G-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
How do you provide opportunities for your students to look for and make use of structure? I’m finding that deliberate practice in looking for and making use of structure is making the practice a habit for my students.
We ask: “what you can you make visible that isn’t yet pictured?”
We practice: “contemplate before you calculate”.
We practice: “look before you leap”.
We make mistakes; the first auxiliary line we draw isn’t always helpful.
We learn from each other.
Months ago, our goal was to prove the Triangle Sum Theorem.
We thought first about what we already knew … what we had already added to our deductive system.
Then we practiced “I can look for and make use of structure”.
And so the journey to make the Math Practices our habitual practice in learning mathematics continues …