# Engaging students: Expressing a rate of change as a percentage

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 Peter Buhler. His topic, from Pre-Algebra: expressing a rate of change as a percentage. How could you as a teacher create an activity or project that involves your topic?

As a teacher, one activity that could be used to engage students would be to use a real world application. This topic is unique, as it can be applied directly to shopping at a store. This activity could include having students bring in a catalog of a sale (either from a grocery store or department store) to the classroom to use. Then students would be encouraged to calculate percent discounts based on markdowns, or they could use a fixed percent discount (ex: 30% off everything) and calculate the new prices of various items from the store.

This activity is not only effective for teaching the topic, but also engages students since this is a topic that everyone deals with on a regular basis. Also, allowing students to bring in catalogs gives the students the freedom to operate within the classroom, as opposed to being given a generic worksheet and asked to solve those problems. An extension of this could be to introduce exponential growth (which is still rate of change and uses percentages) and can be applied to banking, credit, mortgages, and other applications that students may know little about. How can this topic be used in your students’ future courses in mathematics or science?

Although the rate of change and percentages may be introduced at the junior high level, students will continue to use various aspects of these topics even into college level math courses. Derivatives are a huge part of calculus, and it is a known fact that derivatives are simply the rate of change of the original function. On the other hand, percentages can also lead to discussions around probability, chemical compositions within a compound, or even calculating grades for a certain class. All of these deal with using rate of change or percentages in classes outside of pre-algebra.

One application of this could be to introduce derivatives in a class outside of calculus and in a way that students would easily understand. If a student is able to understand the idea behind the rate of change, then they can understand a derivative. Likewise, the teacher can introduce certain applications of percentages outside of mathematics in order to tie in other topics. How can technology be used to effectively engage students with this topic?

As mentioned previously, one method to engage students is through real world applications. Both rate of change and percentages can be found in compound interest. There is a link to a video on YouTube which illustrates how powerful compound interest really can be. The use of graphics and other visuals within the video would allow for student to grasp how large the rate of change is, even after starting with small numbers.

Another useful tool that could be used in the classroom is an online calculator to observe the rate of change. If students have the ability to access the internet, then they could access the URL listed below. The website allows for students to put in different dollar amounts to observe the rate of change in regards to investment. While there is certainly a time to teach students how to calculate this without the website, this could be something that the students use to gain insight into how quickly compound interest can occur. It also gives students the opportunity to observe how different values change the final total and therefore make observations about how compound interest works. The link is: https://www.calculatestuff.com/financial/compound-interest-calculator.

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