Another post from Tap Into Teen Minds. Enjoy!
Multiple Representations of Linear Relations
This is another great task by Jon Orr.
Act 1: Introducing the Problem
Students watch a video of a hummingbird lowering itself to a feeder in what most students will realize is slow-motion.
Teacher will prompt the students to guess what the question is… The question we are trying to get them narrowed in on is:
How fast are the wings flapping?
I prompt students to chat about independent/dependent variables, rate of change and initial value. Once students are comfortable with the independent variable (time) and dependent variable (number of flaps), we then have students ask for more information.
Act 2: Revealing Information
Show the video again, this time with the time and number of flaps counting on the screen.
The video ends at 27 flaps after 0.50 seconds.
Act 3 & Possible Sequels
In this case, I usually have students show the multiple representations of this linear relationship in a table, graph and equation in order to solve some problems.
The discussion allows for us to substitute different values for time and number of flaps in order to organically introduce solving equations for a purpose.
Learning Goals Associated
I usually use this task for both Grade 9 Academic (MPM1D) and Grade 9 Applied (MFM1P) to address learning goals like:
- I can determine values of a linear relation using a table of values.
- I can determine values of a linear relation using the equation.
- I can determine values of a linear relation using the graph by interpolation/extrapolation.
- I can describe the effects on the table, graph and equation of a linear relation when the initial value and rate of change are varied.
Resources
I created this math task template to assist in addressing the learning goals listed above. Note that this task could easily be altered to address such learning goals as proportionality and solving ratios/rates.
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