Math: ratios: making oatmeal: 4:9

Self-tutoring about ratios: the tutor reflects about preparing oatmeal.

The ratio of oatmeal to water, with the brand I use, is 1 and 1/3 cup to 3 cups. As such, it’s a less convenient ratio to scale up or down than some.

Yet, 1 and 1/3 to 3 is actually 4/3 to 9/3, so it’s 4 to 9. That’s an easy ratio to scale up or down. In my case, I scale it up: 2 cups to 4 and 1/2 cups, or 4/2 to 9/2.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Metric system: how big is a hectare?

Tutoring science, the metric system may arise. The tutor mentions the definition of a hectare.

hectare (noun):

a square unit spanning 10000m2.

A hectare can be pictured an as area 100m wide by 100m long.

Another way to imagine a hectare is that it’s 2.47 acres.

Perhaps my favourite way to relate a hectare is that the grassy area enclosed by a school track (400m) is 1.12 hectares.


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Math, engineering, trades: steepness measurement: definition of grade

Tutoring math, you encounter grade. The tutor discusses its definition and why it might be surprising.

Grade is defined as 100%*(vertical/horizontal). In the above diagram, it would be as follows:


By itself, rise/run is called slope.



What follows is a distinction that, to me, is important and interesting:

grade is not

rise/distance traveled

since, of course, you can’t drive along the horizontal course of a hill; rather, you can only drive on its surface.

At level, grade and (rise/distance traveled) are both zero. They remain virtually the same even at 20% grade, when (rise/distance traveled) is 19.6%. As the grade increases, however, they differ dramatically: at 100% grade, (rise/distance traveled) is 70.7%.

My interest in the difference between grade and (rise/distance traveled) is philosophical: why base a value on an indirect measurement (horizontal distance), when a direct measurement (distance traveled) is available?

In math, we use slope, of course; however, it’s usually in a context where actual measurements aren’t used. Rather, it’s just on paper.


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.