Pythagorean Theorem: Real Life applications



Pythagorean Theorem: Real Life applications (and BoardWars)

10 February 2011 Thursday

GOAL: For students to apply the Pythagorean Theorem to real life situations.

I can: Use the Pythagorean Theorem to find the missing side length of a right triangle.

Prior Knowledge

• Students can recall the Pythagorean Theorem, A2 + B2 = C2, and recall that A and B are the legs, while C is the hypotenuse.

• Students can apply said knowledge to find an unknown side length of a right triangle.

Objectives

• Students will analyze three side lengths to determine if they can form a right triangle.

• Given a real life situation involving right triangles in 2 or 3 dimensions, students can represent the situation with a right triangle and correctly find the missing length or distance.

• Students can use apply the Pythagorean theorem to find perimeter and area of given figures, such as a trapezoid.

Materials

• Promethean board and Document Cam

• Calculators for each student

• White Boards for each student

• Rules Sheet for “Board Wars”

• List of problems to use for higher thinking examples (attached below)

• Bellringer worksheet (attached below) and ISAT review questions

• Whiteboard/chalkboard with platform to hold chalk/markers and eraser.

Procedure

• Open up with ISAT review and Bellringer ~10 min

o Because the given ISAT review is of the same topic, but much easier than the Bell-Ringer, we will do the ISAT first today. Students will follow along with the Gold Sheet while Akili works through the ISAT problems as a class.

▪ Make sure Akili stays on task, and walk around to ensure all students are paying attention and participating.

o Students are expected to then work on Bell Ringer (MAKE 20+ size font) for five minutes and then we will go over it as a class. Use for a 4 or 5 minute timer. While this is going on walk around the room to ensure students are on task and answer and questions/misconceptions they may have.

o Today’s Bellringer deals with word problems related to the Pythagorean Theorem

o I will also check completion on the “Drill and Kill” worksheet from the previous day.

• From here, return quick quiz on scientific method. Go over a common missed question or misconception if it seems to occur. ~5 min

• Next, we will take two problems at the students choosing from the previous night’s homework and review the problems. Hopefully this will give me a feel for how the students faired on the lower level problems of this topic. (5 min)

• Begin “Boardwars.” This is a new game for students, so we must explain the rules upfront. At first, let students get into groups of 2-3 to form teams. Then hand out “Rules” sheet and problems.

o See attached “Rules” sheet explaining how the game works.

• Begin the game. I will work the board and keep score while Mrs. Malone checks the answers of the students and monitors the rules.

• The problems for Board Wars are still problems involving Pythagorean Theorem, but are at a higher level than the basic ones seen the day prior. These involve real life applications where the “right triangle” isn’t always described explicitly.

• Students are not to talk out loud, and must communicate silently via their work on each other’s mini whiteboards.

Closure

• Once there about 6-8 minutes left in class, announce the “2 minute warning.” Students will have a chance to finish up their last problem sets for a final chance to score points.

• Explain in further detail the point of using Pythagorean Theorem for real life purposes. Mention the idea of finding distance across city blocks, television size, moving ramps, and other examples.

• Inform students that they are responsible to finish any problems not done in class as homework.

ASSESSMENTS

• During the Bell-Ringer, I will walk around to ensure that students are working and following along. Also, When reviewing that and the ISAT review, I will be sure to call on several students at different times, and use discursive moves such as restatement to ensure that multiple students are following along and understanding the problem solving methods.

• Allowing students the opportunity to solve the examples in class with me will check to see if they are understanding the Theorem, and have a conceptual understanding of how the theorem is applied to any missing side of a right triangle.

• BoardWars will show me how students can apply Pythagorean Theorem at a higher level of thought.

STANDARDS

• Common Core Standards

o 8.G.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real world and mathematical problems in two and three dimensions..

February 10th, 2011 BELLRINGER

On this day in 1863: The fire extinguisher gets patented.

I CAN: Use the Pythagorean Theorem to find the missing side length of a right triangle.

1) If the gym at TJ Middle School is rectangular shaped and sized approximately 120 ft. by 180 ft., then what is the approximate length from one corner to the opposite corner?

2) Is it possible to draw a right triangle with side lengths of 12, 21, and 16?

3) A square has a diagonal length of 10 centimeters. How long are the sides?

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