How to Model and Think Through Analyzing Function Graphs
To introduce students to analyzing function graphs, I start off with a model & think through activity. This activity lines up with Common Core math standard 8.F.B.5 to use functions to model relationships between quantities. This modelling activity consists of a presentation and the student follow along guide. As students follow along, they have to identify where the graph starts, what happens in the middle and where it ends. When they look at how it starts, they’re focusing on what exactly is being measured. They continue to answer all those same questions throughout the activity.
In this post I’ll show you step by step how to show students exactly what they need to do when analyzing function graphs, and how to make it stick in their minds forever!
Starting off with function graph examples
We work through 5 different stories or examples to get started. The story is presented first. Students have to answer three questions to look specifically at three parts of the graph. The questions they answer are:
- Where does it start? At zero or above zero?
- What is its change over time?
- Where does it end?
After students have written down the answers to all of those questions, then they are presented with two graphs. They have to decide which graph matches the story. This really gives them great opportunities to talk through what’s happening in these types of graphs.
While we complete this activity together, I do a couple of different things to help students think through this idea with me. I want to make sure that they’re doing the thinking they need to. For example, I have them draw the graph in the air with their finger while they listen to the story. This gives them a chance to think it through and picture it in their mind. Then, as we get more into it, I start to have them draw it on their whiteboard so that I can see if they’re getting it.
Also, I realize the control during the activity needs to be released from me to them. I do a lot of talking for the first couple of examples. Then, we shift to them talking more. They talk with a partner after they have written their answers. At the end of each example I have a couple of people share their ideas.
Ready to take notes
After analyzing stories and their graphs together, students are ready to take some notes. They’ve already looked at 5 examples and have practiced identifying the beginning, middle, and end of these types of stories. So, the notes pick up where our think-through examples left off:
Chunking out the math practice for student success
Now students are ready to do more of the practice. I want to make sure, though, that I still release the responsibility to them in a gradual way where they can be successful with one part, and then add to that with the next step. So, I love to use “I Can” statements to guide our learning. In fact, this is the first thing that we put into our notebooks (when we’re getting ready to add the foldable above). Then, we practice and reflect on each of them:
You can get this “I Can” statement, as well as I Can statements for 20+ math concepts for 8th grade math (plus blank templates) here:
Send me the FREE 8th Grade “I Can” Statements for interactive notebooks.
Here’s the explanation of what each of the “I Can” statements means when I’m teaching them. Most of them can be seen on a task card with problems that I want students to be able to solve independently after we have taken notes.
I can identify what the variables represent in a function graph.
Students can do this when they can look at a graph and explain what the graph represents. For example, if they read the story above, they need to be able to explain what’s being measured. The graph could look completely different depending on what’s being measured. Sometimes we forget to review the basics like how to read the labels on axis with students. We assume they already know something like this. This is a crucial understanding that students need for this topic, as well as in other topics related to slope.
I can describe what a function graph represents.
In this objective students have to write or tell a story from a given graph. They’ll need to describe where the graph starts, what it does over time, and where it ends. You’ll have to emphasis words like increase, decrease, or stay the same. Also, students need to make sure that they are telling a story that matches the variables on the graph. They can be creative, but not too creative.
I can draw a function graph to match a given situation.
The graphs that students draw in these situations are not exact. Remember that these graphs don’t have numbers on them. This is an exercise in understanding change. You can have students practice drawing these graphs in the air, on a whiteboard, or on paper. It seems that they learn a lot from actually drawing the graphs and not just looking at them.
In the example above students have to draw a graph about speed over time. At first the graph should be at zero a little while. Then, the speed increases rapidly. It slows down initially and then it slows down a lot when the parachute comes out. The students’ graphs needs to reflect that.
I can match a function graph to a given situation.
At this point students will match a story with a graph. First, they need to check where the story starts. For example, in the above example the story refers to starting halfway done. When students look at the graph only Graph B starts above zero. I encourage and require students to explain why they have chosen the answer they choose. By doing this you can see where students need help. If they just choose an answer you really don’t know why they are getting it right.
Take it to your classroom
When you’re teaching students to analyze function graphs, it helps to model the thinking process for them. I think it’s especially important to emphasize where the line on the graph starts, how it changes over time, and where it stops. Then, students can practice analyzing functions in graphs in various ways, gradually increasing in challenge. For ideas on activities to get students lots of practice with this topic, check out “7 Off the Chart Activities for Analyzing Functions”. If you break down this topic for your students, and give them a step by step guide to where you want them to get, then without a doubt your students will be able to analyze function graphs like champs. Thanks for reading! Until next time!
