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:
- 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.
- 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.