Engaging students: Introducing proportions

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 former student Michelle Nguyen. Her topic, from Geometry: introducing proportions.

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

Using the video presented in E1, I would create a project that consists of the students making a poster of their own body with the proportion that they found within their body parts. For example, they would use the measurement of their foot and try to find out the amount of feet needed would create their height. Once they figure out all the proportion in their body, they would make a poster representing their finding. Throughout the project, the students will be able to write the proportion that compared the ratio of their feet to other part of their body. The outcome would similar to the pictures in the video that is shown in the engage. By doing this, the students can refer back to the engage to help them finish their project or use the engage to give them an example of what the project should look like. After the project, the students should be able to understand that proportion is the comparison of two ratios.



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B2. How does this topic extend what your students should have learned in previous courses?

In previous courses, students should have covered ratios. Since proportion deals with fractions and ratios, students should be able to learn that proportion is the comparison of two ratios. This topic also extends the idea of comparing two different items to each others. With the ideas of ratios, the students should understand that units are important because they cannot compare two different ratios that are not related to each other. During algebra 1 the students should learn how to solve equations and when dealing with proportions the students may be required to solve for the missing variable in a proportion. With the knowledge of solving equations, the students will be able to cross multiply and solve for the missing variable. In conclusion, ratios, comparison of items, and solving equations should be learned before this topic is introduced. Proportion is the extended idea of ratio comparison.


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E1. How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?


By showing this video in beginning of class, students are able to understand the basic meaning of proportion. This is a good video to engage students because the students are able to test out the real life situation. For example, in this video, the kids found out that the length of their foot is the same as the length of their face. Students can see that there is a proportional relationship with their own body part. With this whole episode of Cyberchase, students are able to see the different proportionality that is present with their own body. As the episode continues, the kids continue to measure different body parts to see how many foot spans would construct another body part. With the use of one type of measurement, the students will see the different proportionality that exists in the human body. During this episode, the kids measure that seven foot span is equal to the arm length and then they also discovered that the height is the same length as the arm length. Students will be able to make their own connection to proportion after seeing all the measurements mentioned in the episode.

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