Placing any number exactly on a line. Positive, negative, rational, and irrational — all have a precise location relative to zero.
Volume 1 — Numbers and operations
Volume 1
Numbers and Operations
Every number has a location: on a line, relative to zero, relative to other numbers. This volume is about understanding that structure — not as abstract symbol manipulation, but as a description of real things. Debts and credits. Divided portions. Rates of change. Samples from populations.
None of this requires anything beyond counting. But it requires counting carefully, in the right direction, with the right units. That discipline is what the rest of the series stands on.
6 chapters
Grade 7–8
No prerequisites
Chapter Map
Comparing two quantities of the same kind. Scaling recipes, maps, and measurements without changing the underlying relationship.
Expressing change as a fraction of something. Percent as a special ratio, and rates as ratios where the denominator is time or another reference quantity.
Extending the number line in both directions. Debts, temperatures below zero, and elevation — signed arithmetic is arithmetic with direction.
Arithmetic with parts of wholes. Why dividing by a fraction flips it, how repeating decimals relate to fractions, and how to move between representations.
Reasoning honestly from limited data. Averages, spread, and the basics of chance — because any single number is rarely the whole story.