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).

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.

Describe conditions under which a slope will be either 0 or undefined and explain the reasoning.

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."

Justify, using examples and illustrations:

• slope as rise over run
• slope as rate of change.

Analyze slopes of objects, such as ramps or roofs, to determine if the slope is constant and explain the reasoning.

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).

Solve situational questions that involve slope or rate of change, verify and explain why solutions are reasonable or not.