Perimeter, Area & T-GEM

Determining the area of irregular and unusual shapes is one of the more challenging geometry based topics that elementary students encounter. For this information visualization lesson, I have decided to design a lesson around the T-GEM model, and the students will have the opportunity to work with applets from Illuminations and PhET to further explore these mathematical concepts. Simulations, such as these applets, help support students and provide the necessary level of novelty and interest that significantly impacts student approach to learning and processing (Srinivasan et al., 2006). This lesson allows students to build their own 2-D shapes, both regular and irregular, as well as unusual shapes that defy categorization. Working with these applets will help ensure that the students achieve visible results that they can observe and make/modify conclusions upon. According to Finkelstein et al. (2005) although these types of simulations do not necessarily promote conceptual learning, they are useful tools for enhancing student learning when properly designed and implemented.

  1. Generate
  • students will explore the following PhET simulation on Area using Area Builder –
  • students will examine the relationships between area and perimeter for a variety of regular and irregular shapes
  • What strategies can we use to find the area of a shape? How do these strategies differ for regular and irregular shapes?
  • Through observing perimeter and area within the simulation, can you create a rule that describes how perimeter and area change when the scale of a shape changes?


  1. Evaluate
  • based on their observations and findings using Area Builder, students will evaluate their work and identify further questions that they have, and areas that they would like to explore
  • students will collaborate with a peer and exchange findings from their work with Area Builder


  1. Modify
  • students will collaborate in small groups to discuss their findings and observations and share how their initial ideas and predictions have been changed through their interactions with the simulation
  • student groupings will create a list of ideas and strategies that they believe will help determine the area of regular, irregular, and unusual shapes


  1. Further Application
  • students will further apply their understanding of the concepts by using the Area Tool applet on the NCTM Illuminations website –
  • students will attempt to utilize their strategies to determine the relationship between the perimeter and area of trapezoids, parallelograms, and various triangles


  1. Reflecting and Sharing
  • students will reflect on their findings using Area Tool and compare the processes and strategies that they utilized to determine the area of trapezoids, parallelograms, and various triangles
  • Were the findings consistent with the strategies applied previously, or did this require a reevaluation of these ideas?
  • student groups will decide how they would like to compile their observations and understandings to be shared with the whole class – Can these findings be compiled within a table or chart for sharing purposes?



Finkelstein, N.D., Perkins, K.K., Adams, W., Kohl, P., & Podolefsky, N. (2005). When learning about the real world is better done virtually: A study of substituting computer simulations for laboratory equipment. Physics Education Research,1(1), 1-8.

Srinivasan, S., Perez, L. C., Palmer, R., Brooks, D., Wilson, K., & Fowler, D. (2006). Reality versus simulation. Journal of Science Education and Technology. 15(2), 137-141.



  1. Allen,

    The application and simulations you chose to use in this example are great! I have a son who is about to enter kindergarten and I often find I am compiling a list of resources I can use with him that others are using!

    The evaluate portion of T-GEM is so important to deep learning (in my opinion) and I understand this is a discussion activity so we wouldn’t include all of the details but I was curious what this looks like in an elementary classroom? This is again, more from a selfish point of view on my part as I am somewhat ignorant to what an elementary classroom looks like nowadays.

    Great project and thanks for sharing!

  2. Hi Allen!

    I am so glad that you posted this T-GEM as I agree finding the area and perimeter of composite figures can be very difficult for students, let alone the area and perimeter of simple shapes. What I liked about your post was the during the generate phase you allow students to spend time exploring and ultimately attempting to find the path that works best for the student to solve the answer with. One flaw in my implementation of this concept has been to show the students two different methods in solving these types of questions, however, your introduction with simulations allows students to find more than one possible solution. This is exciting because it allows creativity and innovation in their thinking to be shared, especially during the modify and reflection phase.I also like that you include data representation in the reflection phase, as another means of showing what the student knows.

    Thanks for the ideas!


  3. Hi Baljeet and Cristina,

    Thanks for your feedback. The simulations give students the flexibility to work with their ideas and independently experiment as they work towards a range of different solutions. During the final stage, the students would have the opportunity to decide how they would like to share and present their findings. Each of the groups would meet to discuss possibilities and then select a tool or method to share their findings with the larger group. One option that they might choose to use would be Padlet, as this allows for an effective means of compiling thoughts and ideas in order to share with the whole class and help to generate further discussion. Another possibility might be to create a reflection video that could then be shared with the larger group, as this would also create opportunities to offer feedback while considering different perspectives through discussion.

    – Allen.

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