Tag Archives: functions

Project 8: Function Art

Instead of a journal, I assigned this Desmos art project to get kids working and experimenting with graphs. Next time I think I’ll make this first graphing project less free-form, asking them to make a specific image (a face?) or recreate a given pattern.

I improved the assignment sheet for a similar project given later in the year, but this is what I had managed to put together in time for Project 8.

Editable version here: Ch. 8 Desmos Graphing Project

Ch. 8 Desmos Graphing Project

Graphing Stories

Graphing Stories was a great addition to my class this year. It started as the Possible or Not activity that I used during our first unit (about functions, operations, input, output, etc.) and grew as I made my own graphs on Desmos to draw out understandings of new function types.

Screen shot 2014-05-21 at 1.30.04 PMIn addition to the learning value of the stories, they were also kind of fun — especially those for graphs that weren’t functions.

At first I required students to write or type their stories; then I provided individual whiteboards so they could just jot them down; then, sometimes, I let students share their stories without writing them anywhere first. Sometimes I meticulously demonstrated an interpretation of the graphed information, while other times it was merely a discussion.

I dictated that we were looking at distance vs. time graphs, but had the students make decisions about what units the time and distance were measured in and what they were measuring distance from. (In the future I might alternate between determining those measurement details myself and asking the kids to do it.) I almost always had to remind students to include observations about speed. (Relatively slow or fast? Constant? Getting faster or slower?)

On tests I included the extending challenge of providing a story and asking students to sketch the matching graph.

During the end of year review, the student who chose this section (Interpreting Graphs) for which to plan his own review activity took the opportunity to bring us all outside. He had prepared 5 graphs using different function types and distributed copies of those graphs to the two teams. On the basketball court the teams took turns acting out a graph’s story while the other team figured out which graph it was.

An extension that I’ve considered but not tried is taking the graph’s action from a book or film students are studying in another class.

Non-equation Extension of Functions

My trig students are reviewing functions a bit right now. I used this piece of a chart showing average height by country that I found on Wikipedia to build the idea that functions and relations don’t only exist in the isolated world of equations and numbers. By assigning numerical values to information in a chart, you can turn just about any info into a mathematical function, or at least a relation.

Screen shot 2013-08-17 at 12.14.13 PMWe first assigned numbers to the countries of origin (1-11) so that we could have an input value instead of an input country. Using the male data seemed simpler because of it’s proximity to the list of countries,  and had the added benefit of the four N/A entries, so we could talk about whether the input 2 (Argentina) were really part of the domain if no output value exists for it.

We listed the domain and range, illustrated the mapping of input values onto output values, listed ordered pairs, and graphed them.

Viewing a chart as a function was a stretch for some (especially whenever I used the word input–“Input? What are we putting it into?”), but is a step toward breaking math out of isolation and realizing its contented existence beyond the classroom.

Goals Jotted Down

I remember drafting this post in May, but I guess it never made it out of my drafts folder. Until now, that is!

05/23/13 Here are some goals I jotted down for improving Trigonometry next year.

  1. Set better sections for student notebooks. The notebook sections I required this year were basically useless. Here’s what they should be:
    1. Notes and Classwork
    2. Homework
    3. Quizzes and Tests
    4. Journals and Projects
    5. Miscellaneous
  2. Trigonometry is not bathroom and drinking fountain time (yeah, it was a problem this year)
  3. Support the “function box” concept better*
  4. Make better intro learning activity for quadratic functions**
  5. Emphasize slope as a rate of change
  6. Contrast rate of change vs. accumulation
  7. More “discuss/work with a partner”
  8. Follow through on promise of notebook checks

7/10/13 Of course there are others, it seems hundreds more. Tweak that activity. Improve those notes. Allow them to critique their own presentations. Make sure homework assignments are worthwhile. But at the end of the school year, the bulleted eight were the goals that seemed big, essential.

*7/10/13 After coming across the illustration of inverse functions that I featured here, I’m not sure if I’ll continue to use the function box. I might.

**Number 4 is my primary curricular goal. At the end of last year I set a primary goal to improve the way I taught logarithms, with the result that this year the logarithm unit was one of the best of the whole year. Quadratics are the first non-linear functions my students study so their introduction deserves to be genuinely meaningful. Thus, it receives “primary goal” status.