Inverse Variation - What do you notice?

Today's lesson was on inverse variation in Acc Alg 1.  We already learned about direct variation in the fall when we were studying lines.  Now, we are moving into rational functions. 

First, we recalled all we could about direct variation - the graph, the equation, the y-intercept is zero, the relationship as x increases, y increases, the k = the constant of variation.  It was slow, but we pulled it out of the memory bank. 

Then, I went onto this slide and asked them what they noticed:



Some noticed:

• The x's are getting bigger.  The y's are getting smaller.
• There is no x = 3.  I asked if x was equal to 3, what would y be.  They guessed 7.5.  Nope.  We will come back to that one.
• 2010
• 4 and 5 and 5 and 4 are switched
• Someone asked if x = 20, is y = 1.  Yes!
• I asked them to see if they noticed anything going across the row.  It took a little while but they eventually got that they each multiplied to 20.
• I went back to what if x = 3.  They all reached for their calculators - NO!  Think about it.  Umm..a little more than 6.  Okay, keep going.  6.666, give me more exact 6 and 2/3okay, yes.  I finally had to write out 3x=20 --> What is 20?  Oh, 20/3.  These kids are so afraid of fractions.

Lots of good stuff that led us into our inverse variation lesson.