N. was eager to get right out there and begin moving big rocks around, proving his strength and manliness.
But before we could do that, we had some measuring to do. In order to determine the rise on the steps, we needed to know the slope of the hillside. To do that, we used a laser level laid on the ground on the top of the slope. I leveled it and pointed the laser at a plank that Bruce and N. were holding at the bottom of the slope.
The "rise" on the slope was 5 feet and three inches.
N. told us this was the same as 63". He divided 12 into sixty and then just added the three. All that mental math in Saxon is paying off!
Then it was time to measure the "run." N., being quite literal was ready to run up the hill. Bruce explained the run is actually the distance from the bottom of the slope to the top of the slope in a straight line. So N. did run up the slope, with the end of the tape measure in his hand. He held it straight above the laser while Bruce held it at the height of the laser mark on the plank at the bottom.
Here is N. just before lowering the tape measure so that it was even with the laser level.
The run turned out to measure in at 18 feet. N. told us that it was the same as 216". He said: "I even checked it on the calculator, Mom!" He was right.
So then I said: "Hey, N., we need to calculate the slope or percent grade of the hill. You do that by taking the rise over the run. He punched that out on the calculator:
"Let's see. 5.25 feet divided by 18 feet. That would be 0.291666 feet over...feet?"
So we showed how the problem looks by writing it out on the board.
"If you divide something by itself, what does it equal?" I asked him.
"One." N. answered.
"So if you divide feet by feet, then that equals one, too." Bruce said. "They cancel out. We can round off the 0.29 and change to O.3."
"Change?" N. asked in true Aspergian fashion. "Are we talking about money?"
"Figure of speech!" I said. "Bruce means all the numbers after the nine in your answer."
So N. rounded and we showed him how to multiply the slope of 0.3 in order to get a 30% grade for our slope. Pretty steep.
N. decided he was done with math for a while. He took the wheelbarrow off to get big flat rocks.
In the meantime, I calculated the number of steps we'd need if the riser is about 5" and there are about 18" between steps. The number is about 12 steps.
But N. was game for measuring for the cut and fill of the first step.
Since the steps are going to be far apart--more like a rising stepping stone path, and because they will be wide enough for one person, we used a garden trowel to begin the cut and fill.
We found that the soil on the hill was very loose and sandy and yet full of very friable (crumbly) shale that is native to the location, as well as small stones from the gravel in the side garden above, that were brought in by the previous owners of the house.
Of course, as I began the work of cut and full and placing the limestone "fieldstone" steps in earnest, N. got distracted by the sound of tree frogs peeping in the nearby woods. After helping lay the first stones, he was soon disappeared to investigate the frogs. And that was fine by me. The laying of the stones on a narrow path (about 18" wide) is really a one-woman job. And he did give about an hour and a half to the project on a sunny day.
Anyway, he learned a lot! he learned:
- that the Pennsylvanian limestone that caps the Sandia fault block is more than 300 million years old.
- that the notation for that is 3.0 exp 8 years b.p. (3.0 times ten to the eigth years before present)
- to tell the difference between country rock and rock brought in
- to tell the difference between limestone and shale
- that the definition of friable rock is "crumbly" rock
- that the definition of slope is rise over run
- how to cancel out units in setting up a scientific calculation
- that math can be really useful for accomplishing a worthwhile goal
And he was just helping for a "little while."
This is unschooling at its best!