Today's students expect learning to be meaningful to them. One of the most common complaints from students with regard to mathematics education is the lack of relevance to their lives outside the school, and it is true that the type of mathematics that students use outside school is often radically different in content and approach to the mathematics they encounter within the classroom. Homework provides the perfect opportunity for students to make connections between school mathematics and 'home' mathematics. So what would motivating, engaging, challenging and relevant mathematics homework look like? An abundance of research supports the use of a constructivist, student-centred approach to learning, which includes rich problem solving and investigation-based lessons. This article offers some suggestions.