Calculate rate of natural increase and doubling time, and interpret age-structure diagrams and the demographic transition model to explain why countries grow at different rates.
World population grew from roughly 1 billion around 1800 to more than 8 billion today -- a matter-of-fact historical record, not a judgment about whether that growth is good or bad. Rate of natural increase is calculated as (birth rate minus death rate) per 1,000 people, converted to a percent; the "rule of 70" then estimates doubling time by dividing 70 by that growth-rate percentage.
The demographic transition model describes a pattern many countries have followed as they industrialize: Stage 1 has both high birth rates and high death rates (population stays roughly stable); Stage 2 has death rates falling faster than birth rates, thanks to improved sanitation and medicine (population booms); Stage 3 has birth rates falling too, often linked to urbanization, education (especially of women), and access to family planning (growth slows); and Stage 4 has both rates low again (population stabilizes, as in many industrialized countries today). Age-structure diagrams (population pyramids) show this visually: a wide base signals a young, still-expanding population; a rectangular, column-like shape signals a stable population; and a narrowing base signals a population that is aging and may eventually shrink.
Mastery looks like: They can calculate rate of natural increase and doubling time from given birth and death rates, and correctly match an age-structure pyramid shape to a demographic transition stage.
Common stumbles: Forgetting to divide by 1,000 before converting to a percent; assuming every country moves through the demographic transition at the same pace or in lockstep.