This paper describes and analyses two mathematics lessons, one with very young pupils, about subtraction, the other for lower secondary school pupils, about gradients [slopes] and graphs. The focus of the analysis is on teacher knowledge, and on the fundamental mathematical and mathematics-pedagogical prerequisites that underpin teaching these topics to these pupils. I argue that whereas from the mathematical point of view, the subject matter under consideration with the secondary class is significantly more complex than that in the subtraction lesson, the pedagogical content knowledge necessary to teach the latter well is invisible to the uninformed observer, and is rarely made explicit in instruction.