A good way to start, bearing in mind that they have already learned the material in lower grades, is to start asking them what slope is.

 

M wrote this example:

 

Find the slope between the points (-3,5) and (2,1).

 

The answer is m = -4/5, using our definition.

 

At this time, it would be good to draw the graph of the points to check our work. We would see a downsloping line.

 

The next example was to find the slope between (3,-1) and (-2,-4). We get the expression

 

 

When we get our result, one thing we must do in checking the problem is to count the signs. There are two negative signs before the 1, and so it is positive.

 

M then discussed classification of slopes. It would be better to give examples first, following the principle of starting with concrete items before going to the abstract.

 

M said that it does not matter which we call y1 and which we call y2. It may help to explain this saying that the formula for slope is the slope between two points, and it does not matter which point is point 1 and which is point 2.

 

Steepness. The steepness of a line is simply the absolute value of the slope, ¦m¦. M explained this as a steeper line is harder to climb. Good, but we must not forget the formal definition. The picture must not replace the formal definition. Students get confused on tests because they may not think about the formal definition.

 

The teacher should use his/her arm to indicate slope.

Horizontal: 0

Slope 45°, and such.

Vertical: slope not defined.