A B C 

Note 2

The problems in this section use the balance scale as a model for the equality relationship.

Groups: Discuss Problems A1-A3 as a whole group before going on to solve the balance scale puzzles.

For the equation in Problem A3, the equal sign acts as a symbol for students to do something or to perform the given operation. In other words, the equal sign connotes "give the answer to what comes before." This is a beginning notion of equality that at times interferes with a broader concept of equivalence. In fact, many students in elementary and middle school will argue that the equation in Problem A1(c) is impossible because "y" is not an "answer."

Although the equal sign signifies an equivalence relationship in all of the equations, the solution sets are different for some of the equations.

<< back to Part A: Equality

Note 3

Groups: After discussing Problems A1-A3, work in pairs or small groups on the balance problems in Problems A4-A6.

Look for ways to think about replacing specific shapes for other shapes. The point here is not to use algebraic notation or equations to represent these situations. This sort of reasoning is essential in making the transition to solving equations, so it's an important step in the process.

Groups: Share solutions with the whole group, making sure to attend to the kind of reasoning used in solving the problems.

<< back to Part A: Modeling with Balance Scales

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