1. Day 13
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, June 27-July 15, 2005
by Akihiko Takahashi, DePaul University, Chicago IL

2. Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, June 27-July 15, 2005
by Akihiko Takahashi, DePaul University, Chicago IL

3. Designing a Unit by using the idea of the open-ended approach
An example of unit using the idea of the open-ended approach
Area of quadrilaterals and triangles
From a Japanese fifth grade textbook
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, June 27-July 15, 2005
by Akihiko Takahashi, DePaul University, Chicago IL

4. Area of quadrilaterals and triangles 14 hours (45 minutes) - about three weeks -
Developing the formula for finding the area of parallelograms (3 hours)
Developing the formula for finding the area of triangles (3 hours)
Practice (1 hour)
Developing the formula for finding the area of trapezoids (2 hours)
enrichment learning activities (1 hour)
Ideas to finding the area (2 hours)
Reviews (1 hour)
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, June 27-July 15, 2005
by Akihiko Takahashi, DePaul University, Chicago IL

5. Developing an open-ended problem for your students
Determine if the problem is appropriate
Is the problem rich in mathematical content and valuable mathematically?
Is the mathematical level of the problem appropriate or the students?
Does the problem include some mathematical features that lead to further mathematical development?
Anticipating students’ responses to design a lesson.
Making the purpose of using the problem clear.
Make the problem as attractive as possible.
Presentation is prepared for The Park City Mathematics Institute, Secondary School Teachers Program, June 27-July 15, 2005
by Akihiko Takahashi, DePaul University, Chicago IL