Life's Complex Plane

Personal Reflection:
I love when someone, more creative than myself, is able to combine really awesome math with really deep thinking. I keep thinking that if we want to create critical thinkers, the people who create these kinds of images are the epitome of critical thinkers.  So...can we get kids to do the same?

Image Source

Grade Level: 6-9

Course: Pre-Algebra, Algebra

Standards:  6.NS.6.b, 6.NS.8, 7.RP.2.a 
SMP: MP2, MP3, MP4, MP7
Skills: Coordinate plane, critical thinking, graphing, analysis


How to use this as a mad minute:
You have 60 seconds. Explain your interpretation of this graph to a partner.

How to use this as a warm up:
You could ask the students to consider one of the following:
1.  If you had to give a title to each axis that would encompass the extremes, what would it be?
2.  Explain the relationships in each quadrant.
3.  Do sleepiness and joy have a direct or inverse relationship?
4.  Do you agree with the 4th quadrant?  Why or why not?
5.  Do you believe that dreams and reality are opposites?  Why or why not?  Use mathematics to back up your argument.

How to use this as a mini-lesson:
I'm going to assume (bad idea?) that you'll use this with kids who are familiar with the coordinate plane, the quadrants and how to read them.  This is not an introduction, but an elevation!  We've got 20 minutes?  Here we go!

0:00--Take 1 minute to read this, analyze it, and think about whether or not you agree with it.
1:00--Now, without talking, take the next minute to jot down your ideas, thoughts, etc.  You can draw, you can write, you can use notes, anything you want.
2:00--Now partner up and compare your thinking.  You have 60 seconds.
3:00--Ok, let's share out some ideas, thoughts and reflections.  What did you see?  Agree on?  Disagree on?
6:00--Ok, I'm interested in seeing if you can create your own "Complex Plane."  Let's start with 60 seconds of brainstorming opposites.
7:00--Let's list those where everyone can see them.
9:00--Ok, here's the challenge.  Take two pairs of opposites and put them on your axes.  (Dry erase boards, math journals, notebooks, etc.)  Now, try to imagine what each quadrant would represent.  (I'm going to include my own example, because it's not as easy as you might think!  First, the challenge is not to be swayed by the previous example.  I kept thinking of joy and sadness, or night and day, which both felt too close to the original.  I chose Hot & Cold and then Starving & Full.  I was thinking of temperatures of food, but without a title, that might not be clear.  Then I had to think, what food would be amazing hot and would make you full?  Not too hard for a high schooler to choose.  Pizza, Pasta, Cheeseburgers could all work.  Next, what would make you full when it is cold.  Ok.  Done.  But what food would you starve rather than eat?  Hot uncooked fish?  What food would you starve if you ate it cold?  That was the hardest.  Mine is not perfect, but it's my first effort.  I recommend you try this yourself several times before you ask the kids to do it!)

10:00, 11:00, 12:00--Check in on kids' progress.  Encourage them to keep going.  Ask them to create more than one if they struggled.
13:00--Let's partner up and share your results.  DO NOT EXPLAIN.  Ask your partner to study yours and then tell you what they think it shows.  Then flip.  You'll have 3 minutes total.
16:00-There is a fantastic website that creates graphical images like this almost every day.  thisisindexed.com.  Examine these two images.  Then try to create your own!

How to use this as a full lesson?
I probably wouldn't.  I think this is an engaging activity that sparks creativity, but is NOT destined for an entire class period.  However, if you wish, you can explore thisisindexed.com and select other images.  From there you can ask students to explain what is happening and to try to create their own.

Another option is for students to explore the site on their own (warning: a few images do pertain to more mature subject matter) and ask them to select their 4 favorites, analyze them and be prepared to explain them.  Browsing will take a lot of time!

 How to use this as an assessment?
I don't feel this is appropriate for a summative assessment.  Formative assessment will take place as you listen to student discussions and explanations.


Please feel free to use any of these ideas and modify them to meet your needs.  However, please acknowledge the original source of the items and my own lesson outlines.  ©NatalieRSprigg 2013