# Pyramid SA #MFM2P #3ActMath

Not the most exciting problem, but my students were still engaged even if it wasn’t a contextualised scenario. Act 1: What do you notice (facts)? What do you wonder (Qs)? – The shape is a pyramid that has a square base. – The area of the triangle is 1 cm square. – What is the area of the base? – What is the volume of the shape? – What is the surface area of the shape? – What is the height of the shape? It is a triangle What is the lenght and height of the triangle It’s a square based pyramid how many sticky notes do we need to cover the square based pyramid It’s a Square pyramid It’s a triangle and it has 1cm squared What are the lengths and widths of the pyramid Its a shape. what is 10m2? pyramid Square based pyramid, with a sticky note that reads “I cm squared) Why is there a sticky note on one of the sides? That it is a square base pyramid What are the other lengths There is a square based pyramid What does the 1cm^2 represent? There is a triangle What is the value of this pyramid what’s the area of the square based pyramid

Estimate: Act 2:

Each group of students was given a plastic pyramid like the one in the picture. They began measuring dimensions of the pyramid and using the formula from their formula sheets in their binder. They solved the problem on their boards:

I asked the group why they thought we got different answers in different groups and they commented that some of our plastic pyramids were slightly smaller than others. I did a little direct teaching about the net of a square based pyramid and how that translates into the formula on their formula sheet: Act 3:

I then handed out grid paper and asked the students to draw a 1 cm by 1 cm square at the top left of the page. They told me that the area was 1 cm^2 and determined that every 4 squares of our grid paper made a 1 cm^2 area.

I asked them to trace all of the faces of their pyramid onto the grid paper to create a net. Then to colour in alternative 4-square blocks to allow us to count the area in cm^2.  We counted up the area and found the answer to be 114 cm^2; right on with our calculations! Students were assigned a “surface area” practice set of questions on Khan Academy; different ones depending on whether or not they had completed the previous set I assigned earlier in the semester.

The materials for this activity are available here.

– Laura Wheeler (Teacher @ Ridgemont High School, OCDSB; Ottawa, ON)