Paper Folding Challenge Problem Solving Paper Folding Challenge

Goal of the lesson. To find the point at which two triangles of equal areas can be formed with the folding of a paper. (Middle School 8th grade)

What to do? Every student folds and the class observes others and discusses similarity and differences (Tell/show them how to fold the paper) Launch the idea of what they see and how can they tie it into mathematics Put students into groups

Content Discussions Student Driven Angle measures (vertical, complimentary, supplementary, right, obtuse, acute) Perpendicular Iines, parallel lines, transversals, hypotenuse, legs Polygons, perimeter, area & formulas, scale factor, ratios, similar triangles, (scalene, obtuse, & right triangles)

Questions to ask individual groups? What, if any patterns do you see? Any relationships to geometry? What would happen to the polygons if you folded it differently? Why? What are you going to do to find the same area of the triangles? Can you make connections to vocabulary terms?

More questions How do you calculate area of a triangle? Do the areas of the triangles increase/decrease the same as the point is moved? What happens to the sides of the triangle as the point is moved?

Monitor Students Look for discussion of vocabulary terms Getting organized with data definitions Ask what do they see? How do they know? Label everything?

What students will attempt Massively fold forever Slide the point along the bottom Measuring everything Tick marks Cut out shapes Text previous classes for answers

Expected student responses Similar triangles Just some triangles Trapezoid, pentagon, quadrilaterals Sliding the folding point Changes in size, perimeter, area. There is no spoon

Student Difficulties Diverse levels of understanding or relating to geometry Wanting to know exactly what to do from the teacher only Not used to working with others in groups

Students end discussion Describe what they did Why did they do it that way Have students comment on other strategies Would they use different strategies and why Why are some strategies easier/better than others

McAllen e-PCMI Meiling Dang Steve Ferguson Raul Hinojosa Louis Shoe Armando Soto Dai Tolkov