One Good Thing

I'm giving semester tests today.  For algebra 2, I allowed students to have one page of paper to be used for a "cheat sheet" to reference during their test.  I collect them from the students when they are finished with the test, mainly so that they don't write things down during the final and then leave and tell their friends what to expect on the test.  (I not naive - I know kids go and talk to their friends about the final, but this way they at least don't have a way to write things down.) 

If you have never done this before, it's really quite interesting what type of cheat sheets students make without any guidance.  (I simply tell them that they can write down whatever they'd like to help them on the final.)  Some students have really great reference sheets, others have very little written down, and yet others have nothing to turn in.

Today, I had one student have something very cool written on their cheat sheet.  We've talked a lot this semester about Growth Mindset.  Here is the cheat sheet:

"YOU CAN DO IT!!" - One good thing from today.

Vikings / Seahawks win probability

Growing up in Minnesota, it's a state law that you must cheer for the local professional sports teams (assuming that you follow sports).  Being the law abiding citizen that I am, I've had to endure numerous heart breaks and losing seasons from my beloved Vikings and Timberwolves.  (I'm also a closet bandwagon Twins fan, but don't know enough about hockey to follow the Wild.)

Today's Vikings loss was as gut-wrenching as any since the 1998 NFC title game.  As I browsed through ESPN tonight, I did happen to stumble onto this crazy Win Probability graph.  I've seen these graphs before; the best ones are when teams have miracle-like wins, such as today's game.

I'm thinking I can use this graph down the road when learning about probability and / or graphs of functions.

For the article that describes some of the swings, click here.  It hurts to be a Vikings fan.

Desmos Marble Slides: Parabolas

Desmos just released their newest set of activities on Tuesday, aptly named "Marbleslides".  I decided to use the last day before Christmas vacation to let my algebra 2 students give the Parabola challenges a try.  I forced students to work as pairs instead of having them work independently.  I have found that my room is very quiet when students work on Desmos activities by themselves.  I wanted more collaboration and thinking out loud; I wanted more noise.

It appears Desmos hit a home run with their latest release.  More than once I had students arguing about whose turn it was to run the controls.  Many students left class with a new addiction.

Desmos Activity Builder Part 2

In case you missed my first post 5 short weeks ago about Desmos Activity Builder, please feel free to check it out.

It appears as though Santa came early because this was on my wish list.  Great new via Twitter today:

We are now able to copy someone else's activity and customize it to make it fit our specific needs.

For example, we used this activity on rotations by Andrew Stadel in geometry class a few weeks ago.  I now have the ability to duplicate the activity and make small tweaks to fit the needs of my specific students.  I don't have to try to re-create the magic that Andrew already created, yet I now have the ability to put my personal spin on these activities.

One final thought:
This open sharing of resources that is taking place is so powerful.  I love it that the people at Desmos and anyone who shares their wonderful creations through Desmos are not concerned about getting paid or someone else copying their ideas.  Sites like teacherspayteachers.com have some great resources, but it bothers me when teachers aren't willing to share resources with each other without getting something ($$$) in return.  The folks sharing via Desmos are willing to share resources for others to use and potentially for others to improve.  It's such a different mindset when compared to those teachers willing to share but only if they get something in return.

Happy customizing in activity builder!

Using Desmos to find the quadratic model of a real-world image

Desmos is at it again...

Since I started using Desmos more regularly this summer, I have found that it is gradually replacing a number of my other math software options.  The latest instance happened when my algebra 2 students were finding examples of things that take the form of a parabola.

In the past, I have had students find an example of a parabola in their everyday lives and snap a picture of it.  I've seen images of everything from the McDonald's logo to a water fountain to a mug shot of someone's jaw line.  Then I would have students upload their images into Geometer's Sketchpad and construct a number of points along the parabola.  Here is an example...

After that, I would have the students enter the ordered pairs into a TI-84+ or TI-Nspire graphing calculator, find the regression equation, and go back to Sketchpad and graph the function on top of the image.  Again, an example:

Some years I would have students explore around with vertex form a bit to try to fit a quadratic model before we found the regression equation.  But it was a painfully long process to bounce back and forth between Sketchpad and graphing calculator.

This year, I decided to direct students to Desmos to compute the regression equation.  After all, we had used Desmos to find linear regression equations earlier in the year and all students had access to Desmos w/ our 1:1 laptops.  (Not all students would have a TI-84 or Nspire to use in years past.)

It turns out the students had a great idea. Why use Sketchpad to plot the points and graph the regression function?  Why not just use Desmos?  I loved the idea and it really simplified the process.

Students simply inserted their images into Desmos, plotted points on the parabola, created a table with their ordered pairs, and found the quadratic regression equation (& graph) all in one place.

Follow this link for an example (image shown below).

Better yet, using the sliders in Desmos is a breeze.  Simply insert an image of anything parabolic and have students fit the model using vertex form.

Desmos Activity Builder

The team at Desmos has really hit the ball out of the park when it comes to user-friendly math technology.  If you haven't checked out the Desmos Activity Builder at teacher.desmos.com, you're missing out.

I've recently created some inquiry-based activities for my algebra 2 students.  The best part is that there are math educators much smarter than me working on creating activities as well.  Big names such as Michael Fenton and Andrew Stadel are sharing their ideas, and I'm able to use them!

My most recent activities for algebra 2:

Transformations of Functions

Absolute Value Graphs & Transformations

Quadratic Functions in Vertex Form

My most recent activities for geometry:

Equations of Lines - Part 1

Equations of Lines - Part 2

Again, it's great when giants like Andrew Stadel roll out activities (such as this one on rotations) right as we're working on transformations in geometry.

Keep up the great work, Desmos!

Un-structuring Word Problems

This year, I have the opportunity to teach two sections of advanced algebra 2.  My colleague, Todd, teaches the other five sections of advanced algebra 2.  Todd is an excellent educator and someone I have already learned a lot from.

We are both fans of Dan Meyer's TED talk and love the idea of un-structuring our math problems as much as possible.  In an attempt to force our students to think about what information is necessary to solve a problem, we've begun to modify a question or two each assignment in this way.


Here's a question found in a typical systems of equations lesson:

(c) Pearson Education 2015 Algebra 2

We give our students this problem instead:

*1.       You are considering renting a car from two different rental companies.  Write a function that shows the cost of renting from each company.  Which one should you choose?  Explain.

Our students are aware they do not have enough information to complete the task.  Not yet, anyway.
If we assigned this problem on a Monday, students would be expected to think about what information is important and necessary in order to correctly answer the problem.  On Tuesday, to start class, we give students 1 minute to ask anything they want about the problem.   The problem is then part of their homework for Tuesday night and is expected to finished by Wednesday.

It has been interesting to hear some of the questions students ask on problems like this one.  Often times, students ask for the necessary information very quickly and don't ask for anything unnecessary.  There have been times, however, that we get some interesting questions about things that have no effect on the problem.