How overall tumor growth emerges from the properties of functionally heterogeneous tumor cell subpopulations is a fundamental question of cancer biology. Here we combined lineage tracing, continuous monitoring of tumor mass, proliferation assays and transcriptomics with mathematical modeling and statistical inference to dissect the growth of glioblastoma in mice. We found that tumors grow exponentially at the rate of symmetric divisions of brain tumor stem cells (BTSCs). Spatial modeling predicts, and data show, that BTSCs accumulate at the tumor rim rather than in the core. The physiological differentiation hierarchy downstream of BTSCs is preserved in mice and humans: transit amplifying progenitors give rise to terminally differentiated cells. Consistent with our quantification of the mechanisms underlying tumor growth, molecular data show elevated expression of cell cycle- and migration-related genes in BTSCs. Our systematic approach reveals fundamental properties of glioblastoma and may be transferable to the study of other animal models of cancer.