 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Notes for Session 6

Note 1: The problems in this session progress from informal to formal strategies for solving equations. One of the initial stumbling blocks to solving equations is making sense of the equal sign. In Part A, we will explore different interpretations of the equal sign, differentiating between the result of a process and an equivalence relation. Part A Notes: Equality and Balance  Part B Notes: False Position and Backtracking  Part C Notes: Bags, Blocks, and Balance   Later in the session, we will introduce historical and informal strategies for solving equations, such as the method of false position. In this method, we'll take a guess and then modify that guess so that it is a solution to the equation. We'll also introduce the method of backtracking. This method involves solving equations by reasoning backwards from the answer, undoing the operations in reverse order. This is an informal method that seems intuitive to many students. It coincides with a view of equations primarily as a process. (Take a number, multiply it by 2, and add 1. The result is 12. What is the number?) The traditional method of solving a linear equation by doing the same thing to both sides belies a more static interpretation of an equation. Picturing this method as a series of bags and blocks on a scale can help us to think of algebraic expressions as objects. As the equations get more complicated, however, the balance model becomes less appropriate, just as backtracking does not work with certain equations. Review Groups: Discuss any questions that came up on the homework. Be sure to look at solutions to the "undoing" problem (Problem H4, Session 5), because "undoing," or solving, equations will be the focus of today's session.   Session 6: Index | Notes | Solutions | Video