In grade 10 we are working on verifying and proving different scenarios using analytic geometry skills.  We need to first understand what the question is asking.  As we read through, we need to interact with the question.  The question words will make us think of related things, and prior knowledge.  Here’s an example of all the added things we can include for the following question. In English the question asks to verify algebraically that if the midpoints of adjacent sides of a quadrilateral are joined a parallelogram is created.

We set out to draw quadrilaterals, and join up the midpoints, and then use our math skills to prove that the new shape is a parallelogram. We are working well with graphical models, and are practicing a lot of our calculations. Desmos geometry was very helpful for a conceptual visual proof.  We can construct a model on the screen, and drag points around and watch that the middle shape remains a parallelogram. Our second proof involved joining midpoints of 2 sides of a triangle, and comparing the segment created with the 3rd triangle side.  The segment is parallel and also half the length.