I am exploring ideas to design a secondary-level-project-based-10-lessons-unit-learning-plan which can end with a creation from the students involving a tensegrity structure.
My general questions are related to designing lessons:
- Question 1: what could be essential pre-lesson that leads to such creation?
- Question 2: what learning can be derived in each lesson? (... that is generally aligned with secondary math knowledge and skills)
- Question 3: Challenging: How could you involve in a "simplified manner" (secondary level) the use of modular arithmetics, and other element of abstract algebra such rotations, permutation, groups...
- Question 4: what general problem can be be asked that can lead to such creation? essential questions?
So far : From readings, students will have to understand the concept of
- Set of Vertices configure distance constraints that define figure or solid
- struts and cables (terminology used in tensegrity) holding vertices apart and keeping close together respectively.
- A structure is stable if it respect specific distance constraints. the literature use the concept of super stable.
- Not only distances between Edges but also distances between Diagonals have to follow specific constraints to shape a specific structure.
- Geometrical versus physical rigidity
So far my responses to those questions:
- 1st group of lessons: triangle, its property, and its physical rigidity
- 2nd group of Lessons: properties of diagonals in quadrilaterals and its physical rigidity
Students will understand (1) the importance of respecting the diagonals distances constraint to shape 2 dimensional figures by building simple figures (using for of popsicle sticks and fishing lines) using the least amount of struts (2) We can permute struts and cable for the edge and diagonals
I believe this lesson can be fruitful as students have little sense of seeing the need of understanding the properties associated to diagonal of quadrilaterals
- 3rd group of lessons: geometrical rigidity of polygon and transformation (1)enlargement (2) Rotation (3) reflexion (4) translation
Basically here I would use the idea of Abbas Jeffary "Start with an equilateral triangle. Label the vertices one, two, three. Define a rotation to be 60° counterclockwise, for example (or you could go clockwise). Note that the locations of the vertices have shifted. Consider this a new “state“ or “configuration”. Now, what “configuration” does one end up with after n rotations? Then, extend this to any n-sided polygon."
- Last lesson: the project build the highest tower using water pipes and metal strings which can support a weight at the top.
That's an initial brainstorm that I want to refine. Any suggestion regarding this project? What specific other pre-lesson could be taught? I find this final project a bit hazardous as to see what exactly could be assessed in term of school mathematical knowledge.