When we talk about comparing functions in 8th grade math, we’re really focusing on slope and y-intercept in multiple representations. I’ve found that it can become very confusing and complicated for students if we go too fast or if we skip over key information. Because teaching students to compare functions has so many parts for students to understand, this unit is one that takes more time than most.
Overall, we want students to be able to read graphs, tables, coordinate points, equations, and written descriptions and identify the slope and y-intercept in all those forms by the end of the unit. So, how do we introduce all of this? In this post I’ll break down step-by-step what this unit looks like in my students’ interactive notebooks.
As we work through this unit, we begin with the I Can Statements to set the direction for our learning. Then, we remind ourselves of prior learning with building background activities. Next, we work on each representation of a function in isolation. After the foldable in the notebook we complete practice activities. Then, we go back to the notebook for a different representation. This seems like a good flow to our teaching and learning.
Let me break down each of these steps and show each page students add to their notebooks as they learn to compare functions (for more about the rationale of all 5 components I use in interactive notebooks, check out this post).
Comparing Functions I can statements
If you want a way to help you keep track of progress on learning objectives, then look no further. Adding I can statements into the interactive notebook gives students an opportunity to reflect on their learning on a daily basis. These statements help students know what the objectives are, and you can have them think about and discuss their progress before, during, and/or after the lesson. It’s so helpful to have students include them in their notebook at the beginning of a new unit.
This set of I can statements below focuses on finding slope and y-intercept in the different representations. Then, students have to compare them. The I Can Statements build on each other, so you can see the progression as students work through the topic.
Linear or nonlinear functions
Identifying linear and nonlinear functions is a short and simple 8th grade standard related to the rest of comparing functions. Students have to be able to distinguish between linear and nonlinear functions. They also have to be able to do this in three different representations. Even though this topic doesn’t take a lot of time, I wanted to make sure that my students understand it. That’s why it has its own set of I can statements and notes.
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Building background with slope
Before jumping right in to new learning, it’s important to remind students of relevant things they already know. The background building activity for this topic works as a way to remind students of what slope means. First, they have to finish the sentence, “Slope is…” They can do this as many ways as they can think of. Some examples:
Slope is rise over run.
Slope is change in y divided by change in x.
Slope is positive, negative, zero, or undefined.
Let the students see what they can come up with. You’ll easily see who has a strong or weak background with this topic. They’ll also have a chance to find the slope in four different representations.
Taking notes in the interactive notebook
One of the main things we do in the interactive notebook is take notes. This part gives students a place where they can look for steps or lists of characteristics about the topic.
Also, it’s important to send students right back into this part of the notebook when they forget how to do something. This helps them find the steps or explanation that they need. If students don’t know how to do this, then it’s worth taking a little extra time to teach them how to make the most out of their notebook.
Notes for comparing functions
We don’t take notes specifically for comparing functions. Instead we take notes about finding slope and y-intercept and then in our practice we look for what the question is asking. Sometimes the questions ask for the greatest slope or the one with the lowest y-intercept. Our notes get them prepared to tackle these types of questions.
Identifying y-intercept foldable
In order for students to be able to compare functions they have to identify the y-intercept. Up until this point in the year we have seen a lot of slope, but this is when y-intercept appears for the first time. We have to give students multiple ways of see how y-intercept works and they have to know how to find it on multiple representations. This foldable gives them a basic introduction to this concept.
Slope intercept foldable
In 8th grade math you could use this slope intercept foldable in almost every unit. It’s a simple way for students to keep track of what each part of the slope intercept equation means. So, we keep going back to it through out the year.
This foldable also works great as an anticipatory set. For example, you can have the kids go to it and quiz each other. This is one area where they just can’t get enough practice.
Under each flap you can write key words, general ideas, phrases, and other concepts that define each part of the equation. For example, output equals slope times input plus y-intercept. Another one is the total equals the rate times the number of occurrences plus the starting amount. Reference this when students work on problems and they can see how slope intercept forms relates.
Linear vs. nonlinear functions notes
Like I mentioned before, learning the difference between linear and nonlinear functions doesn’t take a lot of time, but it helps students to set aside a little bit of time to learn it formally. They don’t remember stuff just because we said it a couple of times.
In this notes page students fill-in the blanks of sentences about the characteristics of these types of functions. They also complete a couple of examples and defend their choices. This works perfectly as a partner activity.
Working through math problems
Now, we get to some practice. We use two different practice pages because comparing functions and identifying if the function is linear or nonlinear look different from each other. Ideally, you wouldn’t complete both pages on the same day. Typically speaking, students get the linear vs. nonlinear a lot easier than the comparing functions.
Linear vs. nonlinear practice
I’m just going to admit it, I love sorting activities. One of the reason is because they get students to analyze characteristics. Also, they don’t intimidate most kids, so they will try them without complaining. In this activity students cut out the functions and then they put them into their notebook. They have to decide if they fall into the linear or nonlinear function category.
Comparing functions practice activity
After reviewing their skills, students should be ready to jump right in. With this activity students get to compare two functions. They’re given a situation and then they answer three questions per set to get them thinking about what the functions are showing.
I encourage students to justify their answers throughout this practice. They can do this by annotating their work and write brief explanations. Also, students should be writing in complete sentences. Don’t let them get away with answering with one word or a short phrase.
Cheat sheet for comparing functions
Even though we had a unit about functions a month or two prior to teaching this unit, I still like to give students a cheat sheet about functions. It has a collection of key ideas to remember about functions.
In my advanced class I give them the sheet blank and have them write in their own ideas. Even when it’s pre-printed, students should annotate this cheat sheet to make sure they’re making connections. If they don’t interact with it, then it becomes just another piece of paper.
Let’s go compare some functions
Now it’s your turn to get out there and teach comparing functions. I hope you try something new from this blog post to make your interactive notebooks even more interactive. Your students will appreciate how engaged they are when they are taking notes and they can use the notes when practicing as references. It’s a win-win.
Grab the entire interactive notebook unit for teaching students to compare functions here. Then, head on over to this post for more activities and ideas to get students practicing with comparing functions.
Thanks so much for reading! Until next time!
