Gamifying the Unit Circle

Introduction

Precalculus students must be able to evaluate trig functions quickly and easily in order for them to be able to handle later trig topics better. To assist students in that respect, throughout the years I have made sure that students compete in groups against one another in a game called UC Bowl. Below is a description of the game and how it is managed in class.

The Details!

• The class was broken onto three competing teams.
• Each team was allowed to have an ID sheet along with a UC chart.
• Everything else including calculators had to be stashed away.
• And each team was given a small whiteboard to write down final answers to shouted out problems.
• Each rounds will involve a different team member acting as the scribe who would write the answer and quickly raise the board when prompted by me.
• I am standing in the from of the room with a TI calculator and a rubber-head hammer as a gavel.
• The TI calculator runs a Trig UC program written by a former colleague of mine (Thank you Eric Kamichke.) The calculator draws random Trig or Inverse Trig questions for students to answer as quickly as I allow for time-wise in any given round.
• I hit announce the problem to be solved, hit the rubber hammer, the students begin solving the problem, I give a warning to write final answer, and then I hit the hammer once again to have the scribe raise the boar immediately.
• Delays in raising the board results in a zero earned by the group and a word answers leads to a zero as well. Right answers are awarded one point each.
• The scores are tabulated to keep track of the scores.
• Between rounds pauses are taken to allow group members to reflect and discuss amongst themselves.
• The winning group earns sweets and cool treats that vary from year to year.
• Below is a sample of images showing some of the items listed in the above bullets.

Table Set Up for a Group in UC Bowl

Another Group's Table Set Up for UC Bowl

More Table Set Up for a Group in UC Bowl

Scoreboard for UC Bowl after some additional rounds!

Final Scoreboard for UC Bowl after the last few rounds were played!

Closing Remarks!

• The engagements was wonderful by all teams.
• The competition was fierce and even one team emerged as the wild posse team. The members dancing whenever they score points.
• The team that came last had a good comeback in the second class day that the UC Bowl was conducted and they still have chances to redeem themselves.
• The importance of UC and knowing values of trig and inverse trig functions began to sink in as an important part of learning trigonometry.
• In later edition of the game, the trig ID sheets with its UC chart will be removed to allow students to do everything in their heads.

Final Note: Please, use the comments area to share your thoughts on this activity and what kind of games you engage your students in math to make their learning fun and competitive in a healthy way. Thank you

The Value of Discovery through Investigations [Part 1: Inverse trig Functions]

Introduction:

After a review of inverse functions, their domains & ranges, and how their graphs are related, Precalculus students were broken onto three groups to investigate inverse trig functions of the basic three trig function (sine, cosine, & tangent) themselves prior to me teaching about them. This process was pursued to achieve the following educational goals:
(a) To offer students the chance to review past material, trig functions, their graphs, and domains and ranges of functions and their inverses.
(b) To help the instructor to gauge how well prior material was grasped by students that other means of assessment may not have captured.
(c) To assist the instructor in figuring out how much transfer of concepts students can do on their own without much intervention from them.
(d) To enable students to use technology as means of verifying and rectifying some misconceptions they may still have held prior to the coverage of inverse trig concepts.

The Prompt & Group Findings:

The following figure shows the smart board with the prompt written on it.

Activity Prompt

The groups then began drafting their own papers in which they addressed the tasks of the prompt. Following are copies of the raw work the groups did without being allowed to use any references of any kind nor any calculators.

Sine Group work shows what they understood and what they misunderstood about sine functions.

Cosine Group work shows that the concept of inverse of a function was understood in terms of reversal of roles of inputs and outputs. But graphically speaking, the idea did not sink in yet in terms of the use of the y=x line and restricted domain.

Tangent Group work shows that the concept of inverse of a function was understood in terms of reversal of roles of inputs and outputs. But graphically speaking, the idea did not sink in yet in terms of the use of the y=x line and restricted domain.

Once the groups were done with the prediction phase, they were instructed to use technology to verify the outcomes of their work and then update their findings regarding inverse trig functions and reflect upon them. Below are a few images that illustrate the checking process followed by a sample revised group results with reflections.

Desmos and a TI graphing calculator were used during the verification phase of the activity.

Desmos and a TI graphing calculator were used during the verification phase of the activity.

Desmos and a TI graphing calculator were used during the verification phase of the activity.

Desmos and a TI graphing calculator were used during the verification phase of the activity.

After using Desmos and a TI graphing calculator, the Tangent Group seems to have hit the jackpot of discovery.

To ensure that no group members are left twiddling their thumbs when peers are still finishing their activity, another activity was added. The activity consists of looking at a flier that features the school's organ and then connect what they observe to the subject matter at hand. The organ picture is shown below and the Tangent Group's reflection is shown in the picture above this text.

Cool Math Connection with Organ Pipes

Conclusions:

• The formal coverage of inverse trig functions was preceded by this activity to achieve the goals stated above. The results reported after the technology portion of the activity showed that three quarters of the students made great strides toward understanding inverse trig functions, their graphs, and their domains and ranges. 
• The task of teaching the subject matter went smoother now because it was a mere strengthening of ideas for students who grasped the concepts while it was an eye opener for the ones who missed to understand the concepts initially on their own.
• This activity also made it clear to me that there were still gaps in students' understanding of the basic trig functions (especially their graphs) and the concept of inverse functions in general. So, a nice review of the unit circle and its connection to the basic trig graphs followed. The method of review that was used consisted of a series of class-wide UC-Bowl games that will be featured in another blog post. Inverse functions (especially how to draw their graphs) was also reviewed but now through the official coverage of inverse trig functions.
• The spiraling in tackling concepts was definitely a pleasant outcome of this activity and for this alone I believe the whole activity is worth replicating with other mathematical topics.

Note:

I hope the ideas shared in this post would encourage you to post in the comments area your own wonderful approaches to how you assist your students in internalizing challenging topics such as inverse trig functions. Thank you