Background. Children vary greatly in the mathematical knowledge they bring to school. These differences are related to social class; young children from low-income families generally lag behind peers from more affluent backgrounds. The differences appear to have large, long-term consequences; children who start behind in kindergarten tend to stay behind many years later. Aims. The present paper presents a theoretical analysis of the problem and reviews several experiments that indicate that a brief, targeted intervention can improve a wide range of mathematical competencies in 4- and 5-year-olds from low-income backgrounds. Arguments. We hypothesized that playing a linear, numerical, board game similar to the first row of Snakes and Ladders would produce substantial gains in numerical understanding. In such games, the greater the number in a square, the greater the distance that the child has moved the token, the number of discrete moves the child has made, the number of number names the child has spoken and heard, and the amount of time since the game began. Thus, playing the game provides visualspatial, kinesthetic, auditory, and temporal cues to numerical magnitude. Playing the game for four 1520 min sessions produced large gains in low-income children's understanding of numerical magnitudes, counting, number recognition, and ability to learn answers to novel arithmetic problems. The gains in knowledge of numerical magnitudes endured for 9 weeks and exceeded gains produced by engaging in other numerical activities or by playing a circular version of the board game. Conclusion. Targeted interventions can produce large and lasting gains in low-income children's numerical knowledge.