T-GEM, Illuminations & Angles


Model-based learning is a theory that allows students to learn from building, critiquing and changing our ways of thinking on how the world works (Khan 2007).  One of the big ideas from BC’s grade 6 math curricula is: Properties of objects and shapes can be described, measured, and compared using volume, area, perimeter, and angles. I’ve decided to use a T-GEM model to support student inquiry while using an information visualization technology from a website called Illuminations. In particular, to examine the challenging concept of how the angles of shapes add up when manipulated. Triona and Klahr argued that computer simulations can be as productive a learning tool as hands-on equipment, given the same curriculum and educational setting (As cited in Finkelstein et al., 2005).

T-GEM Model for understanding how angles in shapes work:

Introduction: Students will be introduced to pictures of different environments: downtown of cities, houses, construction, buildings, cars et. What shapes do you see? Patterns? Can you determine the measurement of each angle? The sum of all angles within these shapes?

Generate: Using the following link below, students will choose a polygon and reshape it by dragging the vertices to different locations. The students will see that when the figure changes shape, the angle measures will automatically update. Are there any patterns? What relationships do you see with triangles, quadrilaterals, pentagons, hexagons? Does the sum of all angles change or remain the same when they are manipulated? They will record their observations down.


Evaluate: Find a formula that relates the number of sides (n) to the sum of the interior angle measures. Why are we learning this? Can you think of any real-world examples when you would need to know the different angles within shapes? On the applet, play the animated clip in the lower right corner. Is there a different result for different shapes? Compare your results with a different group. Did you find the same formula?

Modify: Can you now look at shapes and determine the sum of all angles? Are there instances where you are not sure? Do shapes must be a certain size?

Reflection: Students will revisit the simulations again and create their own shapes. They will test their peers by asking them questions such as, “What will happen to sum of all angles when I move vertices upward?” They will reflect on their findings by posting a response to a collaborative tool called Padlet.

Finkelstein, N. D., Adams, W. K., Keller, C. J., Kohl, P. B., Perkins, K. K., Podolefsky, N. S., … & LeMaster, R. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physical Review Special Topics-Physics Education Research1(1), 010103.

Khan, S. (2007). Model‐based inquiries in chemistry. Science Education91(6), 877-905.


  1. Hi Sean,

    First, I must say how excited I was to learn about this illuminations website as a tool to use in the classroom. Providing extensions to some of my students (Grade 5) who are capable to explore different concepts associated with angles is encouraging. I like that you have given the students opportunity to discuss in small groups/pairs as I find this reinforces concepts when students work together. As well, according to Finkelstein et al. (2005) article this week, they mention that “Researchers in education and in physics have described the benefits of “messing about.” I think this is an important element that can be built into your lesson plan as it allows students to take risks and figure out what they are working on together. This was something that I felt you did well in your reflection piece, when students revisit their work and create their own shape.


    Finkelstein, N. D., Adams, W. K., Keller, C. J., Kohl, P. B., Perkins, K. K., Podolefsky, N. S., … & LeMaster, R. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physical Review Special Topics-Physics Education Research, 1(1), 010103.

    1. Hi Christina,
      Thanks for your comment. I also agree with Finkelstein et al. (2005) and that students need to roam free with what they are learning to fully grasp the concept at hand. By allowing the students to create their own shapes, they can hopefully see the bigger picture.

  2. Hi Sean

    I really liked that the activities of the reflection step. The first activity enables students to refine the knowledge acquired from the previous step. Edelson (2001) states that refining knowledge can be supported through the processes of reflection and application. The refining process enables the students to reorganize their knowledge and to link the newly acquired knowledge to existing one. I think that the second activity
    promotes an excellent student-centered learning by allowing students to facilitate the learning by testing new knowledge within peers.


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