The constant of proportionality is a core topic for 7th grade math in my state. Trying to get students to pronounce it, let alone to understand it, can be a challenge. In this post, I have a few tips that help my students that I would like to share with you.
Tip #1 Hook the concept of constant of proportionality to previous knowledge.
I relate the constant of proportionality to what they learned in the previous grade. In sixth grade, in my state, students learn all about unit rates and unit prices. So, as I do in any unit, I start by reminding them what they did last year concerning ratios, rates, unit rates and unit prices. This gives me something to build on and it provides them with a level of success right at the beginning of the unit because it is something they have practiced before.
Tip #2 Break it down into bite-sized chunks.
Constant of proportionality is a huge concept with lots of pieces. It is also a foundational concept for many years of math to come. Take it slooooow and break it down into bite-sized chunks.
I start with how to identify proportional relationships from a table. Once students can tell me if a table is a proportional relationship or not then we move on to actually identifying that constant of proportionality from the table.
Click on the video below to see me teach a lesson on constant of proportionality. I include this video in my Google Classroom™ for students who are absent or on independent study. I also attach it to assignments so that students can review the concept if needed.
When they are feeling comfortable with a table, then we move to a graph. We discuss how the table is related to the graph. You can also use a discovery process with this by giving them different graphs and having them sort them based on what they learned about tables. They can explain how they sorted them and why. Eventually, we talk about the two rules. The graph must be linear and it must go through the origin in order for it to be a proportional relationship.
Next, we move on to writing equations from the tables and graphs. This is usually a small step for students. I give them the basic format for the equation y=__x. They catch on pretty quick but it is imperative at this stage that you have a conversation about variables. They need to understand that y=kx, y=rx, y=mx, or d=rt might all be used interchangeably so they shouldn’t get too hung up on the letters. Rather it is the “form” of the equation that they should focus on.
Tip #3 Give them a story to go with the problems.
Throughout this process, I am weaving in verbal descriptions or “stories” as I call them to the students.
Students love the problems with a “story” the best because it helps them to visualize the problem and what the data from the table and the graph actually mean. I find these are also the most helpful for my English Learners and my students receiving special services. It makes the math more real to them.
Tip #4 Show them where they are going.
Now some teachers might stop here with proportional relationships but I always like to dip our toes in the world of non-proportional relationships because it gives the students something with which to compare. We spend a day or two talking about how the tables, graphs, and equations are different with proportional and nonproportional relationships and where that constant of proportionality fits in. We talk about the vocabulary such as constant of proportionality versus rate of change.
I motivate them through this section by telling them they have been doing so great with the seventh grade proportional relationships that I am going to challenge them with the “eighth grade work.” They eat it up.
Tip #5 Make it fun.
Anytime you can make it fun, your students are more likely to remember it. Give them the opportunity to talk about what they are learning with their peers in a structured way. Sometimes they learn better from their friend than from the “authority figure” in the room.
Play games. Use station rotations or write the room activities. Get them up out of their seats and have them move around the room. Get their entire bodies involved in the learning. Your kinesthetic learners will appreciate it.
Those are my five best tips for teaching constant of proportionality. Please leave a comment below and tell me how you teach students about constant of proportionality. I would love to read your thoughts.
Plus, if you are interested, check out these resources in my TPT store that I use in my classroom to teach Constant of Proportionality.
And as always, thank you for being a teacher.