M.S. and Algebra I: How to Teach Slope in a Creative Way

I have taught secondary education math classes for over twelve years. During this time I have had to get creative when teaching Algebra concepts.

A major concept in Algebra involves slope, "rise over run". Quite often, students have to identify a line's slope in general, naming it as "positive, negative, zero, or undefined."

I created a story for teaching such a task, which also illustrates WHY the slope takes on each of the four properties. Students need as prior knowledge division rules of positive and negative numbers, and the rule about dividing by zero.

I draw the blank mountain, desert, and cliff on the board. I explain that today's story is about Sam (short for either Samuel or Samantha.) I draw Sam as a stick figure walking up the left side of the mountain.

Sam has decided to go on a hiking trip. However, for our story there are two important rules:
1. Sam can only travel from left to right (the same direction that you read a book)
2. The only item Sam has with him/her is a parachute.

So Sam decides to travel up the mountain. Slope is defined as "rise over run" as a fraction. Knowing this, as Sam goes up the mountain, does he have positive or negative rise? (Positive) How about the run? (Also Positive) Then I draw the Pos / Pos label on the left side of the mountain. A positive number divided by a positive number is what? (Positive) So I label that part of the image with the word "Positive".

Likewise, I continue with Sam going down the mountain to generate a "Negative" slope. I mention that the mountain's steepness or length does not effect the "negative" property of the line. I often draw other little mountains to illustrate this point.

Continuing on, Sam has finished crossing the mountain and heads East into the desert. He is hot and thirsty, and crawls across the desert. How much "rise" does Sam have? ( zero) What kind of "run" does he have? (positive) And zero divided by a positive number is what? (zero) So I label the desert with "zero"

Finally, Sam approaches the edge of the cliff. There is no breeze, and thankfully Sam has a parachute. Sam would drop straight down. Since he can't stay at the top of the cliff forever, and since he can't travel to the left, he is forced to jump. He hooks up his parachute and leaps. He falls straight down to safety. What kind of "rise" did Sam have? (Negative) How much "run" did he have? (zero) A negative number divided by a zero is what? (Most kids will say zero, but the answer is "undefined".)

At this point we debate the issue by trying to divide any negative number or positive number by zero on a calculator, and the students see the "Error" message. I label the final vertical segment with "undefined."

Using this visualization story, students were able to perform at 100% when labeling the type of slope given a line. Students remembered to read from left to right and often referred back to going "uphill", "downhill", "across the desert", or "down the cliff." I have used this story every year with success and hope you will find it helpful, too!