Playing Around with Pythagoras-Day 1

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Objective

SWBAT to demonstrate an understanding of Pythagorean relationship using models and manipulatives.

Big Idea

After a brief introduction, students will explore the Pythagorean relationship with color tiles and then apply that understanding by reconstructing a Pythagorean proof.

Warm-Up

5 minutes

Today's Warm-Up is a review of the relationships between equations, tables and graphs.  It is important for my students to continue to practice with this concept as some still struggle with manipulation of negative integers in linear equations.

Introducing Academic Vocabulary

5 minutes

While some students may be familiar with the vocabulary related to triangles including 'leg' and 'hypotenuse', I want students to have personal access to the definitions by recording them in their journals. For the definition of 'Pythagorean Theorem', I include animation in the notebook (see video link) that I think gives students a strong visual example on which to hook their new knowledge from today's lesson.

Work Time- Part I

10 minutes

For the first part of today's work time, I have provided each table of four with a basket of color tiles.  I want them to use these manipulatives to discover the length of the hypotenuse of the given triangle by physically building two dimensional squares. I circulate as groups work, offering scaffolded support when needed.  For example, if a group is not sure how to begin, I ask them the length of one of the legs of the given triangle. I then instruct them to build that with color tiles.  This is usually enough to get the group going.

For groups that finish quickly, I give then another to solve (5, 12, ?). When the 9-minute timer sounds, I ask material monitors (pre-determined by seat number--e.g. all students seated in chair 3 at each table) to return the color tile baskets to the materials table.

I then ask table groups to report out their findings and verify the solution on the SmartBoard.

Work Time- Part II

15 minutes

While a variety of proofs for the Pythagorean Theorem exist, I have recreated one of the area model ones to use with my students.  I explain that a theorem is an idea in math that has been proven true.  I then distribute copies of the Pythagorean Proof puzzle to each student. I share the directions on the SmartBoard. Then, students cut out the puzzle pieces and work to arrange the pieces in the largest square. This is a perfect opportunity to reinforce Mathematical Practice 1 as students quickly become frustrated when the pieces don't fit easily.  Once one student in the room discovers the solution, the answer quickly spreads throughout the room.

I want students to articulate their understanding of the proof so I ask them to respond in their journals to the question, "What does this model prove?". Typically, some students respond simply with "It proves the Pythagorean Theorem", so I ask them to explain how it is proof. This pushes students to think at higher levels about theorem.

Reviewing Square Numbers and Square Roots

5 minutes

Before closing the day's lesson, I spend five minutes explaining the importance of students having a strong working knowledge of perfect square numbers and their square roots. To facilitate this, I explain that students have three opportunities to show their proficiency by taking a 10-question quiz on Wednesday, Thursday, and Friday of this week. Any student who has not achieved 100% proficiency by Friday will be assigned after school tutoring. I then distribute lists of square numbers 1-20 to students and review them. I point out that I keep a basket of these square root lists next to the homework baskets so they can easily get another copy if they lose track of the first one.

Ticket Out the Door

5 minutes

To help students consolidate today's learning and to provide me meaningful feedback, I ask students to complete a ticket out the door on 3 x 5 note cards. To support struggling students, I suggest a sentence starter: To find the missing side of this right triangle, first I need to...

Although it is only the first day of unit, these exit tickets provide me valuable information about how I may need to reteach the concept or give additional support to struggling learners.