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Problem Solving

Engage 8th-grade students in a problem-solving activity where they explore the folding of paper to find the point at which two triangles of equal areas can be formed. This lesson encourages student-driven discussions and connections to geometry concepts.

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Problem Solving

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  1. 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

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