There are two sets of algebraic identities usually taught at the school level - (i) the quadratic ones and (ii) the cubic ones. Both can be modeled in a low-cost way. Nets of solids can be used for the cubic identities. Layouts of both are included along with links to uses.
In many programs of study, the material on the formulas relating the sides and special segments in a triangle does not appear as part of the study of mathematics in high school. On the other hand, in many programs of study the background required to understand this subject is studied already by the ages of 13-15. This situation gives us the opportunity to teach the relationship formulas at an early stage, even before the studies of geometry have begun in the precise manner at the higher level of difficulty.
Are certain individuals born to be teachers and can only those be truly competent? Or can people without such aspirations develop to become ‘great teachers’? Are there certain conditions, the presence of which foster such development?