This lesson provides an opportunity to listen to ways in which students make use of structure and repeated reasoning to design a Number Talk. In the Warm-up, students are given a typical Number Talk, with four expressions, and discuss how the expressions are related. In the first activity, students practice anticipating the different ways someone might reason about addition and subtraction for a group of expressions, and then create expressions that would fit with the given string of expressions. In the final two activities, students are given incomplete sets, with a decreasing number of expressions, and asked to write new expressions to create a Number Talk. This lesson can take 1–2 days if students facilitate their creations with other groups.

Think about two questions you asked students today: a question that yielded insight into students’ thinking and one that you wish you had framed differently. How do the questions compare? How would you ask the latter differently to elicit the desired reasoning or insight?