I went to an interesting talk by Ed Southall (author of Yes: But Why?) at Mathsconf. He talked about area of triangle problems, which I thought about again as I was teaching it this week.
In his opinion, we often test the wrong skill. That is, we test that students can multiply and half, but not which lengths to multiply and half. He has a nice worksheet where you just identify the height and the width of various triangles.
I was looking for a worksheet on finding the area of triangles, and was reminded of this and struck by how many simply gave two sides. I was also struck by how much of the extension focused on compound shapes (which in my mind is a different skill), rather than on giving students more information that they needed.
In this worksheet I have tried to design a progression. From counting squares all the way up to giving students information overload and expecting them to pick out what to do.
If I were to add more extension I would include the angles. I think it would lead to interesting discussions.
These are lessons to be taken ‘off the shelf’. Each ppt contains an explanation, several different tasks, a problem solving task and a learning check. These require no printing.
Compound measures: Speed, density & pressure.
Area and volume scale factors : I think the questions here are possibly too dull. Maybe when I tweek this I might link it with standard form as a way to deal with large and small numbers.
These are lessons to be taken ‘off the shelf’. Each PowerPoint contains an explanation, several different tasks, a problem solving task and a learning check. These require no printing.
Angles at a point on a straight line and right angles: With these PowerPoints I focused on drawing the shape in GeoGebra so that each angle was accurately represented. When I come to edit them and tweek and update them I will include more focus on estimating the answer first, before calculating.
Angles at a point: Ronseal
Angles in a triangle: When I come to tweek this I will definitely add some algebra in here.
Angles in quadrilaterals: Same. This needs some algebraic content to extend it.