The most effective way I have found to introduce functions is with a little storytelling.
At 16 when applying for my driving permit, I just knew that by the time I got my license, I'd be 5 feet 5 inches tall. Five had always been one of my favorite numbers, so how could it not happen? As it turned out, by 16 I was done growing. Once I came to terms with this sad fact, it became a great story to tell to introduce functions.
"Can I be 5'4" and 5'5" at the same time?" My students always give me a, "seriously, this is Math?" face when I ask this question. I mean, obviously not! Vertical lines are not functions because they make no sense in real life! So then I draw 2 graphs on the board and asking students which of the two could possibly happen in real life:
"I'm 5.5 feet tall when I'm 15, 16, 17 and 18 years old." or
Every student knows which one "makes sense" every year pretty quickly.
We then move into identifying functions in tables, equations, sets of ordered pairs and graphs. We complete a function or not? sorting activity to get warmed up before moving on to more in-depth practice.
I really like matching activities because, like sorting activities, they can be given early in a unit and students can still work confidently on their own.
The cards above are from a matching function graphs to stories activity where students match function graphs to story problems about the motion seen in the graph. I was a HUGE Dexter fan (before the last season -- ok, before the last 3 episodes of the last season), so all of the names in this activity are names of characters in the show.
Another fun way to introduce nonlinear functions is with this water lab that the teachers in the math department at my school developed. Every year without fail my students can explain nonlinear movement after this lab.
The cards above are from a matching function graphs to stories activity where students match function graphs to story problems about the motion seen in the graph. I was a HUGE Dexter fan (before the last season -- ok, before the last 3 episodes of the last season), so all of the names in this activity are names of characters in the show.
Another fun way to introduce nonlinear functions is with this water lab that the teachers in the math department at my school developed. Every year without fail my students can explain nonlinear movement after this lab.
This pink card is from a set of evaluating functions task cards. Students are asked to evaluate functions given tables, graphs, equations and word problems and the activity usually takes us multiple days to complete.
I like to count it as a quiz grade because of how much work my students have to do to complete it.
Another fun way to practice working with function notation is with function dice (free download).
Students roll the dice and then perform the operation. The dice are editable to make them easier or harder, depending on each year's student group.
I like to count it as a quiz grade because of how much work my students have to do to complete it.
Another fun way to practice working with function notation is with function dice (free download).
Students roll the dice and then perform the operation. The dice are editable to make them easier or harder, depending on each year's student group.
The dice give us good practice before we move into a set task cards on function operations. I like using task card to evaluate students. That they are lower-stress than exams lets me see what students really know.
And here is a free function or not? sorting activity in the shape of a Venn diagram. Anything hands-on works so well to introduce a new topic or concept.
I added references for function vs. not a function into an 8th grade math word wall. In my own classroom, having references available on our walls has helped both my teaching and student learning.
With a math word wall, students can independently access the help and supports they need and I can easily point to those reminders to quickly move past any confusion. I wrote more about how much word walls have changed my teaching in this post.
And here is a free function or not? sorting activity in the shape of a Venn diagram. Anything hands-on works so well to introduce a new topic or concept.
I added references for function vs. not a function into an 8th grade math word wall. In my own classroom, having references available on our walls has helped both my teaching and student learning.
With a math word wall, students can independently access the help and supports they need and I can easily point to those reminders to quickly move past any confusion. I wrote more about how much word walls have changed my teaching in this post.
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