Engaging students: Congruence

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Kelsie Teague. Her topic, from Geometry: congruence.

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Many students in high school go to the county or state fair yearly. I would start off by giving students a picture of a ferris wheel and having them find as many triangles in that ferris wheel that have what seem to be the same sides and angles and see how many different answers I get. After defining congruence, I would continue to ask the students if they thought this ferris wheel could be constructed without the idea of congruence. If the shapes in this ferris wheel were different sizes would it still work properly? I would then use this as a basis of what people need the idea of congruence to do their job.


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Congruence shows up in art work all over the place. It can show up in photography with taking picture of identical twins. Those twins are congruent but they are not the same person therefore they are not equal. I would post some pictures of art work and talk about the differences and have the student explain to me what they see. The bottom piece is made using the exact same shape and the idea of congruence. I would show my students some pictures and how the lesson for that day can be related to art work in real life.



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The above website is a great hands on activity. It lets the students move triangles around to see if they can form triangles that aren’t the same. It also uses previous knowledge to guide them into the idea of congruence. Khanacademy.org also has other activities that can help with previous knowledge and then activities that take the concept of congruence and build on it. The activity I did was really good, it let me drop and stretch triangles to try and make them non congruent. It also gives one where you can’t lengthen the side but you can move it around and try to make a triangle out of it. I think this activity could show students about congruence in a different kind of way.

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