We examined the relationship between parents' behaviour and children's use of simple arithmetic strategies while playing a board game in contrast to solving arithmetic problems. In a microgenetic study spanning 3 weeks, 5-year-old children who were just beginning kindergarten played a modified game of "Chutes and Ladders" with one of their parents, computing their moves from the throw of dice. Children also solved math problems (math context) given to them by their parents at the end of each session. Children's arithmetic strategies and a variety of parental behaviours (prompt, prompt after error, affirmation, disaffirmation, cognitive directives, provide answer) were coded for children's game moves and the math context. As in past research, children used multiple and variable strategies, both when computing their moves during the game and in solving the math problems. Parents displayed different patterns of behaviours during the game and math contexts and showed different relationships among behaviours and strategies as a function of context, reflecting their sensitivity to the cognitive demands on their children of the different tasks. The results were interpreted in terms of the need to integrate contemporary strategy development theory with a sociocultural perspective and to recognise the dynamic nature of parent-child interactions with respect to the social construction of cognitive strategies. (Contains 5 tables, 3 figures and 4 footnotes.)