Winner of the 2017 Mathical Book Prize. Every colourful page of Christopher Danielson’s children’s picture book, Which One Doesn’t Belong?, contains a thoughtfully designed set of four shapes. Each of the shapes can be a correct answer to the question “Which one doesn’t belong?” Because all their answers are right answers, students naturally shift their focus to justifications and arguments based on the shapes’ geometric properties.
 
In the companion teacher’s guide, Danielson shows how to facilitate rich discussions and teach mathematical argumentation using Which One Doesn’t Belong? He models how to listen closely and respectfully to students’ ideas about shapes. Danielson synthesizes research about how children learn geometry, discusses the role of geometry in the mathematics curriculum, and gives plenty of practical advice about different ways to implement Which One Doesn’t Belong? in classrooms. He also discusses the mathematical ideas likely to emerge on each page and—drawing from his direct experience using Which One Doesn’t Belong? at several different grade levels—helps teachers anticipate and think about students’ likely answers.
 
Most curricula treat geometry as little more than vocabulary lessons. Which One Doesn’t Belong? and its accompanying guide are powerful, flexible resources teachers can use to provoke lively discussions and deep learning about shapes with students of all ages.