In precalculus today, it was time for students to work with a real-world application of sinusoidal functions while also engaging is sense-making discussion with their peers. I used the matching activity in an awesome Ferris Wheel Project I found at Mathematics Assessment Project: Assessing 21st Century Mathematics. The MAP project is a collaboration between the Shell Center team at the University of Nottingham and the University of California, Berkeley. There are lots of great Common Core based authentic lessons, so take a look.
The matching activity included three sets of cards: Card Set A: Graphs, Card Set B: Functions and Card Set C: Descriptions of Wheels. The students cut out the three sets of cards and began to match them. Interestingly, there were only 6 descriptions but 8 graphs and 7 equations (with a blank one for one graph that did not have a predetermined equation).
The discussions were fabulous and the support materials give teachers a guide for listening to student discussions and possible prompts and interventions that help but don’t inhibit the students’ sense-making. Many kids were up out of their seats to work together.
Many student groups thought they had the matching figured out and then realized that they had an equation that didn’t fit the graph after all and had to re-think their strategy.
The activity took approximately 30 minutes. I had an photo of the answers so the activity was also a “self-check.” Fun times and good learning took place.
We’ve spent a few days working on transformations on sinusoidal functions, particularly focusing on the horizontal transformations. So today, they need practice and time to discuss the process. So I use the “20 Minute Poster” activity. And I teach the transformation form for transformed trig functions: y = A trig [B(x – C)] + D rather than the form our book uses: y = A trig (Bx – C) + D for pedagogical reasons….I want the skills and concepts to transfer beyond trigonometric functions. Obviously, we then tackle what to do (and what is happening physically) when the equation is given in the “Bx – C” form.
Because of teaching AP Statistics over the years I have collected dice….lots and lots of different kinds of dice…and I love them all! I put the dice used for this activity in a small container (found the idea on Pinterest) so they don’t go flying around.
I use them in this activity by having each type of die represent some variable of the basic trig equation:
- Roll the 6 dice in the plastic pouch. Use the numbers in the following way to determine your random equation:
- Orange: even = sine, odd = cosine
- Green = A
- Red = sign of A: even = +, odd = –
- Blue = B = π/number shown
- Black = C = number
- +/- die: + phase shift, − phase shift
- Yellow = D
- Write the Random equation in the correct form using the letter values above.
- Identify the following and color-code (when possible) on your equation and graph.
- Interval length
- Phase displacement (for + cosine)
- Sinusoidal axis location
- Sketch three cycles of your created function. Show units on the two axes.
- Write the related cosine equation for a sine graph or sine equation for a cosine graph.
I have the time limit set because of what I learned about authentic and dynamic group work in a workshop on Complex Instruction that requires all kids working together to get a product completed.
As you can see, all hands are working and discussing their product. Such a great activity and my students walk away from the experience feeling confident in their skills.
In AP Stats today we did the Probability Review Stations. Seemed to go well and having the answers available really helps kids take ownership for their own understanding.
We started the study of two variable data a couple of days ago in AP Statistics. The students watched a video for homework and then were to come in ready to present their completed scatterplot and description. They worked in their new groups, using a different color for each student and putting their name in that color. Students then did a gallery walk to see other groups’ results. Good conversations!