Will it Topple? Day 2 of 3

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SWBAT mathematically investigate the Leaning Tower of Pisa with trigonometry and determine when/if the famous tower will fall.

Big Idea

Students work as engineer pairs to reach a conclusion about the leaning tower!

Homework Collaboration

10 minutes

To open the class period, I ask my students to take time to collaborate on their Pythagorean Theorem homework assignment from the previous lesson.  These instructions are written on the whiteboard as soon as the students enter the classroom.  Occasionally, I like to open class like like this because no verbal direction from me is needed, and the students are able to get right down to business.  While the students are collaborating over the homework assignment (MP3), it is important to rotate the room and help resolve any discrepancies.  

Note:  This homework assignment does not directly connect to any Algebra II Common Core Standards; the Pythagorean Theorem is taught at lower levels.  However, we will be using this as a launching point for our trigonometry unit and it serves as a nice connector to the students' prior knowledge.  

After about 5 minutes, I verbally bring the class back together and ask if there are any of the problems that they would like to see worked out on the board.  I do not foresee a lot of questions being asked, but it is nice for the students to know that they always have that opportunity.  

How to Become 4 Teachers in one!

5 minutes

Do the math....

3 Virtual "Mr. Hammel Clones" providing differentiated instruction + 1 "Real Mr. Hammel" = 4 Classroom Teachers!


Investigating Slope Ratios Workshop #1

15 minutes

The following workshops are accessed through my course webpage.  The students can download and watch the videos at their convenience.

In this workshop, students explore introductory trigonometric properties with their partners.  I intentionally provide minimal instruction as the focus is to activate prior knowledge and promote discussion.  Many of the questions in this activity are designed to get the students to think critically, and question how this workshop might apply to the Leaning Tower of Pisa (MP4, MP1).  If you have followed any of my application lessons in the past, you have probably noticed that I did not specifically designate time for Know's/N2K's here.  This is intentional, in hopes that students tend to this task on their own.  If I notice a Know/N2K happening, I will make a big deal about it to the class and acknowledge that they have perfected and taken ownership over the problem solving process!  Even if the mathematics fades, this skill will stick with them for a long time.

It is also worth noting that this "similar triangles" theme will serve as a great connector and "ah ha!" moment in a future shoe-string where the students begin investigating the unit circle (MP7).  The similar triangles that are formed create reference angles that correspond to co-terminal angles on the unit circle.  


Changing Lines Workshop #2

10 minutes


You might be thinking that this feels a little bit like Geometry... not Algebra II.  So why I am taking the time to make a connection to Geometry in the first few lessons of this unit? Having taught a variety of math classes, I have at times been frustrated when students are unable to make connections between multiple math courses.  When I went to write this unit, I consulted a Trig teacher at our school about her frustrations she may have encountered teaching a trigonometry course so that I might proactively plan and hopefully remedy this in planning my unit.  One thing that she shared was her amazement at students' lack of ability to connect "SOHCAHTOA" (basic trig ratios) to the work that they do in Trigonometry.  Students actually made the claim (even high achieving students) that they didn't know that "trig" in Geometry was the same as "trig" in Trigonometry.  This makes me cringe as a teacher, and pushes me to do a better job stressing connections between courses - we should have students leaving Geometry thinking that trig is only about triangles, and leave Trigonometry thinking that trig is only about periodic functions.   

Investigating Trig Ratios Workshop #3

20 minutes

In this workshop, I attend more closely to students than in the previous two, however, I still do not conduct a formal lesson.  Instead, I continue working to get the students drawing conclusions based on their findings.  Workshops like these are beneficial to student growth because they begin to view teaching and learning through a new lens.  In my class, it is no longer acceptable to see the teacher as the "sole keeper of knowledge" - I want my students to collaborate, question, and engage with each other (and me too!) as they experience mathematical breakthroughs.  Without relinquishing some of this control as a teacher, the students never get to experience this!  Trust me, it would be much easier (and comfortable) to be at the front of the room doing a review of Geometry as we transition to trig.  HOWEVER, the Common Core (and effective teaching) calls for a culture of engaged student learning centered around the math practice standards.

Closing Remarks

2 minutes

To conclude the lesson, I provide the students with a timeline for the remainder of the week.  Highlighting this timeline is the fact that I would like for them to meet with me tomorrow by the end of class to discuss their findings about when the tower will collapse.  I tell the students that tomorrow they will have the entire class period to finish the video workshop series (and their corresponding worksheets) as well as attack the Leaning Tower of Pisa problem.  Although much of the work has been done together, I ask the students to each submit to me their OWN written response to the problem.  (See the Entry Document and the Mathematical Expectations in the previous lesson for details).  

Finally, I give the students a manila folder to keep all of their workshop documents in.  This will be submitted at the end of the week along with their papers.  Although tomorrow is the last in class work day, I always give my students at least two additional days to work on their write up.  This allows students the opportunity to see me before or after school if they have questions.  I purposefully avoid assigning any additional homework until after the deadline for the papers because I want my students to submit high quality work.  It is not that different from the types of activities that they are asked to do in college!