There is increasing global commitment to establish early childhood interventions that promote the development of the millions of disadvantaged children in low- and middle-income countries not reaching their developmental potential. However, progress is hindered by the lack of valid developmental tests feasible for use at large scale. Consequently, there is an urgent need for such tests. Whilst screeners and single-domain tests ('short tests') are used as alternatives, their predictive validity in these circumstances is unknown. A longitudinal study in Bogota, Colombia began in 2011 when 1,311 children ages 6-42 months were given the Bayley Scales of Infant and Toddler Development (Bayley-III) by psychologists and randomized to receive one of two batteries of short tests under survey conditions. Concurrent validity of the short tests with the Bayley-III ('gold standard') was reported. In 2016, at 6-8 years, 940 of these children were given tests of IQ (Wechsler Intelligence Scale for Children, WISC-V) and school achievement (arithmetic, reading, and vocabulary) by psychologists. We compared the ability of the short tests, the Family Care Indicators (FCI), height-for-age, stunting (median height-for-age <-2 SD), and the Bayley-III to predict IQ and achievement in middle childhood. Predictive validity increased with age for all tests, and cognition and language were usually the highest scales. At 6-18 months, all tests had trivial predictive ability. Thereafter, the Bayley-III had the highest predictive validity, but the Denver Developmental Screening Test was the most feasible and valid short test and could be used with little validity loss compared with the Bayley-III. The MacArthur-Bates Communicative Development Inventory at 19-30 months and the FCI under 31 months predicted IQ and school achievement as well as the Bayley-III. The FCI had higher predictive validity than stunting and height-for-age, and could be added to stunting for use as a population-based indicator of child development.