## Mathematical Expectations.pdf - Section 2: Groups Revealed

# Will it Topple? Day 1 of 3

Lesson 1 of 16

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

*50 minutes*

#### Will it Topple?

*15 min*

The lesson launches with a video showing the collapse of a four-story commercial complex in the middle of Mahidharpura diamond market in Surat, India. A new construction project on the site next to the complex caused the foundation of the complex to be compromised, which provided a great deal of excitement (and no injuries) when the building collapsed!

Show the building toppling video at the start of class.

The goal of this lesson is to provide the students with an opportunity to collaborate, research, and mathematically argue the potential collapse of the Leaning Tower of Pisa. The resource document kicks off the lesson. After allowing the students to read through the document quietly by themselves, I also read the document to them. Following this, I tell the students that they will be working in partners as “engineers” who will summarize the potential collapse of the world famous tower.

#### Resources

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#### Groups Revealed

*10 min*

Following the roll-out of the problem, I reveal the partners that the students will be working with. As always, prior to roll out I tell my students that I expect professionalism at all times when they hear who they will be working with. I reveal the groups on a PowerPoint slide and then send the students to find a new seat next to their partner. After allowing them to get settled and discuss the problem for an additional 1-2 minutes, we are ready to continue our conversation about the problems.

Note: In this problem, I group students in like ability pairs. This problem is structured so that it allows the "high flier" students to dive deep into the investigation. Activities with a non-cookie-cutter end product have worked better for like-ability groupings in my experience.

After getting settled, I provide the students with the Mathematical Expectations sheet. I do not read this sheet out loud to the students because they can now begin discussing these its elements with their partner. This is all part of them becoming "collaboration reliant" rather than "teacher reliant".

#### Resources

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#### Know's and N2K's

*10 min*

In this lesson, I use my Know's/N2K's strategy to get the students to connect the real world problem to the mathematics that we will be studying.

#### Resources

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#### Homework

*5 min*

It is important to note that the core standards to not call for us to go back and totally reteach the Pythagorean Theorem. However, since Trigonometry is defined as the study of triangles, it is important to make connections to the students prior learning and one of the most significant properties of a right triangle. Don’t set the tone for the students that it is a “Review Lesson”… but rather a familiar launching point for new breakthroughs!

To ensure my students all have a foundational knowledge of the Pythagorean Theorem, I assign the Will it Topple - Day #1 as homework. Please note that the problems themselves are not aligned to Algebra II Common Core Standards. However, I am assigning them as a necessary review of right triangles before we get too deep into our trigonometry unit. Although the Pythagorean Theorem does not need to be used to determine how close the tower is to toppling, we still revisit the skill because of its importance in trigonometry.

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Will it Topple? Day 1 of 3
- LESSON 2: Will it Topple? Day 2 of 3
- LESSON 3: Will it Topple? Day 3 of 3
- LESSON 4: A Sidewalk Investigation of Radians
- LESSON 5: Radian Stations - A Rotating Review
- LESSON 6: Radians Quiz
- LESSON 7: Graphing Trig Functions By Plotting Points
- LESSON 8: Shifting Trig Functions - Student Discovery
- LESSON 9: Simon Says... Transform!
- LESSON 10: Modeling with Predator/Prey Populations
- LESSON 11: Trig Memory Game
- LESSON 12: Bay of Fundy: A Tidal Investigation
- LESSON 13: Bay of Fundy Investigation and Unit Wrap-Up
- LESSON 14: The Pythagorean Identity
- LESSON 15: Trig Review Football!
- LESSON 16: Trig Tidbits Unit Test