra and I wanted to find an engaging way to get them hooked. I proposed this question to the students and asked them think & discuss with their groups:

A king has offered you a handsome reward for all your service to the kingdom. You may choose either:

- $1,000 on each square of a chess board until it is filled

- $0.01 on the first square, $0.02 on the second, $0.04 on the 3rd, until the board is filled

Which do you choose and why?

Naturally, most of them picked the $1000 deal- because obviously it will yield more money! Only one student bothered to actually do some calculating...like by the 17th square you'll start getting way more than $1000 per square. 

I had two students come to front of the room and handed them an envelope with the amount they would receive in it. They went nuts. Why would this happen? They thought & discussed. Geometric vs. Arithmetic sequences.... counter-intuitive but captivating!

I then showed them this clip of Hercules fighting the hydra. They then broke into 5 groups and each had a different type of hydra- one that loses one head and grows 3 back, one that loses one head and grows 4 back, etc. They had to make a table of the number of heads in each round, then write a function equation for it. This, of course, led easily into graphing and seeing the growth. Which hydra would you least like to face? The one with the biggest common ratio/rate of growth! Vi hart wrapped it up beautifully for the day with her binary trees video. Fun day!