I recently participated in the Mississippi Department of Education Geometry Institute. In our session on Geometric Measure & Dimension, we moved from areas of special quadrilaterals in the coordinate plane to proving the area formulas for a kite and a rhombus.

We had practiced look for and make use of structure on two kites, c and f. Participants had shared their thinking on kite c.

Could they transfer what they had done in the coordinate plane with known segments lengths to a rhombus and a kite with diagonals d_{1} and d_{2}?

Just like our students would, some teachers struggled with the idea of generalizing the formula. Several used rulers to measure the lengths of the diagonals or made up numerical lengths for the diagonals and calculated the area.

Can you tell how these participants generalized their work?

I gave the kite as an assessment item for my students last year, and I asked them to practice “I can look for and make use of structure” along with “I can show my work”.

Whose work can you understand without asking for clarification?

What opportunities do you give your students to practice “I can look for and make use of structure” along with “I can show my work”?

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The Area of a Rhombus and a Kite”