Led by James B. Thomson Simulacrum
About this course
Two things you have been carrying separately now turn out to be one thing. Module 1 taught place and order — each order ten times the one to its right, increasing leftward. Module 4 taught fractions — a denominator naming the parts, a numerator counting them. A decimal is what happens when those meet: a fraction whose denominator is never written down, because the position of the figure states it.
Thomson does not decree this; he argues it from symmetry, and you will make the argument yourself in the first sitting. Tens are ten times greater than units, and each succeeding order ten times greater than the last. Tenths are ten times less than units, and each succeeding order ten times less. Tens sit in the first place on the left of units. So where must tenths sit?
The consequence is worth stating plainly, because it is what stops students misplacing points for the rest of their lives: the decimal point is not a boundary between two kinds of number. It marks where the units place is, so that you can count outward in both directions.
After that the module is mostly consolidation. Adding decimals is Module 2's columns with the point supplying the alignment. Multiplying them is Module 4's rule for multiplying fractions in different clothing — the places add because the denominators multiply. And money is simply a decimal number with a sign in front, which is Thomson's own point: the denominations of a currency increase and decrease by the scale of ten, and it is thence called decimal currency.
One honest difficulty is met head-on: some fractions have no exact decimal form, and which ones is not arbitrary. You will work out the rule from the prime factors of the denominator — Module 3, spent again.
Led by James B. Thomson Simulacrum
The question
Eight sittings, Thomson's pages 129 to 157. You begin without
Outcome
The student can read, write and operate on decimal fractions of any
Sub-units
Practice scenarios
You are checking accounts prepared by a competent clerk. The arithmetic is sound throughout — every addition, every extension correct — and the total is out by a factor of ten. He has checked it twice by re-adding and found nothing, because there is nothing wrong with the addition. He is beginning to doubt himself and is talking about checking every figure a third time.
Your goals