Advice: "If it's not about the students, just say NO!"
The most valuable classroom time is the very beginning and very end of class. Sadly, these are also the most wasted times.
Recommendation: Use Exit Tickets to maximize end of class. And, use Tickets In The Door to maximize the beginning of class.
Tickets in the door were a new concept to me. Here's how they work: give students a short assignment that they must have the next day to enter your classroom. Students who have not completed the assignment cannot enter your classroom until it is completed.
You can use a tool like Remind101 (now just named Remind) to remind students of their upcoming ticket in the door.
"You have to be at least a little bit uncomfortable to be learning!"
After a quick review of the unit circle, we got out our graphing calculators to work through another activity from the Balanced Assessment in Mathematics Project.
The file for this activity and an answer key can be downloaded here. I'll be teaching trig for the first time this next school year, and I'm excited to use this activity in that class! I'm sure my students will be shocked to realize that the answers to 1-3 are all the same! Should lead to a great conversation about why...
Formulas and Function Notation
The next activity we worked through was an example of how we could take something we were already doing in our classroom and raise the rigor of the activity. For example, we expect our Algebra 1 students to be able to rearrange literal equations to solve for any variable. A typical problem would read: "Solve the formula C = 2*pi*r for r." Not exactly exciting.
To step these problems up a notch, we were asked to write the equation for the area of a circle as a function of its circumference. Or, write the equation for the area of a circle as a function of its diameter. Another: write an equation for the volume of a cube as a function of its surface area.
As we sat and worked through these problems, we really had to think. Were these super hard questions? No. But, as teachers, we can get so used to always approaching something a certain way that it can take a minute to reorient yourself when a question is asked differently. We weren't just going through the motions and solving for a single variable. Instead, we had to look at both equations, see what they had in common, determine which equation to solve for that common variable, then plug the result into the other equation.
There are tons of ideas out there on the Internet for data collection activities for linear, quadratic, and exponential functions. But what about rational functions? Those are rare!
This activity comes from a collection of data collection activities for an introductory physics class. You can download the file here. The same publishing company that made this file available for free has some other files online that may be of interest.
|Paragraph Functions Activity|
The activity begins by giving students this page of paragraphs to measure. Ask students: what is constant on this page? What is changing from paragraph to paragraph?
Measure the width (x) and length (y) of each paragraph. Record your data in a table and create a scatter plot. Predict the mathematical model that would best represent this data. Find a regression equation that models this situation. Why is this appropriate?
To be honest, my unit on rational functions has always been BORING. I'm hoping that my students will be able to see why this must be modeled by a rational function. After all, would it ever be possible to have a width of zero? Can't wait to try this out with my students! (Plus, it also fits in some much needed measurement practice. My students are the WORST at reading rulers.)
I Really Gotta Go!
After working through some basic constructions, we moved on to an activity called I Really Gotta Go!
We received a paper that had three points, labeled A-C, and these instructions: There are 3 playground areas in the park indicated by A, B, and C. The recreation department wants to place restroom facilities so the will be an equal distance from each playground. Show where the restroom facilities will be located.
I had trouble with this activity. I bisected each side of the triangle, but I wasn't sure what to do afterwards. One of my tablemates was able to show me what to do next. Geometry really is one of my weak areas. I haven't really needed to do geometry since I took the class in the 9th grade!
Too Hot to Handle
The last activity of the day was from NCTM Illuminations. It's called Too Hot To Handle.
|Too Hot To Handle|
You can download all the resources for this activity here. Because we were running out of time, we had to slightly modify our data collection. We put the thermometer in the water, removed the thermometer, and recorded the temperature every 10 seconds. The actual activity calls for you to leave the thermometer in the water and record the temperature every 3 minutes.
It was suggested that you could have your students research several of the questions from the worksheet packet before doing the project. They could even be a ticket in the door! For example, have students research "What temperature is considered scalding? or "At what temperature is it safe to take the first sip of coffee?"
Gligs and Crocs
One of our homework problems was a task called Gligs and Crocs from the Balanced Assessment in Mathematics Project.
|Gligs and Crocs|
You can download the file for this activity as well as an answer key from the Balanced Assessment website. This problem was a fun little challenge. My first attempt at working out this problem did not go well. But, I regrouped, tried a different approach, and succeeded. This is one of those problems that doesn't have a pretty answer. But, I should give my students more problems with messy answers. They shouldn't immediately think that they got something wrong just because they got a fraction/decimal.
Other Random Notes
Website Recommendation: Inside Mathematics
Ask Students: "What's your takeaway for the day?"
If you're using technology to replace student thinking, that's inappropriate!
If using technology encourages student thinking, that's appropriate!
Technology doesn't have to plug in or have a battery.