I have a really good relationship with my students this year. They feel like they can be honest with me, and I LOVE that. On a couple of occasions this year, they have told me (in droves) that the one thing they really don't understand from previous years is the concept of slope. We're about to hit slope in two or so weeks, so I've been thinking hard about how to help clear up their issues with slope.
Here are my thoughts:
Use a life-sized coordinate plane in gym. I made two a few years ago out of drop cloth and duct tape. Call origin point A.
Make up a scenario. Let's say we're going to make Banana Bread. In fact, let's say we're making this recipe.
Ask the kids to find how many bananas we need. 3 bananas. 3 bananas to make 1 loaf. Let's label the x-axis bananas and the y-axis # of loaves. So, we get the ordered pair (3,1). Give a student a picture of 3 bananas and a picture of 1 loaf. They go stand on (3,1). Call this point B.
Same scenario. You happen to have 6 bananas sitting on the counter. How many loaves of bread can we make? 2. Give student a picture of 6 bananas and 2 loaves. They go stand on (6, 2). Call this point C.
Same scenario. You happen to have 9 bananas sitting on the counter. How many loaves of bread can we make? 3. Give a student a picture of 9 bananas and 3 loaves. They go stand on (9, 3). Call this point D.
Extending the line into quadrant III is more of a stretch. Let's says you needed to buy three bananas at the store, but you forgot them. You are three bananas in the hole from what you need. Since we are three bananas in the hole, how many recipes are we in the hole? Give a picture of -3 bananas and -1 loaves (maybe make them red, so students know they are negative). Student goes and stands on (-3, -1). Call this point E.
Same scenario. You meant to buy 6 bananas but forgot to purchase them. How many loaves are we in hole? 2. Give student a picture of -6 bananas and -2 loaves. They go stand on (-6, -2). Call this point F.
Same scenario. You meant to buy 9 bananas but forgot to purchase them. How many loaves are we in hole? 3. Give student a picture of -9 bananas and -3 loaves. they go stand on (-9, -3). Call this point G.
Okay. Now, have rest of class "tour the line". I would start with a quadrant 1 tour. Student stands on the origin. Then, he/she walks to point B. How many bananas did s/he increase by? How many loaves? Record on a sheet. Walk to point C. How many bananas did s/he increase by from Point B? How many loaves from Point B? Record on sheet. Have student continue this tour for all points, eventually going back and picking up Quadrant III.
After they have recorded all data, ask them to make a comparison. What is happening from each point to the one to its right? We are increasing by 3 bananas and 1 loaf.
Since slope is change in y/ change in x. Let's test this theory. Have student start at (-9, -3). Our y is loaves, so let's rise/increase by 1 loaf. Our x is bananas, so let's run/increase by 3 bananas. Have them continue to step off 1/3 until they get through the line.
You could repeat this scenario with quiz grades and # problems missed for negative correlation.
So... what do you think? Will this work or be a disaster? Anybody have better scenarios that make sense in Quadrant III for positive correlation and Quadrant IV for negative correlation?