## What Did Peregal Prove? Activity - Section 4: What Did Perigal Prove?

# What Are We Gonna Learn?

Lesson 1 of 6

## Objective: SWBAT look up course requirements as well as learning goals, vocabulary, and key dates for the unit. Students will understand how dissection and transformation strategies can be used in a proof.

#### Lesson Open

*5 min*

The Team Warm-Up prompt for this lesson asks students what questions they have about the course. This is the first day of the new semester, so today's lesson is all about expectations. I ask students to follow our Team Warm-up routine, which involves sharing their responses with the other members of their cooperative learning team. I choose students at random to write the team's chosen response on the board.

I answer the team questions briefly, or tell students that their question will be answered when we review the Course Requirements and Expectations or the Unit Syllabus.

I display the Agenda and Learning Targets Slide for the lesson and briefly review them with the class.

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#### Administration

*20 min*

Since this is the first lesson of the spring semester, I use some time to review Course Requirements and expectations. Usually, a few students have questions about course policies, grading, and the like. It also helps to review classroom rules and expectations, since students might otherwise conduct experiments to see if these still apply in the spring semester.

#### Resources

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#### Pre-Test and Goal-Setting

*10 min*

I use the Would You Rather?... Slide as a transition, since the preceding section may be a little dry. I tell students to read the question silently and keep their answers to themselves. I also tell students that we will be answering questions like these in this unit--beginning today, in fact.

Next I distribute the Pre-Test for the unit. For an explanation of how I use pre-tests as a kind of advance organizer, see the explanation in my Strategies folder. After students complete the pre-test, I hand out the Unit Goals and Syllabus for the unit and ask them to look it over. When they finish reviewing the learning goals, they should write a personal learning goal.

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#### What Did Perigal Prove?

*15 min*

My goal during this section of the lesson is to introduce students to the use of transformations to prove theorems about area. I hand out the Activity and make scissors and glue available. I give students up to 7 minutes to solve the puzzle. By that time, enough students have completed the puzzle that I can display a student's solution using the overhead projector.

I use the slides in the slideshow to check whether students understand what Perigal proved. Will they recognize that this is the Pythagorean Theorem? (Often, students will only have learned "a squared plus b squared equals c squared". This is an opportunity to address the misconception that the Pythagorean is about the lengths of the sides of a triangle.)

Using the slides, I briefly explain that Perigal published this proof in a book, which was all about using dissection strategies and transformation strategies in a proof. Of course, that is the subject of this unit.

Before moving on, I ask for a student to explain what 'dissection' means in their own words. Then I ask students to describe how Perigal used dissections and transformations in his proof (**MP3, MP5**).

#### Resources

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The Lesson Close prompt checks for student understanding of the terms "dissection strategy" and "transformation strategy". The lesson close follows our individual size-up routine, and students write their responses in their Learning Journals.

**Homework**

For homework, I assign problems #1-3 of Homework Set 1 for this unit. Problems #1 and #2 ask students to review postulates related to measurement--expecially area measurement--and require students to practice representing measurements algebraically. Both skills will be needed in the next lesson. Problem #3 reviews a transformation that students will use to relate the area of a triangle to the area of a parallelogram in later lessons.

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