We introduce the word “functions” to students in 8th grade math. They, of course, have worked with functions in earlier grades. However, functions were previously referred to as input/output tables. Often teachers show input/output tables as a machine with a rule giving students their first introduction to the topic. But just because students should have some background with the concept of functions, it definitely doesn’t mean that you don’t have to teach this topic to students. They need to have a deeper understanding of functions before going into comparing functions and unit rates later on. Today I’m sharing with you the step by step way that I use interactive notebooks to introduce functions and activate students’ prior knowledge. By the end of this unit, students are prepared for other 8th grade topics with functions.
It’s important with this topic to remember that in our classrooms we have a variety of learners, and not all of them really understood functions when they were introduced in the past. I’ve learned that if you want to make sure that students have this background, then you have to teach it to them. I’ve made the mistake of glossing over this topic and we paid for it all year long (so not fun!).
Teaching functions with an interactive notebook
I’ve found that interactive notebooks add engagement to note taking and learning. In each unit I use 5 components in student notebooks. These components include building background, instructing, and practicing. Let’s look at how what each of those components look like when teaching a general introduction to functions.
I can statements
Using I can statements gives students a chance to know what their goals are for their learning. It’s a student friendly way to present learning objectives. I like to have them read the objectives at the beginning or end of the hour. Also, together we look at the verbs to know exactly what mastery will look like.
These I can statements are based on the standard. They guide us through our learning and practice. As you can see, the big emphasis for this topic is that students can identify a function and see how ordered pairs are graphed as functions. We do a lot of looking at the characteristics of functions throughout the unit.
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Building Background
After introducing the unit’s goals to students with the I Can Statements, the next piece is to build students’ background and give them the words and language they’ll need to talk about this concept. For functions, this page focuses on the idea of an “input” and an “output.”
Teachers typically get students working with input-output charts starting in 3rd or 4th grade. What they’re really working on with these charts is functions, but students don’t usually make this connection without a bit of help. That’s why it’s so essential to build students’ background and activate their prior knowledge for this concept. Since many have seen input output charts shown with a machine, I like this visual and chart to help students connect what we’re talking about in 8th grade with what they’ve learned about previously.
Using foldable notes and graphic organizers for instruction input
Back when I was in 8th grade, the teacher just talked and wrote some steps on the board. We wrote it down in our notebooks and then we did a whole bunch of practice. I love that today’s math teachers use graphic organizers instead of the old way of doing things. It helps all students organize the information they’re expected to use. It provides a powerful resource that students are more likely to refer back to. And it engages students’ brains more during the “input” part of the learning cycle.
For this topic I use two different foldable notes pages. The first is to help students understand the characteristics of functions. The second foldable notes page presents functions in table form and in graphs.
Is it a function?
First, we teach students the characteristics of functions and what functions look like in the different representations. The big idea here is that in a function each input can only have one output. They have to understand how this looks in an equation, on a table, and on a graph.
That means that in an equation there has to be an output, so students look for a y variable. In a table no input (x) can have more than one output (y) value. Students look for where there are two inputs that have the same value and then they know it is not a function. On a graph they will perform the vertical line test. If the vertical line only goes through the line one time then it is a function. In all of the representations you’re looking for the same characteristics expressed in different ways.
One of the easiest ways to show this to students is to present them with non-examples of functions along with the examples. This helps them key in on the essential characteristics of a function.
Functions between tables and graphs
One concept that I really like to emphasize with my students is that graphs and the tables are related to each other. Sometimes students may feel like they learn everything in isolation and then they don’t see the connection between things. I created this foldable to show the connection between a table and a graph. Students get a chance to plot points from a table onto a graph and take the points from a graph and put them on a table. The more opportunities to see this connection, the better.
Also, working through this notes page gives you a chance to emphasize some other fundamentals. This is a great time to review the basics of coordinate planes. Each repetition, or interaction, with a concept gives students another opportunity to commit it to long term memory. I like to have students talk about what they see in these graphs with a partner, activating their prior learning while getting a good introduction to functions.
Let’s practice
I have two types of guided practice for this topic. I always include guided practice in the notebook to 1) make sure that we take time for the “We Do” in the “I Do, We Do, You Do” process, and 2) give students another reference to use during independent practice.
The first practice page for functions gets students looking at a variety of equations, tables, and graphs and identifying the ones that are functions. Students can use their notes and they should annotate their thinking. I like to do a couple of examples as a whole class and then let them work alone or with a partner. This exercise seems simple, but it works as a great way to reinforce this concept.
The other practice activity has students matching graphs with their tables. They also have to add the next coordinate pair onto the table. Once again, this activity reinforces the connection between a table and a graph.
With this activity I have students complete it on their own and write their reasoning. Then I have them work with a partner that is not their table partner and share their reasoning. I want to make sure that students do more than just complete these practice activities. They really need to share with a partner. This is not an assignment. It’s still part of the instructional input.
Cheat sheet
This functions cheat sheet is the last thing we add to the interactive notebook for this unit. It’s one of my favorite cheat sheets from the whole year. My understanding of how to use cheat sheets has evolved over the past few months. Now I see it as an essential component of the interactive notebook. It gives students a great reference to use during practice and reminds them of important keys to success with a topic. This cheat sheet emphasizes prerequisite skills that students have seen in the past. For example, I like for students to have a picture that the x-axis goes left and right and the y-axis goes up and down. Also, one of the biggest downfalls for students is not paying attention to the sign of the numbers.
Another thing we have on this cheat sheet are some rules for functions. This part of the cheat sheet serves as a quick summary of the rules and what we have learned about functions.
Remember that you can use cheat sheets at the beginning of the unit, in the middle, or near the end. Cheat sheets can be referred to from time to time during other related units (for more about cheat sheets in interactive notebooks, check out this post).
You’ve got this
So, as you can see interactive notebooks work great as an instructional tool for introducing and teaching the characteristics of functions to students. I hope that you take the parts that speak to you and use them with your students, or even use the complete unit. I think you’ll see that having a solid instructional plan with your interactive notebook will improve the learning in your classroom.
You can use these ideas as a jumping off point for your own notebooks, or grab the whole unit of functions notes here.
