Demonstrate concretely, pictorially, and symbolically (with and without the use of technology) an understanding of slope with respect to:
- rise over run
- rate of change
- solving problems.
C, CN, PS, V
| (a) |
Research and present contexts that involve slope including the mathematics involved (e.g., ramps, roofs, road grade, flow rates within a tube, skateboard parks, ski hills). |
| (b) |
Analyze and generalize relationships between slopes in given contexts such as 3:1 and a 1:3 roof pitch or slopes that are usually described by a colour for downhill skiing and snowboarding, and explain implications of each slope including safety and functionality. |
| (c) |
Describe conditions under which a slope will be either 0 or undefined and explain the reasoning. |
| (d) |
Critique the statement, "It requires less effort to independently use a wheelchair to climb a ramp of a certain height that has a slope of 1:12 rather than a slope of 1:18." |
| (e) |
Justify, using examples and illustrations:
|
| (f) |
Analyze slopes of objects, such as ramps or roofs, to determine if the slope is constant and explain the reasoning. |
| (g) |
Analyze, generalize, and explain, using illustrations, the relationship between slope and angle of elevation (e.g., for a ramp (or pitch of a roof, grade on a road, slope in pipes for plumbing, azimuth in the sky) that has a slope of 7:100, the angle of elevation is approximately 4 degrees). |
| (h) |
Solve situational questions that involve slope or rate of change, verify and explain why solutions are reasonable or not. |
