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

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.

The most effective way I have found to introduce functions starts with a 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. 

"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

Function or Not in Special Ed Algebra 2

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


Function or Not in Special Ed Algebra 2

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. 

function graphs to motion stories 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 Actiity - 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

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

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

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 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

And here is a free function or not? sorting activity - print and digital in the shape of a Venn diagram. 

Function vs. Relation Venn Diagram Sorting Activity - print and digital

Anything hands-on works so well to introduce a new topic or concept.

I have been working on digital math activities, including digital math escape rooms and updates to my printable math activities. Below are a few more posts that are related to digital math. 





More posts:




Scaffolded Math and Science blog


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