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Proportionally Speaking - Comparing Proportional Relationships


Summer time was always the time where I tried to explore new activities for the upcoming year - not only to add excitement for my students, but to change up what I did every year to add excitement and change for ME! Let’s face it. It’s easy to get into the habit of doing the same thing every year, especially when you are teaching the same curriculum, same grade-level, etc.  That is the easy way out - i.e. recycle and reuse. My personal opinion is this leads to burnout and boredom. So, why not change things up…even if it’s just changing out a few activities…it makes the next year feel new. Here’s the challenge - same math content - but what can you do DIFFERENTLY?


I know we teachers are always looking for great ideas and resources, and I know I am not alone in my love of Illustrative Math. There are many providers of this amazing math curriculum, which many of you may already be using. I tend to go to the source itself, where I can get free lessons to align to the grade-level and content I am teaching. Casio has been creating some middle-school resources to align to some of the Illustrative Math lessons in v.360, so I am going to focus on a lesson from Grade 8, Unit 3: Lesson 4 - Comparing Proportional Relationships. Illustrative Math provides you with a Student Lesson and Teaching Guide and resources. (In the video below, I show you how to access those from the IM site).  


I chose this activity because proportional reasoning is a concept many students struggle with, and providing them with opportunities to compare representations is so important to help them make connections and understand and apply that idea of rate of change. The IM activity has students working with equations, tables, and then graphing, so they are comparing several representations and making connections to the real-world meaning of the rate of change in the context of the problems. The problems they work with, as you will see, are earning money over time for mowing lawn, and then a recipe for lemonade for a lemonade stand, so both situations students can relate to and apply their understanding of proportions.


As students are working, they can obviously use different tools - i.e. paper-pencil, graphing calculators, graph paper, etc. Casio has created a companion resource for this activity, which I have included below, that using the fx-991CW scientific calculator and its QR code capability to show the graph of the situation, making it a powerful tool students could use for this problem. In the video below, I show you how to access the IM activity and then walk through the Casio companion resource using the fx-991CW emulator in ClassPad.net, to model how to enter the information and show the equation, table, and graph so students can compare the proportional relationships and make connections.


This is a great activity to incorporate into your own classroom for this upcoming school year! Here's a video that models the activity with the fx-991CW.


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