Triangles: Lesson Two


Big Idea – We can describe, measure, and compare spatial relationships.

  • to build on students' knowledge of triangle and to develop students' reasoning with properties of triangle
  • to develop students' language related to attributes of triangles (e.g., from 'it looks like a triangle' to 'it has three straight sides')

Overarching Aims:  

1.    To expand students mathematical understanding of non-prototypical triangles as children frequently develop very restricted conceptions of geometric shapes. They often identify them solely based on their resemblance to prototypes:

        e.g., a shape will be called a triangle if it looks like an equilateral triangle with a horizontal base – all others are considered ‘wrong’.

2.    To develop an understanding of the composition of 2D shapes – that we can triangulate any polygon:
        e.g., putting two triangles together to make a square

Activity – Whole Group

1.    Triangle review - have the students close their eyes.  Ask them to imagine a triangle, then imagine:

make it bigger
make it really small
let it grow a little
if it had a colour, change the colour
make it striped
turn it – roll it on the ground
imagine you have a pair of scissors, now cut off the top corner – what shapes do you have now?

then open their eyes and describe what they saw.

2. Have the students imagine they have to tell someone on the phone how to draw a triangle.   Ask "How would you do it?" Follow the children’s descriptions. They will usually say something about making three lines, so you can do that (on board or Sketchpad) and then encourage them to say how the three lines have to connect. You can even draw three curved lines to motivate the idea that the sides have to be straight.

Triangle examples: open and closed shapes; with or without straight sides

5. Move to Sketches 1 through 7 where the students will have several challenges to complete.  They are to use the given triangles to complete the shapes. 

6. Whole group discussion about the strategies for filling in the shapes. Look at different ways of doing it.

Assessment – Individual or Partner

  1. Have the students draw a design made of just triangles 
    - Encourage the use of a variety of triangles sizes and orientations.