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Day 80: The Multi-Purpose Trig Equation

Today was so much fun as a teacher!!  As an opener problem, I had the students solve the following equation: 2sin²x+9sinx+3=4cscx.  Then I wrote the problem on the board and opened it up to the kids to add lines to the solution.  They could only add one line at a time and they signed their first name.  Scrumptious discussions and collaboration.  In fact, one gal commented that the activity was great because of the “collaborative nature” of presenting the solution.  Lots of joy and fun, too.

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What I like best about this problem (since we are approaching final time) is that it incorporates skills from previous topics while also reinforcing the current learning.  They did great!  The only addition I needed to make (in red) was the restriction on the solutions.  Great way to review polynomial factoring, rational function equations, etc.


Day 62: Thankful Times

Today was assessment day just before Thanksgiving Break.  I hate to have assessments on the day before a break, but in AP Stats, the kids actually voted to move the test to Wednesday and they promised to show up…which they did!  I am so thankful for these kids ‘cuz they are honorable and interested young people.  This test was on probability and it seems they either “get it” or they don’t.  I may have to consider a test re-take option based on the standards of the chapter and the AP curriculum, but I need to ruminate on it for a day or two.  Students are doing homework and most of the class notes, but I think some students aren’t using them to make sure they really understand the material.  This may be because they don’t know how to use homework as a tool for deep and authentic learning, so I’ll need to consider how to develop this important and leveraging study skill with seniors who think they know it all (tongue in cheek and smile on my face).


In precalculus there was a quiz after a discussion around the opener:  Given the portion of a sinusoidal function at the right, state its critical attributes, and then write its equation in terms of cosine and sine.

Unfortunately we had slightly shorter periods due to early release, so timing was an issue in one of my classes.  They did a really nice job on the quiz, even on this cool question:  Find the average rate of change between the two points on f(x)= sin(x).

Trig Assessment Graph

A few were confused about what the “average rate of change” was asking (but this is critical for next year’s experience in Calculus) and small number of others forgot what the output of the function f(x) = sin(x) is the ratio for the input angle, but overall the rest of the kiddos nailed this problem “even though they had not seen one like this before.”  After the quiz, they asked and were smacking their foreheads knowing they “should have known that.”

I truly believe it is critically important for kids to actually transfer learning in unfamiliar settings…and I preach it daily.   I almost always ask a question that they “haven’t seen before” but uses only those concepts and processes they have practiced a great deal.  I tell them that I can’t ask them anything that they don’t have the tools to approach and find an answer, but they may have to use their knowledge in a new way which requires them to really understand the concepts underlying the process they are learning. And they are beginning to embrace the expectation.  I am so thankful for that willingness to stretch and learn and retain that my precalculus students are growing into this year!

Happy Thanksgiving!  What are you thankful for this year?

Day 19: Polly-No-Meals


In my precalculus class today, we did an opening activity to assess their recall of Alg 2 polynomial work and to review some of the key ideas in one problem.  We reviewed synthetic division, rational root theorem, factoring, precise use of vocabulary: root vs. solution vs. zero.  Our Alg 2 teachers are amazing ‘cuz these kids remembered a lot!!  How do you reinforce prior learning and emphasize the importance of long-term retention in your classroom?

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