Having taught grades 4, 5 and 6 for the last six years, I have found that area and perimeter are concepts that we revisit each year. Year after year, the students’ understanding of the topic varies widely. Some have an excellent grasp of the concepts and are ready for a challenge. Others really struggle with the topic and have trouble grasping what area is and how we calculate it. I find it difficult to have challenging and engaging activities ready for each of the students in my class that represent such a wide ability range. I have several sets of resources and different manipulatives that I try to reach each student with, but until today I wasn’t sure of a way to include technology into teaching this topic. (A BIG thank you to those who have already posted on T-GEM, as I previously hadn’t been aware of PhET – what a valuable, and free!, resource!) I’ve sought to combine the PhET area builder simulation with T-GEM to create a new way of teaching area and perimeter to intermediate students.
Generate:
Allow students to explore the area builder simulation on PhET under the explore section. Initially, have them create one shape, noticing the change in area and perimeter as they go along. Encourage the students to think about and try different shapes, for example, a line of 4 as opposed to a square of four. What do they notice?
Suggested teacher questions:
- Can you recognize any patterns when you add a square onto your shape?
- With the same number of squares, will the area always remain the same? Why or why not?
- With the same number of squares, will the perimeter always be the same? Why or why not?
As students to generate a hypothesis – will the answers to these questions always be the same?
Evaluate:
Instruct students to try the side by side shapes on the PhET area builder. Ask them to test their hypothesis. The visual aid and ability to construct multiple shapes quickly should help them to deepen their understanding of area and perimeter. At this point students could work together, one using each side of the screen to see what they notice about the effect that increasing size or creating different shapes has on area and perimeter. Do they need to modify their original thoughts?
Modify:
Ask students to use the game feature of the PhET area builder simulation. One aspect I really like about this is the true levels of differentiation that can occur. For example, level one of the game is very basic. Level six, on the other hand, becomes quite complex and asks them to draw upon more of their mathematical skills. (See examples below). I am confident that this simulation could help to strengthen and modify each of my students’ understanding of area and perimeter.
In her work on T-GEM and teaching with computer simulations, Samia Khan (2011) argues that, as educators, we need to provide opportunities for students to compare data. Further, Khan states that computer simulations visually draw attention to patterns and assess scope of relationships. I think that the PhET area builder simulation, used in the way that I have demonstrated, touches on all of these concepts. Additionally, this simulation can adapt to the students own ‘mental models’ in a way that I cannot (Khan, 2007). I can’t wait to try this out in my classroom now!
References
Khan, S. (2007). Model-based inquires in chemistry. Wiley InterScience, 91, 877-905.
Khan, S. (2011). New pedagogies on teaching science with computer simulations. Journal of Science Education and Technology, 20(3), 215-232.
Hi Kathryn,
I love this idea! I am teaching grade 7 this year and my students still struggle with both area and perimeter. They understand the basic shapes, but when we move into more complete (multi-shape), things fall apart a bit. Based on this, I realize that they do not fully understand these concepts. Does Phet include more complex shapes? I haven’t explored this program with regards to area and perimeter yet. I’ve added it to my list!
Nicole
Hi Nicole,
I realized after posting that I kept the shapes quite simple in the examples. You can create more complex shapes, but a limitation of this is that they are all straight edges with right angles and I haven’t yet found a simulation that allows you to find the area and perimeter of, for example, a trapezium. Also, this week we took on area and circumference of circles and it was all done with pencil, paper and compasses. I think it would have been so beneficial for the students to be able to manipulate and change the data in a simulation. Please let me know if you find anything!
Thank you!
Kathryn
Hello Kathryn,
Today during my Grade 5 math block, a group of students came to me to tell me their frustrations with Area and Perimeter and how in class they are having a difficult time understanding the difference between the two and how to solve for each. They are unable to understand the differences event though we use hands on manipulatives and have gone through the basic steps. How did using this interactive approach work for your students? Thanks!
Hi Amanda,
I have to admit, I haven’t tried this yet! I wish I had known about the PhET simulations earlier in the year! I’m going to give it a try in the next couple weeks so I’ll update you then!
Thank you for your interest,
Kathryn
Hey Kathryn,
I can totally connect with this struggle. The past few years I’ve tried a few different strategies, particularly to do with perimeter. I’ve tried “Peter the Perimeter Worm” that counts as he crawls and a few other strategies. I’ve never used anything from PhET before, but this really looks like a great resource. I am definitely writing it down to use next year. I especially like how you are able to finish with a game. Takes the modify step to the next level as it partners with all the engagement benefits of gamification.
Hi Caleb,
The students in my class always love a game! Hope this resource works for you. I really like your idea of Peter the Perimeter Worm.
Thanks!
Kathryn
Hi Kathryn
I like the fact that you shared a wonderful lesson. I also, concur with you that there have been a lot of wonderful T-GEM ideas.
I wonder if students are motivated by the game function. Do they wish to beat their classmates?
Christopher
Hi Christopher,
I definitely think that some students are motivated by games! Many are very competitive and I hope that this simulation would allow them to learn at that same time as competing against a friend!
Thanks
Kathryn
Hi Kathryn,
Thank you for your post. I will definitely be passing this simulation on to our Intermediate Math teachers or incorporating during a Technology class with them in the future!
Hi Jan,
I hope your intermediate math teachers find this simulation helpful!
Thanks
Kathryn