Triangles: Lesson One


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’

Activity – Whole Group

1. Ask "What is a triangle?".

2. Using Sketchpad, create a variety of shapes (examples and non-examples of triangles). Begin with open and closed shapes, and shapes with or without straight sides.

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

3.  Then create shapes that have differing orientations and sizes.

Elicit discussion around the definition of a triangle.

Stretch a triangle out so that it’s long and skinny. Some students will say it’s not a triangle. Come back to the three connected sides idea. Continue making the triangle different shapes and size so that the student see a variety.

Triangles examples: differing orientations and sizes

4. Together decide whether or not the shapes are triangles and drag examples and non-examples to separate parts of the screen. Have students create triangles using Sketchpad.

5. Ask "How do you know that it is a triangle? "What's the same/different in our triangles?".

You can also use the Trace feature to show examples of many triangles at the same time.

Or the Animate feature to display families of triangles. Have the students notice that the triangle always has three sides.

Assessment – Individual or Partner

  1. Have the students draw triangles using pencil and paper.
    • Ask for examples of triangles that are very different and very similar.
    • Ask for an example of a shape that is almost a triangle.

Sample Student Work