Sunday, October 28, 2012

Converting between Exponential and Logarithmic Expressions - The Snail Method

The last unit in trigonometry was Exponential and Logarithmic Functions. One of the early learning targets of the unit was converting between exponential and logarithmic expressions. Now this topic can be taught a variety of ways and initially, I had asked the kids to look at the patterns and what usually was happening. I then had a very excited hand shoot up in the room and ask if she could teach her classmates a trick. I can take no credit to this trick as she had learned it from a previous teacher but she called this method, The Snail Method. It's best to approach this by going from log to exponent and then doing the reverse.

The method goes like this. Create a snail head around your log base b. And then you create the snail shell by raising this b to the power and being set equal to our last part.  Now, my kids loved this method  but weren't truly convinced that it looked like a snail (we slightly forced it).

It's important to also discuss the inverse property of log base b and the exponent with base b as this leads into being able to solve exponential/logarithmic equations but if you constantly refer back to this method, it creates a comfort zone, a Linus blanket, if you will. I used this method to also discuss graphing logarithmic functions in terms of an exponential function.

Welp, that's really all there is to this short cut but it did create an "ah hah" moment and also created some of the success in this unit. 98% of my trig class doesn't have to retake their test. It's part of my policy that kids have to retake a test if they do not master any learning targets. When I announced this stat, both classes applauded. I haven't heard applause since the day I let them listen to Dr. Seuss. So thank you, my student, for your enthusiasm and helping your classmates out, a practice, which I always ALWAYS encourage!

Winning Miss Rudolph, Winning :)

Thursday, October 25, 2012


Are your kids just not motivated? Do they think they can get by with the bare minimum? Do they keep blaming you and making excuses?

A facebook friend of mine had posted a video that she had showed to her kids in order to motivate them to take ownership of their work and be more accountable for their grades. I thought that it could really apply to my class. A couple of weeks ago, it was the halfway week of our semester (I think I had said this before but my kids take a year long course in a semester, yeah, it's pretty fast). Being the halfway mark and seeing how the kids, for the most part, were struggling to stay up to speed and do well in my class, it was time for an intervention. Our administration had mentioned in a faculty meeting that it might be a good idea to offer an "intercession" where the kids get time in class to continue to work on their missing assignments or low grades (likewise, we're on a mastery systems so my kids are constantly doing corrections or other work to fix their test grades).

Now being the stubborn person that I am, I didn't want to completely just hand the day over to them. I wanted my kids to think about it. So I showed them this video.

After watching the video, this is when I said, "I wish the ending had said "Earn Mastery" because you have to work for it. My class isn't easy, it's the last class you take for your required high school credit and next up, is college level courses. I won't just give you mastery. Just like Michael Jordan did, you will have to work for it and there might be some failure along the way but learning from your mistakes and fixing them, is what will get you mastery."

I then explained how the day would work and for the most part, I had a pile of grading to do with kids handing me all sorts of old material and tests corrections (I had also printed out a grade report for each kid with highlights and notes for each child).

So the next time you want to motivate your kids, maybe use this video or find another. If you do find another, I'd love it if you'd share :)

Thursday, October 18, 2012

Additional Assignment - I don't know, Prove it to Me!

Do you have those students in class who sincerely want to understand why? And this question of why came from them playing around with a few things and noticing a pattern? Have you ever been asked one of these questions in the middle of class when you are teaching something such that this new additional topic would completely lose your students?

What do you do in this case?

Scenario: "Miss Rudolph!!!!!!!!!!!! MISSSSSSS RUDOLPH!!!!!! Can you explain to me why ln(4)/ln(5) = log(4)/log(5)????????"

Me: Wait, where did this come from? (We were in the middle of another problem so I was caught off guard) ..... After a few moments....... Can I look into this a little and get back to you?

Child: But, but, but, but.... fiiiiiiine

So I tried googling it a little, because that's what everyone always does, right? Because of course I don't remember all the proofs that I did in college.... good times..... But I couldn't find it.

Now, let it be known, I put all of maybe 5 minutes into googling when I had other students come in that afternoon so I decided to provide the child with the additional assignment.

The next day in class... "Miss Rudolph, did you find out why?"

Me: No, I did not. So I give you this challenge, you prove it to me. You find out why, and I will give you points.

This child looooooooves points. So needless to say, the game was on.

The following morning:

Child (walks straight into my room): Okay, give me the points now. I've done it!!

The child proved ln(a)/ln(b) = log(a)/log(b) and let me tell you, wow do I feel silly for not having done it myself.

Let's think of it using the Change of Base Property!

ln(a) = Log(a)/Log(e) and ln(b) = Log(b)/Log(e)

Well, do a little division magic and poof! You get log(a)/log(b)

I felt like a very silly math major.... but the child got his points.

Challenge your kids, they may or may not surprise you. This lead into a discussion about possibly looking into being a math major. I informed the child that the proof and process that he went through by using properties was exactly what I spent 4 years doing.

Sunday, October 7, 2012

Children's Book - Inverse Functions [The Results]

This past week, students turned in their children's book where they created a story that lead the reader through the process of finding the inverse of a variety of functions. The following day, we had story hour. To prepare the kids for story time, I had a little story time with the kids myself. I linked the post to the youtube video where the kids and I watched and listened to Dr. Seuss' "One Fish Two Fish Red Fish Blue Fish." This was the first time where there was applause in my classroom, sigh. They really liked watching the story time and they were even more ready to read their own stories. One suggest that a child produced was for me to show this when introducing the project. Next time, I might do this or perhaps I'd read them a story or ask a leading question: What stories did you love to be read at bed time as a child?

For the most part, the products were wonderful and the students were able to illustrate their ability to find the inverse of functions step by step. Mastery obtained.

I've uploaded a few highlights. Enjoy!

Below is the link to the rubric that I used when grading the projects. I liked the project, overall, because it helped the kids work on their explanations and ability to justify steps (common core friendly?) and not to mention, it gave kids a chance if they don't test well. The results for the project were alot better than a test, more work to grade but definitely more enjoyable to do in general. Story time in math = fun :)

Update: Barnes and Noble offers free online story time with tons of stories that could have been used to present this project!
Trig Unit 3 LT4 LT5 LT6 LT7 Mastery Project Rubric
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