Exploring Triangles

thingiverse

Students investigate an incorrect statement about isosceles triangles made by the scarecrow from The Wizard of Oz, seen at http://www.math.harvard.edu/~knill/mathmovies/swf/ozz.html. Next, they examine right triangles with a related clip from The Simpsons, viewed here https://www.youtube.com/watch?v=fO1Vhc88QkM. This leads to the Pythagorean Theorem. Students are shown an existing model and asked to create their own. More detailed instructions are included in the Worksheet Solutions handout attached. Print Settings Printer Brand: MakerBot Printer: MakerBot Replicator Rafts: Yes Supports: No Resolution: standard Infill: 10% How I Designed This I decided to use rectangles and break down the 3 by 3 square into separate shapes, leaving the 4 by 4 square intact. I used Tinkercad to make these shapes individually. Your students may use different shapes, but it should be easy to work with the given geometric shapes or shape generators. Overview and Background Students get to act like real mathematicians as they decide if two conjectures are true and then try to prove or disprove them. All they need to know is the definitions of a right and isosceles triangle and some algebra. Objectives: * Students will see why these two conjectures are false and end up with the Pythagorean Theorem. * They will then design a model to help show why the Theorem holds true. Skills Learned (Standards): CCSS.Math.Content.8.G.B.6 - Explain a proof of the Pythagorean Theorem and its converse. Lesson Plan and Activity First, students are given the property that in any triangle, the sum of any two sides must be greater than the third side. They do a practice problem to ensure they understand this concept. Next, show the clip from The Wizard of Oz where the scarecrow says "the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side" and ask students if this is true. If it ever will be true. Then, show the clip from The Simpsons where the triangle is said to be a right triangle and ask students if this statement is true. Ask what the correct theorem is. Show an existing 3D model that demonstrates the Pythagorean Theorem and ask students to design their own model. Duration of Lesson Two days Preparation Students should know the definitions of a right and isosceles triangle and have knowledge of algebra. Rubric and Assessment Here is a sample rubric to use with the worksheet: Question (points) 1: 5 2: 5 3: 10 4: 15 5: 2 6: 13 Total : 50 References Some things you can review beforehand: * In an isosceles triangle, two sides are equal. * In a triangle, the side opposite the largest angle is the largest side. * Sides of a triangle have to be greater than 0. Custom Section Project: Exploring Triangles