Led by James B. Thomson Simulacrum
About this course
The hardest module in the school, and Module 5 told you why: money behaved because its denominations run by tens, and every carry you have learned was a carry of ten. Weights, measures and time do not run by ten. They run by twelve, sixteen, sixty, twenty-four, three hundred and sixty-five — and every one of those scales carries differently.
The operations do not change. What changes is that the ten you have been taking for granted is gone, and the right number must be put in its place at every step.
Thomson's definitions do more work than they look like doing. A simple number contains units of one denomination; a compound number contains two or more of the same nature. Measure a table in inches and you have a simple number; measure the same table in feet and inches and you have a compound one — the table has not changed, only the description. But two feet and four pounds is not a compound number at all, because the units are of unlike natures. That is the like-and-unlike rule from the very first sitting of the school, arriving for the third time and now governing a whole module.
On the tables: they are not the lesson. Reduction is the lesson, and it is the same procedure at any scale. So the course drills it on the tables you will actually meet — time above all, which nobody escapes and which is irregular in every interesting way — and treats the obsolete ones as reference rather than as memory work.
The metric system gets a sitting of its own, placed late on purpose. Its scale is ten throughout, so reduction within it is movement of a decimal point and needs no multiplication at all. After four sittings of reducing through irregular scales you will be in the right position to feel what that means: not simplified, eliminated.
Led by James B. Thomson Simulacrum
The question
Nine sittings, Thomson's pages 158 to 192. You begin with the
Outcome
The student can reduce any compound number ascending or descending
Sub-units
Practice scenarios
A builder has quoted for flooring a room. His arithmetic is correct: he measured, multiplied, and ordered that quantity of boards. The boards have arrived and there are nowhere near enough. He has re-measured and re-multiplied and gets the same figure, which is the figure he ordered. He is now convinced the supplier short-delivered and is preparing to complain.
Your goals