Tuesday, January 29, 2013

A Fun Lesson

I've had a chapter stretch out longer than I would have liked, so I'm not going to get two tests in this grading period as I'm required to.  I came up with this short, fun little project for my students to do in class this week.  I'll count it as a test grade, which should serve a dual purpose - I get the second test grade I need and my students have an opportunity to boost their grade while showing their creativity!

The activity requires the use of two FREE iOS apps:

Funny Movie Maker

Lots of my students have their own iPads and iPhones, but I'm also borrowing a few iPads from the science department.  I'll preload these two apps on the iPads.  I'm handing out the following instructions.  I can't wait to see what my kids come up with!

Show What You Know Project Instructions

Here are a couple memes that I came up with:

Thursday, January 24, 2013

Applications of Transformations Activity

I found this online here.  I modified it to make the first part a matching activity.  Students are given the graph of the original function and three sets of cards - a set of graphs, a set of transformation descriptions, and a set of function notation cards.  They are to match one card from each set.  The second part I made into an assignment for students to complete individually.  I really like how it turned out and I REALLY like that it gives some purpose to studying transformations.
Transformation Application Activity

Wednesday, January 23, 2013

The meaning of f(x)

I've discovered over the past 8 years teaching Calculus, that my students don't really have any idea what f(x) means. Don't get me wrong - they know that "f(x) is the same as y" and "f(2) means plug 2 in for x" - those things have been drilled into them. But what they don't understand is how to work with function notation if there is no equation involved - i.e. from a table or from a graph. Since I'm the Pre-Calculus teacher, I decided to tackle this issue myself when I reviewed functions. And it has proved to be a challenge! Some kids get it right away, but some REALLY struggle with it. And I'm having a hard time putting my finger on what the problem is exactly. For example, I gave my students this table to fill out -
They had a really hard time filling it out. One problem was they had trouble applying the order of operations correctly - "Should I apply the change to x and then find the corresponding y, or find y and then apply the change to it?" But a lot of their problem was that they simply didn't understand the top two rows of the table and how they related to the other rows. I always get them to understand it by the time they get through Calculus with me (if I had a nickel for every time I say f(x) gives you y-values, f'(x) gives you slope, and f''(x) gives you concavity....). But I wonder how much faster (and better) they would understand reasoning from graphs and reasoning from tabular data if they got this skill down a little better while they were in Pre-cal (or earlier).... Anyone else experience this? Found a good way to address it? Should we address it from the beginning of function notation in Algebra I? When we're reviewing it in Algebra II? As I'm doing it now in Pre-Cal?

Tuesday, January 15, 2013

Monday, January 14, 2013

Leap Frog Activity

Here's a fun little activity that I picked up at a Pre-AP Summer Institute a few years ago.  I'll be doing this specific version with my pre-cal students on Wednesday.

Leap Frog

Materials needed:
One set of games cards for each student
One set of questions

Basic Directions:
Have students arrange their game cards on their desks
Ask questions from the set of question cards, directing students to hold up the most complete correct answer
Students who answer incorrectly will remain in their seats
Students who answer correctly will proceed to the next available seat, "leap frogging" over the students who were incorrect
Play continues until a student returns to his/her original seat

The set I posted above covers vocabulary associated with function behavior.  Additional applications include:
Create student game cards containing appropriate vocabulary words or math terms, reading the definitions to the students
Create student game cards with various numbers that work as solutions to equations you ask them to solve
Create student game cards with common trigonometric values on them, and then ask students to evaluate trigonometric expressions.

Ideally, the problems can be done quickly with a minimal amount of pencil-to-paper work.

If you are pressed for time (or your classroom layout doesn't really accommodate the "leap-frogging") you can just make one set of game cards for each group and have them hold up the correct answer in the group. Then just award points for each correct answer.

Wednesday, January 9, 2013

Flyswatter Activity

I set a personal goal for myself this year to try and reduce the number of book assignments and worksheets I did and instead replace them with activities that, while they could use the same problems as before, would be more engaging to my students and would allow me to do more informal assessment.
One of my favorite activities has been the "flyswatter activity".  I got this idea from Pinterest (a real surprise to anyone who knows me, I'm sure!).
First, I printed out a whole bunch of these bug outlines.  I have 8 groups of 4 in my class, and to give me the option to have up to 15 bugs in an activity, I printed out 90 bugs!  I had my teacher's aides cut them out and laminate them so I could reuse them.
Bug Outline 1
Bug Outline 2

Today I'm doing function/not a function with them, so each group only needs two bugs - one with "function" written on it and one with "not a function" written on it.
I found flyswatters 2 for $1 at wal mart, so each student gets a flyswatter.
The groups put the bugs out in the middle of their desks where everyone can see and reach them, then one at a time, I'll place a set of ordered pairs, a table, a graph, or an equation under the document camera.  The first person to correctly identify it as "function" or "not a function" by slapping the corresponding bug with their flyswatter gets 2 points.  Everyone who correctly identifies it but isn't the first, gets 1 point.  Anyone who gets it wrong loses a point.  I give some sort of prize to the person in each group who gets the most points (they keep up with the points in their groups themselves).
I teach juniors and seniors and they LOVE this!  It works best with problems that can be done quickly and preferably in their heads.  I did it earlier in the year with trig values for the special angles on the unit circle.  I highly recommend it as a way to rework a worksheet into something much more engaging and fun!
Here are the worksheets I cut up for today's activity:
Function/Not a Function WS 1
Function/Not a Function WS 2

Tuesday, January 8, 2013

Rallying the Troops, part 1

Shaheen and I met with the teachers at one of the two elementary schools in our district yesterday and it was AWESOME!  We used this powerpoint presentation.

I started off with "the numbers" - showing them what we perceive the root of our problem to be and Shaheen followed up with our first suggestions for improvement.  Shaheen is so passionate about what we're doing, and he's a very engaging presenter, so I think we really accomplished our goal of getting people excited about being a part of the solution!  I'm sure it doesn't hurt that Shaheen's wife, Shannon, is a teacher at the school and everyone loves her (and by extension, Shaheen).  :)  We've set up a time to go present to the teachers at the other elementary campus.  We're gathering steam.....

Here are a few articles that are worth reading: