Engaging students: Solving for unknown parts of rectangles and triangles

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 again comes from my student Brittney McCash. Her topic, from Pre-Algebra: solving for unknown parts of rectangles and triangles.

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A2. How could you as a teacher create an activity or project that involves your topic?

As a teacher, I want to do activities that the students would enjoy as much as possible. In doing so, I came up with a festive idea to incorporate my concept. Gingerbread houses. They are fun to build, while at the same time your thinking mathematically without realizing it. My job would be to bring these concepts forth. My engagement for the activity would probably be video on the shapes it takes to build a gingerbread house. Then I would pass out a blueprint of a gingerbread house that has missing angles or sides and have the students solve for them. This allows them to either set up proportions and see the similarities, or to solve for the sides using the characteristics of the shapes given. After the exploration of the blueprint, would come the construction part. I would have pre-cut pieces of graham crackers or other materials I would use, and have the students pick the pieces that match their blueprint; not every student will have the same. This is where the fun part would come. They would get to construct their gingerbread house, but if they made mistakes during their blueprint, their gingerbread house wouldn’t look right. Shapes wouldn’t fit, or maybe the gingerbread house wouldn’t stand because it didn’t have the right support. As these issues come up, I would be there to guide them in their discovery of “What went wrong.” This leads them to see how important having the corrects measurements truly are and how major they can effect the outcomes of things. Depending on the length of class time you have, this would probably be a two day activity.

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B1. How can this topic be used in your students’ future courses in mathematics or science?

To engage the students with this topic, I would pose a question asking the students, “What would happen if the Eiffel Tower wasn’t congruent on all four sides?” This question alone opens the floor for many different discussions to take place, but my main goal would be to establish what congruent is by definition, and how does that effect shapes and their placement. Through this question we would come to the conclusion that  the tower would either lean, not be sturdy, or maybe not even stand at all if the sides of the Eiffel Tower were not congruent. This shows how important measurements are when building buildings. My next step would be to go over how to solve for sides of triangles or squares if they are congruent. Once this is established, I can pose the question, “Now what if we were not given any angles or measurements? How could we tell if triangles are congruent?” This opens the room up for ideas how this would be done, and I would introduce the Theorems of Side-Angle-Side, Side-Side-Side, Angle-Side-Angle, and Angle-Angle-Side. Without going to extreme detail, I would express how important it is for them to grasp the concepts of solving for unknowns on triangles so that they are able to later, in Geometry, understand and utilize the idea for the theorems.

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E1. How can technology, be used to effectively engage students with this topic?

No matter where you go these days, technology is everywhere, so why not embrace it? There are two ways that technology can be useful in the classroom. One with websites or activities online that shed new light to a topic that is being taught, and also by helping students learn skills on technology that they will need later on. There are not many jobs out there, if any that do not use technology, so helping students get a grasp on it sooner rather than later may help them later on. My engagement for this aspect on my topic would be to do an online activity. Depending on the school, this will either be done in the classroom or a computer lab. I’ll have the students log on and open up this website: Cool Math . This website would be terrific in opening up this subject. I believe this because it doesn’t just jump right in to solving for unknowns. It gives you a quick overview of the relationships certain shapes have, then it gives you an odd geometric figure to find the perimeter of. This figure only has so many measurements given to them, and they have to solve for the rest using the relationships and definitions of the shapes involved. Another really interesting attribute I liked about this website, was that each shape had its own color. When it came time to solve for the big oddly shaped geometric figure, each shape involved was colored differently. This is great because I know how hard it is for some students to distinguish shapes from one another, and this might be a way for them to better visual the shape and its encountering partners to help tell what the relationship may be.

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