Day 2: Displaying Categorical Data, Functions and Radians

It’s Day 2 and I’m tired.  I need to work on my conditioning.  My lessons were a bit dryer than I’d prefer today.  Here are some highlights from today.

AP Statistics:

The goal today was to be able to summarize univariate categorical data (and start the conversation about summarizing quantitative data).  The lesson started with having my students collect some categorical data and telling them organize/graph the outcomes.  Every student chose to make a bar graph.  We discussed features of a bar graph and its advantages over a pie chart.  The most interesting part of the lesson, however, happened with this slide:

1.1 Bar Graphs, Dot Plots, Stem Plots_6

We used remote responders so I could get instant feedback from the class and found that 80% of them missed this question (the answer is E by the way).  After discussion, we came to the consensus that there was a reading issue.  Whether they read too quickly, or not carefully enough, I need to keep an eye on this and help with their critical reading skills.

Algebra II Honors:

In class today, we had a crash course on everything they should know about functions.  Discussions included domain and range, with proper notation.  Interestingly enough, they did struggle with the domain and range of the triangle here:

1.1 Intro to Functions lesson_4

They wanted to tell me that the triangle had three points.  After quelling that misconception, we realized that we can write domain and range using inequalities.  I’m glad we came across that gap in their knowledge.

After domain and range, we discussed the input/output idea behind a function…and we got to watch one of my favorite educational videos.

The conversation we have during this video is really rich.  The nuggetizer really gets to the input/output idea without an equation.  good stuff.  and it’s entertaining.

Precalculus:

Today we explored radians.  The warm-up allowed them to review circumference and arc length.

1.1 Radians and Arc Length_1

I’m finding they’re a little rusty/apprehensive about fractions.  I need to make sure we get better quickly.

My hope today was that they would figure out the conversion to go from degrees to radians.  I found an intriguing activity in the textbook we currently use.  I modified to fit my style, but it has the same bones:

1.1 Radians and Arc Length_2

I was thrilled with how quickly they found that the s/r ratio is constant (in this case pi/3).  We defined that ratio as the number of radians, and my students decided that ratio measured the angle.  pi/3 is equivalent to 60 degrees.  Then we derived how to convert from one measurement to the other.