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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.

such as

cube

or enter image description here

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

  1. Set of Vertices configure distance constraints that define figure or solid
  2. struts and cables (terminology used in tensegrity) holding vertices apart and keeping close together respectively.
  3. A structure is stable if it respect specific distance constraints. the literature use the concept of super stable.
  4. Not only distances between Edges but also distances between Diagonals have to follow specific constraints to shape a specific structure.
  5. Geometrical versus physical rigidity
    https://math.stackexchange.com/questions/490242/what-is-the-precise-definition-of-a-rigid-shape

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

enter image description here

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.

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    $\begingroup$ Are you intending to actually teach tensegrity? If you're just using it as a construction tool, I think you run the risk that the materials won't complement the lessons very well. $\endgroup$ – Hurkyl Apr 2 '18 at 0:24
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    $\begingroup$ For example, I'm particularly concerned about triangles as a rigid shape -- that evokes to me a lesson about more traditional construction out of sticks and joints that I'm not sure apply as well to a construction based on tensegrity. (but that could simply be my lack of imagination; the experience I had building things like this was brief and rather long ago) $\endgroup$ – Hurkyl Apr 2 '18 at 0:28
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    $\begingroup$ This seems like a solution in search of a problem. $\endgroup$ – Ben Crowell Apr 3 '18 at 3:22
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Maybe just do a general unit on solid geometry--it is a bit undercovered in schools. Just have the last class or two be model building and discussion. With the self standing nature of the models being a little extra fun. Can discuss the mensuration formulas or the like a little, but just have fun too.

I don't think that the theoretical mechancis issues are appropriate for the grade level or easily taught. So just make it more of a fun activity and maybe have a little student discussion where they speculate about how they stand up. Maybe show some pictures of suspension bridges or the like so they can see some connection to real world engineering. But don't teach them statics. At the end of the day, some parts of early education may be more about evoking interest and having fun rather than proving things. Gives the motivation for maybe proving it, learning it later. And even the kids who never learn the math behind the equilibrium structures get the idea that such things can happen. Which is maybe even more important than knowing the details.

I would also skip discussion of point symmetry operations as that is better done in a chemistry class, because of the direct connect to an application. It is also more easily done with rigid models that don't fall apart when you rotate them.

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  • $\begingroup$ Thank you for the input, greatly help $\endgroup$ – gegu Apr 13 '18 at 15:36

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