Many of my students can't remember the formula for the area of a triangle. I think it is silly to teach two separate formulas for the area of a rectangle and that of a triangle, because it provides such a great opportunity to engage kids in mathematical reasoning and gets them to pay attention to and use structure (MP7). It also gives kids greater ownership and joy at discovering the formula for themselves. In this lesson students are given a floorplan similar to the ones they have already worked with, but containing a triangular room. The key to this lesson is letting the students struggle productively and help them articulate their thinking within the group.
Instead of our usual warm up today, I want students to work together sharing ideas from their homework. In yesterday's lesson (Floorplan day 1) students got to choose from 3 floorplans (Ironman Flats, The Twins, Pokemon Palace) to calculate the amount of flooring needed for the common living area. Today students join peers that worked on the same floorplan. My intention is for my students to compare the different strategies they used to find the total area and reconcile dissagreements.
I give students a new floorplan that has a triangular room included in the common living space (rockstar). They work together in small groups to calculate the flooring needed.
As I circulate I am listening for signs of struggle. I expect them to make mistakes, dissagree, or be confused by the triangular room. When I see puzzled faces or hear hesitation or dissagreement I ask them questions to get them to clarify what is confusing or troubling. My questioning focuses on helping them define as clearly as possible what doesn't make sense to them and why it does not make sense.
I expect some groups to use the wrong formula for the area of the triangular room and not even notice that they have made a mistake. When I see this I will ask them how they found the area of each section and ask if it makes sense that the same formula will give them the area for both the triangle and the rectangle. It also may help to ask what the relationship is between the rectangle and the triangle.
Each group presents to the class their solution For example, one student shows us how she uses the formula for the area of the rectangle to find the area of the triangular room. I ask them in particular to share some of the difficulties they had and how they overcame them. My hope is that focusing on the confusing part helps them see the relationship between the two area formulas without mixing them up.