1. Paper Folding Challenge
Problem Solving
Paper Folding Challenge

2. 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)

3. 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

4. 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)

5. 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?

6. 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?

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

8. 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

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

10. 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

11. 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

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