To function or not to function? That is the question.

In this post are ideas for teaching algebraic functions, including activities, a story I tell students to help them remember function vs. not a function and why HOY VUX makes sense, a math word wall and an awesome introductory activity to introduce nonlinear functions.

The most effective way I have found to introduce functions starts with some version of this story: 

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. 

algebraic functions cartoon
Function cartoon

"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

Starting our algebraic functions unit with a story

I'm 4 feet, 5 feet and 6 feet tall when I'm 16 years old.


Starting our algebraic functions unit with a story

Every student knows which one "makes sense" every year pretty quickly. 

In this post are ideas for teaching algebraic functions, including activities, a study that I tell students to help function vs. not a function stick, a math word wall and an awesome introductory activity to introduce nonlinear functions.

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. 

Interpreting Function Graphs Matching Activity - print and digital
Interpreting function graphs matching activity

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 an Interpreting Function Graphs Matching Activity - print and digital that I recently updated with a digital version. 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. 

Graphing Functions Water Lab
Graphing functions water lab

Another fun way to introduce nonlinear functions is with this water lab that the teachers in the math department at my school developed. The activity is also on Desmos. Every year without fail my students can explain nonlinear movement after this lab.

Evaluating Functions Task Cards
Evaluating functions tasks

This pink card is from a set of evaluating functions tasks - print and digital. These were also recently updated to include a digital version on Google Forms. 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. 

function dice activity
Functions dice

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. 

function operations task cards - print and digital
Function operations tasks

The dice give us good practice before we move into a set task cards on function operations task cards - print and digital. I like using task card to evaluate students. That they are lower-stress than exams lets me see what students really know. 

Function vs. Relation Venn Diagram Sorting Activity - print and digital
Function or not? Venn diagram - print version
This is a free function or not? Venn diagram - print and digital in the shape of a Venn diagram. Students sort their relation cards that are functions into the inner circle.

I added a digital version in 2020 to help with distance learning. It comes in the same file so that you have both formats.

Composing Functions Digital Math Escape Room
Composing functions digital math escape room


Some of the newer math activities I've been making are digital-only, like this composing functions digital math escape room. It's self-checking and built in Google Forms. Students analyze the data given in tables and graphs (and one equation), then compose the functions.




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