##
* *Reflection: Station Rotation
Applying Pythagoras' Theorem with 7 "Choice" Problems - Section 2: Application Gallery Walk

I find that grouping students homogeneously is helpful for students who would normally not participate actively in a heterogeneous group. As used in this lesson, giving students choices is another tactic that helps me to increase student participation. Allowing students to choose classroom tasks or assignments gives students more opportunity to show what they've learned and whether they've met the objectives.

For this lesson I created seven tasks to give students choice and to allow for some differentiation. I am often impressed by how good my students are at self-differentiating. Even when tasks deal with the same content, the solution can be more or less obvious. Confident students often choose to challenge themselves. Others choose to practice problems that they recognize as difficult for them. And of course, students always feel you are doing them a favor when given options to choose from. In my mind, I am only being fair.

*Station Rotation: Giving Choices and Student Motivation*

# Applying Pythagoras' Theorem with 7 "Choice" Problems

Lesson 9 of 10

## Objective: SWBAT apply the Pythagorean theorem to solve interesting problems, including some with 3-D figures.

## Big Idea: At different stations in the room, students tackle abstract applications of the Pythagorean theorem.

*60 minutes*

#### Launch

*10 min*

I begin this climactic lesson by projecting Slide 1 of the Two Slide Intro. As students view the first slide I ask them to recall the geometric proof of the Pythagorean theorem demonstrated in previous lessons. After a few moments I'll then say, **"H****ave you ever wondered if the theorem holds true if we used other shapes on the sides of the triangle?" **And then I reveal Slide 2.

When they see Slide 2 some students will instinctively say, "Yes, of course I can see it." Others will shake (or scratch) their heads. I'll say:

**Look at this slide for an example, then take a few minutes to explore this idea. Can you prove that the Pythagorean Theorem works for shapes other than a square on each side of a right triangle?**

My plan is to give students as little information as possible. "The formula for the area of a circle?" I'll say, "Better ask your neighbor." Ultimately all of my students will see that the Pythagorean Theorem works for other shapes, such as a semicircle. I hope to have a volunteer go up to the board and show the class his or her work. Once he or she has finished, I'll make a point of explaining to students that there are many proofs of the Pythagorean Theorem, including one by a US president (Chester Arthur) and one by Napolean Bonaparte. To conclude this Launch and give students a sense of how some people may find beauty in proof I'll show the following video of six visual proofs of the Theorem:

Pythagorean Theorem, Six Proofs by Beau Janzen

URL: http://vimeo.com/106024746

#### Resources

*expand content*

#### Application Gallery Walk

*40 min*

Before beginning this activity I make sure to create homogeneous groups of students who will work well together as they travel from station to station. From the 7 Pythagorean Problems resource I place copies of today's explorations at each station, one problem per station. I want my students to have the opportunity to get up and move throughout the lesson. Students can complete the problems in any order that they choose. I tell the class that each student should do their own work, but I will collect one paper per group at the end of the lesson.

In groups, students will visit each of the seven stations. I ask them to complete (successfully) any four of the problems. Of the four, at least two of the chosen problems must involve a 3-D figure.

When students begin working I will keep an eye out for students who I know have been struggling this unit. I may just ask that they skip (or choose) certain problems in order to make sure that they practice problem solving, and complete the four assigned problems. I generally check-in with groups at each station, or ask them to check in with me, before they move on.

#### Resources

*expand content*

I forget where I picked up this strategy, but I use it in this lesson with good results. As we came to the end of the lesson I asked my students to write a response completing each of the following prompts:

** "I used to think............."**

** "But now I think............"**

Before we depart for the day I call on various students to share their responses. It is is a great way of gaining insight into how students' ideas about the Pythagorean Theorem may have changed during this unit.

#### Resources

*expand content*

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- UNIT 1: Number Sense
- UNIT 2: Solving Linear Equations
- UNIT 3: Relationships between Quantities/Reasoning with Equations
- UNIT 4: Powers and Exponents
- UNIT 5: Congruence and Similarity
- UNIT 6: Systems of Linear Equations
- UNIT 7: Functions
- UNIT 8: Advanced Equations and Functions
- UNIT 9: The Pythagorean Theorem
- UNIT 10: Volumes of Cylinders, Cones, and Spheres
- UNIT 11: Bivariate Data

- LESSON 1: A thought is an idea in transit
- LESSON 2: Reasoning with Pythagoras
- LESSON 3: Fluency with Pythagorean Triples
- LESSON 4: Hypotenuse Hype
- LESSON 5: Missing a Leg (Day 1)
- LESSON 6: Missing a Leg (Day 2)
- LESSON 7: Pythagorean Theorem Converse
- LESSON 8: Draw a Right triangle! You can´t go wrong.
- LESSON 9: Applying Pythagoras' Theorem with 7 "Choice" Problems
- LESSON 10: Round Robin Review (Unit 9/L1-7)