But Why Does it Work?

 

This sample from But Why Does It Work? introduces a teaching model designed to help students formulate mathematical arguments.

Key features of the model include:

  • noticing relationships and patterns across sets of problems, equations, or expressions
  • articulating a claim about what they notice
  • investigating their claim through representations such as manipulatives, diagrams, or story contexts
  • using their representations to demonstrate why a claim must be true or not
  • extending their thinking from one operation to another.

Included in the sample is a complete instructional sequence for you to try: “Changing a Number in Addition or Subtraction.” Following the step-by-step teaching model, this sequence will help your students gain a deeper understanding of the properties of addition and subtraction.