The San Francisco School broadly defines mathematics as a powerful tool to decipher the patterns that abound in our physical world. We believe that all students can learn important mathematics in a coherent and well-articulated program focused on actively building new knowledge from experience and prior knowledge. Teachers create an intellectual environment where serious engagement in mathematical thinking is the norm. Students learn to take control of their own learning and become confident in their ability to tackle problems, explore new ideas and persevere when tasks are challenging. They combine factual knowledge, procedural facility, and conceptual understanding in powerful ways. This approach gives students a rich store from which they can develop mathematical insight and creativity while also appreciating the inherent beauty of mathematics itself.