### Background Information for Teachers

These professional resources come from Learning Math, a series of online workshops developed for elementary and middle school teachers by WGBH-Annenberg Media. Each course includes video, problem-solving activities, and case studies that show you how to apply what you have learned in your own classroom. You can use the material for personal review of a topic, but you may profit more from working on it with colleagues. You will find that group discussion is built into the workshop format.

Solving Equations In this online workshop session, K-8 teachers explore different methods for solving equations. You would investigate, in depth, the meaning of the equal sign, equality and balance, and various strategies for solving equations.

Proportional Reasoning In another algebra session, teachers work together to develop proportional reasoning skills. You would investigate ideas of scale, explore what is meant by a proportion, and interpret graphs showing direct variation. Created for K-8 teachers, the session includes online video, class problems, and case studies for discussion.

Similarity This interactive math game provides exercises in substituting for variables. Players must help the mail carrier deliver letters to houses with addresses like 3(a + 2). The value of a is held by Dougal, the dog guarding the house. The algebraic expressions become more complex according to the level of difficulty selected. Tips for students are available as well as an explanation of the key ideas underlying the game.

Volume Consider volume from its basic definition and, most important for middle school teaching, explore how volume formulas are derived and related to one another. Problems and their solutions, questions for group discussion, and even a video of the workshop session are available in this online workshop.

Surface Area and Volume Do prisms with the same volume have the same surface area? Here you can explore the relationship between surface area and volume through insightful problems and their solutions. A particularly interesting section deals with human measurements, such as the surface area of the body in relation to its volume.

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