Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 6, Part A:
Equality and Balance

In This Part: Equality | Modeling with Balance Scales

 A balance scale is a good visual model for representing an equivalence relationship. Picture a two-pan balance scale, with two weights on the left side and one on the right. If the weights on the left side are 10 and 21 grams, and the weight on the right side is 31 grams, the scale will be balanced. Note 3 As you will see in Part C, using balance scales is also a good transition to more formal, symbolic techniques for solving equations.

 Problem A4 In this balance puzzle, determine what will balance with the rectangle in the third scale. Throughout the three scales, the same shape always has the same weight.

 Video Segment In this video segment, Frederick explains his solution to Problem A4. Watch the segment after you have completed Problem A4 and compare your strategy with Frederick's. If you get stuck on the problem, you can watch the video segment to help you. What strategies did you use to solve the problem? See if you can use Frederick's or your own strategy to solve the following problems. You can find this segment on the session video, approximately 5 minutes and 51 seconds after the Annenberg Media logo.

 Problem A5 What might be a solution for scale D, assuming that the same shapes have the same weight?

 Think about the strategies used by Frederick in this video segment. Additionally, think about what you can do to each side of a scale while keeping it balanced. Any such step can be done to any of the scales above.  Close Tip Think about the strategies used by Frederick in this video segment. Additionally, think about what you can do to each side of a scale while keeping it balanced. Any such step can be done to any of the scales above.

 Problem A6 What might be a solution for scale D, assuming that the same shapes have the same weight? Note: The shapes in this problem may not be the same weight as the shapes in the previous problem.

 Think about the strategies used by Frederick in this video segment. Additionally, think about what you can do to each side of a scale while keeping it balanced. Any such step can be done to any of the scales above.  Close Tip Think about the strategies used by Frederick in this video segment. Additionally, think about what you can do to each side of a scale while keeping it balanced. Any such step can be done to any of the scales above.

Problem A7

Look at the following equations from Problem A1. For each equation, draw a balance scale to represent the equation. How can you use balance to decide when an equation is true or false?

 A. 5 + 3 = 8 B. 2 + 14 = 12 C. 5 + 3 = y D. x + 3 = y E. 3x = 2x + x F. 3x = 3x + 1

 Problems in Part A are based on The Partners in Change Handbook: A Professional Development Curriculum in Mathematics, developed under the direction of Principal Investigator Suzanne Chapin at Boston University in 1997. Preparation of the handbook supported by the U.S. Department of Education.
 Session 6: Index | Notes | Solutions | Video