4 Volume 1 — Numbers and operations
The central move of this volume is placement.
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.
You already know that numbers exist. What this volume builds is fluency with how they relate — how to scale them (ratio), express them as parts of wholes (fractions and decimals), talk about change (percents and rates), move in both directions from zero (integers), and reason about collections of them (statistics and probability).
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.
4.1 Chapters
| Chapter | Title | Core move |
|---|---|---|
| 1 | Numbers and the number line | Placing any number exactly |
| 2 | Ratio and proportion | Comparing two quantities of the same kind |
| 3 | Percent and rates | Expressing change as a fraction of something |
| 4 | Integers and signed arithmetic | Extending the number line in both directions |
| 5 | Fractions and decimals | Arithmetic with parts of wholes |
| 6 | Statistics and probability | Reasoning honestly from limited data |