Pythagorean Theorem

Grade Level/Course: 8th Grade Math Concepts: Using the Pythagorean Theorem to determine the length of the sides of a triangle. Performance Objectives: Objectives Evaluation Questions Eighth-grade Math students will be able What is the length of the hypotenuse of a to calculate the missing sides of a right triangle with side lengths 3” and 4”?' triangle using the Pythagorean What is the second side of a triangle with a Theorem with little to no assistance. hypotenuse of 13” and a side length of 12”?

Applicable Standards CCSS.MATH.CONTENT.8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Materials List Construction paper, markers, scissors, small fruit candies, evaluation page Engagement: 5 minutes

Student responses and/or What the teacher will do: Probing/Eliciting Questions misconceptions: Show Pythagorean Theorem What are some of the things They’ll probably think it’s a Rap video. he says about the little goofy. https://www.youtube.com/wat Pythagorean Theorem in the ch?v=nbopLhP4kpo video?

What type of triangle can you use the P.Thm on? Can you use it on an acute or obtuse triangle? What are the parts of a right triangle? Which of these sides is the hypotenuse?

Exploration:10 minutes

Student responses and/or What the teacher will do: Probing/Eliciting Questions misconceptions: Demonstrate how the What other integers would Misconception: Students may Pythagorean Theorem

Pythagorean theorem works make up a right triangle? think all right triangles have using fruit candies. Will the side lengths always side lengths that are integers. https://www.youtube.com/wat be integers? Students may be familiar with ch?v=uaj0XcLtN5c a few other Pythagorean Teacher will do what is done What would you do if you triples. in this video, using candies came up with a non-integer (or other small object) in answer? place of the unit squares.

Explanation: 20 minutes

Student responses and/or Probing/Eliciting Questions What the teacher will do: misconceptions: Hand out paper and pencils What are you drawing Fold, cut, and decorate to students. Each group underneath each flap? What foldable as directed by (cluster) gets a different color pictures could you use to teacher. of paper. help you remember the As a group, discuss what Show students how to fold P.Thm? goes under each flap of the paper in half hotdog style and foldable and solve for the cut half way 3 times (paper missing values of the triples will have four flaps). given for the last flap.

Flap 1: Pythagorean Misconception: A, B and C Theorem are interchangeable. In Inside: reality, A and B are, but C is Flap 2: How to find the always the hypotenuse. hypotenuse Inside: An example of how to find the hypotenuse Students can share what Flap 3: How to find a missing they’ve written under each leg flap with their neighbors. Inside: an example of how to find the missing leg Flap 4: Pythagorean Triples Inside: A list of triples to remember Give list of unfinished triples for the last flap

Write down what students are telling you on the flaps of the example foldable you are Pythagorean Theorem making.

Elaboration: 20 minutes Student responses and/or What the teacher will do: misconceptions: If there is extra time, give practice As a group, find the third part of a given problems as a game. Each group is a team. triple. Give two parts of a Pythagorean triple, and have students solve for the third part. Do not only use perfect triples. Call on the group who raised their hands first to tell the class the answer. Everybody in the group will raise their hands when the group has the answer. Give candies to group who does each problem the fastest.

Evaluation: 15 minutes Student responses and/or What the teacher will do: misconceptions: Hand out Pythagorean Theorem evaluation Students will complete evaluation. page. Pythagorean Theorem

Name: ______Calculate the length of the missing side of each figure using the Pythagorean Theorem. 1. a = 7, 2. d=8

b=24 e=______

c =______f=17

3. g=1 4. j=_____

h=1 k=21

i=______l=29