The Big Square Root Trick for Remembering the Unit Circle

I learned this "trick" at an APSI several years ago.  I know lots of people use the "hand trick", and I do teach that to my students, but I like this trick better because I can write it down on paper and "see" what I'm doing a little easier.  I taught it in Pre-Cal and I review it in AP Calculus.  I tell the students who take the AP Exam that the first thing they should do when they get their test is write this down.  If you combine it with a trick for remembering what's positive in each of the four quadrants of the unit circle, they can evaluate most any trig function on the test.

Drawing the Square Root:

Using the Square Root:

Trig T-Shirt Project

In the spirit of the last post, I wanted to share another one of my favorites from my trig unit.

When we are wrapping up transformations of trig graphs, I assign a t-shirt project to my students.  I love this project because it's easy to grade - they just stand in front of me and I check their work.  It's also great because the back of the shirt really lets them show their personality and sense of humor.  I'm always surprised by some of the stuff that they come up with as "reasons for studying trig"!  I could only find one example to share - not sure what I did with all the others I know I saved, and I know the scale on the x-axis in this example is a little off, but it still gives you an idea of what a finished product looks like.

Trig T-Shirt Project

What is a Radian?

I didn't get to teach Pre-Calculus this year, which was really rough because I LOVE Pre-Cal, especially all of the trig!  I was feeling nostalgic and thought I'd share an activity that I used at the very beginning of my trig unit.  This activity helps kids understand the concept of a radian.  And best of all, it involves CANDY which is the universal motivator!  Students use twizzlers as a measurement tool.  You need to use the pull up apart twizzlers, which can sometimes be a little hard to find, so make sure you don't wait until the last minute to get them!

What is a Radian Activity

Moving on Down the Line

One of my Calculus students' favorite lessons is the one I do to introduce particle motion.  It's actually an activity that I got several years ago at a training I went to at our regional educational service center.  It's called "Moving on Down the Line".

I ask for volunteers, but I don't tell them what they're volunteering for.  The first 5 volunteers get a secret instruction card that only they can look at.  The next 6 volunteers get data collection cards.  The last volunteer will be the timekeeper.  If you have enough students in your class you can make two groups and repeat the process for the second group.

I borrow a really long tape measure from the track coach - the kind they use to measure the long jump and triple jump.  We go out in the hallway and we roll out the tape measure.  Mover one goes to the starting point indicated on their card.  The timekeeper starts the timer and calls out the time as mover 1 follows the instructions on their card.  The first time is just a practice one so that the data collectors can figure out about where they need to be in order to record their data.  They measure where the movers back heel is at the times indicated on their card to the nearest foot.  Once the data collectors get an idea of where they need to be, the mover repeats their walk and we record the data.  We repeat this process for the other 4 movers.

We go back to the classroom and I give them the handouts where they will make tables and graphs for each mover.  We have the data collectors call out their information for each mover so we can all fill our tables out together.  Then the students create the graphs.

Once all of the graphs are made, we try and figure out what the secret instructions on each movers card was.  I ask questions like:

Where did they start?  How can you tell?
What direction(s) did they move?  How can you tell?
Did they ever stand still?  How can you tell?
Did they ever speed up?  Slow down?  How can you tell?
What was their displacement?  Total distance traveled?
Which mover moved fastest?  Slowest?

There are many other questions that naturally arise from the graphs, and it's interesting to see the kids come up with their own conclusions about the movement.

This activity leads right into the introduction to particle motion and all of the vocabulary associated with it.

There's an associated activity called "Moving with Technology" that uses a CBR/CBL and has the kids create graphs that meet certain criteria.

Creating GIFs to Show Learning

This past weekend I was fortunate enough to get to attend #TXGOO16 in Frisco, Texas.  It's the Techs4Tex Texas Summit featuring Google Apps for Education.  I attended six different sessions and learned so many amazing things that I can use in my classroom, but I wanted to share my FAVORITE thing - student created GIFs to show learning.

Here's a couple that I created:

It was so fun making these!  And you REALLY have to think through the problem step by step to make sure you show ALL your thinking in the GIF - I love thinking of the students having to go through that kind of thought process when making these!

Graphing a Line GIF- Google Slides

Function Graph to Derivative GIF - Google Slides

I started by creating the images using Google Slides.  You just make your first slide that shows the problem, then duplicate the slide and show the first step.  You keep duplicating the slide and then making a change until you get to the end of the problem.  Then you download each slide as a jpeg.  I used gifmaker.me to create my GIFs - you just upload your jpegs in the order you want to them to appear in the GIF.  I set the animation speed on both of these to 1000 and then you just click the big "Create GIF Animation" button on the right hand side of the page.  Once the GIF is created, you'll see a link that says "Download GIF".  Voila!  I cannot wait to use this as an assessment tool next year!

Algebra I STAAR Review

Despite the best of intentions, I know I haven't blogged much in the last couple of years.  I'm hoping that is going to change going into next year.  But I thought I could try and get the ball rolling with my blogging again by sharing what I came up with for reviewing my Algebra I students for the STAAR test this year.

The first thing I did was teach my students the "Five STAAR Strategies".  On the day of the test, we gave each student a pencil with colored stickers on it to remind them of these strategies.  The first strategy was "Fix Your Formula Chart" which simply means for them to add a few useful things to the formula chart before they even begin answering questions on the test.  I gave them a "blank" copy of the formula chart to practice fixing every day at the start of class for the month leading up to the test.

Then I found this amazing website and immediately downloaded all of the worksheets.  I combined the worksheets for each Reporting Category into two files - one containing all of the Readiness Standards for that Reporting Category and one containing all of the Supporting Standards for that Reporting Category.  In case you aren't familiar with the blueprint for the Algebra I STAAR, the Readiness Standards make up 60-65% of the test, so we started with them.

Readiness Standards
RC 1
RC 2
RC 3
RC 4
RC 5

Supporting Standards
RC 1
RC 2
RC 3
RC 4
RC 5

I would work the problems on the worksheets out with my students together in class one day, and then have them complete a Quizizz containing similar problems the next day.  The problems on the worksheets came from the 2013 released STAAR and old TAKS tests.  The problems on each Quizizz came from the 2014 and 2015 released STAAR tests.  (I gave the kids a hard copy of the questions because some of the problems are hard to read on the Quizizz.)

RC 1 Quizizz - hard copy
RC 2 Quizizz - hard copy
RC 3 Part 1 Quizizz - hard copy
RC 3 Part 2 Quizizz - hard copy
RC 4 Quizizz - hard copy
RC 5 Quizizz - hard copy

We ended up not having time to do very many of the supporting standards, so I went through and picked out the ones I thought would be very easy for them to understand and remember, like independent/dependent, function/not a function, parent functions, and intercepts.

We won't get results until right before school is out, so I don't know how effective all of this was, but I really liked the structure of it.  There are SO MANY problems that can be worked using the "GRAPH" and "TABLE" features of the calculator, so I think it really helped for the students to see that and get practice doing it.

How do you review your students for your End of Course Exam?