The cornerstone of 8th grade math is learning about slope and y-intercept. Basically, it’s all things functions for the majority of 8th grade. What I realized a few years ago is that comparing functions is a multi-faceted beast. It seems simple at first, just find the slope on both functions and compare. Then, I realized that students have to be able to find slope in at least 4 different ways. As a part of that they have to recognize if it is positive or negative. Then, you introduce y-intercept in its many representations and they have to understand that they aren’t related to each other. So, in this post I’ve compiled ten activities that help students get lots of practice comparing functions in several different ways.
The fact that this skill builds a foundation for so many things in 8th grade math and beyond makes me glad that there are multiple standards to practice it. Comparing functions is somewhere near the beginning of our journey with slope and y-intercept. What I’ve found to be absolutely crucial for students learning this topic is repetition. There are so many micro-skills and the kids just need to see a lot of situations and go through the thinking process as many times as possible.
The list of 10 comparing functions activities:
Let’s dive in
There are many ways to practice comparing functions. These 10 ideas and resources can be used as classroom practice, anticipatory sets, homework, or cyclical review. So, let’s look at each of these activities and how they can help in your classroom.
With these comparing functions task cards students identify the slope and y-intercept of two functions and then compare different characteristics. They fill-in a chart as part of getting the right answer. I find that sometimes students don’t like to write down all of the things that they should write down (is that in my class? I didn’t think so!). When they don’t write everything down, especially when they’re first learning about functions, they tend to make mistakes. I like that these task cards force them to write more down.
Also, in this set of 16 task cards, students do a lot of explaining of their reasoning using complete sentences. My kids like to rush through task cards sometimes, but this particular set gets them to slow down. In addition, if they work on these task cards with partners, they get to do a lot of math talk. These cards are great to use to play the SCOOT game or have students work in partner to complete them.
The Slope Slider works as a visual and quick discovery activity. It’s an online manipulative where students can see the relationship between changing the slope and y-intercept in an equation and how that looks on a graph. I use this as an anticipatory set. First, I challenge the kids to play around with the slope and y-intercept and try to see a pattern. Then, I have them discuss their ideas with others. I find that it helps to do this a couple of times over the course of a week. They don’t seem to just remember it from seeing it one time. They love to do activities like this. Plus, it’s an activity that requires no additional prep as a teacher.
First Example: Students enter an equation for a line with a given slope and y-intercept.
Second Example: Students adjust just the y-intercept of the same equation and note the change.
Third Example: Next, students keep the same y-intercept and change the slope. Again, they note how the line on the graph has change.
Through manipulating and looking at graphs of different lines, students should get a more clear understanding of what the y-intercept really represents, and what the slope looks like on a graph.
If you haven’t played Kahoot with your students before, it’s a fun way to practice skills in a game-based way. Playing Kahoot is a whole class activity that is played through the computer. To play all you need is a projector and an internet connected device for each student. Once everyone joins the game, each student answers each question, gaining points as they go.
This game is a great way to review comparing functions. It can also be a great check for understanding. After playing you can download a report through Google Drive and you can see how each student did. The questions in this particular game will help students practice comparing functions with different representations.
This Compare the Slope Knockout Game is a fun way to review as a whole class. It focuses solely on comparing slope. It’s a fun game to use towards beginning of the slope unit. Also, it works well as a review in a math lab or special education class for struggling students. There are 16 questions which give students the opportunity to see slope in tables, equations, stories, and equations. They have to read questions and identify what the question is asking. Then, they have to compare the slopes.
Knockout games are played through PowerPoint. Students choose a a character on the board and it reveals a question. All students answer the question on their whiteboard and show the teacher. The questions are assigned a point value. If you get it correct, you get the points and keep track of them on your board. Some of the characters actually reveal or good or bad bonus, and that’s the part the kids really love. They think it’s hilarious when they lose all of their points! I hope you’ll give it a try.
This graphic organizer is one of my favorites. We used it this week in my class. For so many kids, they really started to see the connection between the different representations of slope and y-intercept by completing this graphic organizer several times. And by several times, I mean we completed it a few times each day for three weeks. Each time they completed it, students got to see a lot of representations in a short amount of time. Plus, it took very little prep on my part. Using this graphic organizer, the students make the connections between all of the representations of slope and y-intercept and can see them all in the same place.
How to use this graphic organizer:
- Students place the graphic organizer in a plastic dry-erase sleeve, page protector, or you can just do it on paper.
- The teacher draws a line on the graph portion and displays it for the students.
- The students copy the line on the graph.
- They then identify the slope and y-intercept, write the equation, the unit rate, and finally they make the table that matches this information.
- Students share their work with the teacher and the teacher gives them feedback.
- After a few tries, you can start by just giving students the equation or the table and let them go.
We completed this graphic organizer a lot during our time working with functions and comparing functions. The kids seemed to really like it and it helped them to see it in a different way. One of my more vocal students even told me that she loved this and thought it was the “perfect activity” (her words) because it helped her really get it. I’m not going to lie, it feels pretty great when students are enjoying math practice and having those light bulb moments.
You can download this graphic organizer here.
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This comparing functions matching game uses a hands-on approach. Students are given three graphs, three equations, and three tables. They have to find the matches between the nine functions. Then, they line them up on a work mat and check their answers. One thing that I really like about this activity is that it increases in complexity. There’s a total of 5 different matching mats, perfect for differentiation and cyclical review. This activity is a fun break from pencil and paper practice. Sometimes students just need something that’s more hands-on.
So, my kids have a tendency to not really see how the tables relate to the rest of the slope representations. Like I shared earlier, I’ve learned how important it is that students get lots of repetitions. This worksheet gives students more practice. It gives kids a little different view of what is happening between the equations and the tables. This is just a good old-fashioned worksheet that is great as a bellringer or a practice activity after giving notes.
This comparing functions task cards game can be used many different ways. There are 32 cards included that each show a representation of a function. For each function, students can identify the slope and y-intercept. Also included are game cards. The game cards give students challenges like, “Draw 3 cards and identify the one with the greatest slope”. Another one might say, “Draw 5 cards and separate them into negative and positive slope.” Once your students are somewhat proficient with functions, this can be a great reinforcement of their understanding. It would also make a great math station or practice activity.
Also, you could use these task cards with the whole class as a sponge activity. You could keep these handy throughout the year and use them as cyclical review. They also work well as a scoot game or a partner activity. Like I said before, you really can’t practice this skill enough. You definitely want to make sure that students are seeing it after the unit is over.
This activity comes from a blog post from Mathiness is Happiness. It’s a great idea that you could easily make yourself. This activity gets students practicing with the different representation of a function, and it looks like fun. I like how she put each group’s cards on a different color, so the cards don’t get mixed up. That’s ingenious. Matching activities work well for students because they have to look at things differently. This one looks a little complicated, so you might want to use it with fast finishers. Another thing you can do is to model your thinking process in finding some matching pairs.
I remember the other day when we completed this y-intercept coloring activity how excited the kids were at how easy it was. That might sound weird, but sometimes they need something easy to complete. Also, it reinforces that not everything in math has to be so strenuous. The concept of finding the y-intercept should seem easy to them and this practice activity let’s them have a little fun while they practice. Plus, it’s a good way to isolate practice with just the y-intercept of a function, which is really important with students who need more support in math.
This resource includes 2 different coloring pages. Each page has 8 questions and shows y-intercept in tables, graphs, and equations. For each page there’s a picture to color according to the answers that you get on the questions. This coloring activity gives students a nice little brain break.
Try one thing
Choose an activity or maybe two to add to your tool belt. When you increase the engagement in your classroom, you reap the benefits when you see students remember the concept better. Maybe you need an activity to get the whole class awake or something that gives students a chance to work with a partner. All ten of these break things up and get students high quality repetitions with comparing functions. Try one and let us know how it goes.
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