We started our unit on Geometric Measure & Dimension with a Mathematics Assessment Project formative assessment lesson on Evaluating Statements about Length and Area.
I chose the card that each group would explore ahead of time. I only gave each group one card, and I had another task ready for them if they finished early. They didn’t. Students chose whether they wanted to explore on paper or using technology.
Each card had a hint, which I held until I felt like the group might need it. While students were working, I monitored their progress.
The second group had Sliding Triangles.
If you slide the top corner of a triangle from left to right, its area stays the same.
If you slide the top corner of a triangle from left to right, its perimeter changes.
They read through their card and drew a few diagrams, but they decided to spend most of their time building the scenario using our dynamic geometry software. This group did not need the hint card.
When it was time for this group to present their work, we sent the Quick Polls so that we would know what students instinctually thought, even though they had not all had time to explore the statements in depth. I am learning to make use of the TI-Nspire Navigator allowing me to send more than one Quick Poll at a time.
I showed the results, but I deselected Show Correct Answer before doing so. I wanted the group to know what their peers thought before they just told them the results.
I used the Live Presenter feature of Navigator to make one of the student’s calculators live on the projector at the front of the room. They grabbed and moved the point that changed the top vertex of the triangle, noting with the square they had constructed off the base that the height of the triangle remained constant.
The area of the triangle will always be the same.
What about the perimeter? The perimeter changes.
Does the perimeter always change? Sometimes the perimeter is the same.
When is the perimeter the same? When one triangle is a reflection of the other about the perpendicular bisector of the base.
And so the journey continues …