In the measuring stacks of cups activity, the height of the stack changed by some number of units (for example, one cm or 1/2 cm) every time a cup was added.
When we plotted points to graph our results, the pattern of dots lined up to suggest a slope. Drawing vertical lines to show the change in y (stack height) and horizontal lines to show the change in x (number of cups) created the "up and over" stairsteps that are associated with slope.
The slope as a number tells us about the steepness of the graph.
The slope written as rise units in the numerator and run units in the denominator represents the rate of change.
A rate is a ratio which means how the y units change every time the x unit changes by 1.
In our cup stacking the rate of change is, for example, 0.5 cm per cup, or 0.5 / 1.
Other examples of rate of change:
7 cents per minute of phone usage.
Gasoline costs $3.75 per gallon.
Driving at 60 miles per hour
Counting 16 ounces each time you weigh a pound.
Rates in word problems are indicated by language prepositions: per, for every, each time.
No comments:
Post a Comment