TEXAS REGIONAL COLLABORATIVES for Excellence in Science and Mathematics Teaching Conference for the Advancement of Science Teaching Dallas, Texas November 17-19, 2011 Joshua Nielsen - Lynn Seman Cari Quillen - Dr. Shirley M. Matteson Hanging in the Balance

Introduction Students will explore the concept of balance by first creating a balance scale and leveling it. They then explore equivalence by working with equations and applying number properties. Students will gain an understanding of the torque rule by working through a sequenced set of balance problems on a virtual manipulative applet.

Focus Questions What properties of numbers can be demonstrated with balance scales? How can physical models of balance scales be used to model mathematics equations? How does distance and weight influence the balancing of physical and virtual balance scale models? How does working with physical and virtual balance scales lead to a better understanding of the torque rule?

Teaching Time Day 1: pre-test using Appendix A Day 2: build the balance beam Day 3: explore combinations of distance and number of paperclips (we created our own worksheet) Day 4: virtual balance beam practice (online) Day 5: post-test using Appendix B and/or C

Make Your Own Balance Beam

Materials Cardboard (cereal box thickness) 1.5” x 11” Paperclips (same size and brand) Dressmaker pins Clothes pin Hole puncher Clean soda bottle Tape (masking, clear)

Balance Beam Find the midpoint of the strip of cardboard and place a make above that point Measure from this point every 1 inch and mark it ¼ to ½ inches from the edge

Balance Beam Use the hole puncher on these marks (not the one in the center) and label them Use the dressmaker pin on the midpoint and check the beam for balance (adjustments may be made using the tape)

Holder Cut 2 strips of cardboard and tape them over the ends of the clothespin. Cut a “V” into each of the strips (this will hold the dressmaker pin and allow free movement of the balance beam.

Stand Place the clothespin on the clean soda bottle Place the beam inside the “V” of the clothespin Check for balance (adjust with tape)

Virtual Balance Beam /balance.html /balance.html You could do either a teacher demonstration or have the students gain an understanding of the features of the Balance Applet on their own. Students need to understand and explain what happens when they move the various color blocks and/or input different values.

Virtual Balance Beam

Students solve the problem first time

References Asquith, P., Stephens, A. C., Knuth, E. J., & Alibali, M. W. (2007). Middle school mathematics teachers’ knowledge of students’ understanding of core algebraic concepts: equal sign and variable. Mathematical Thinking And Learning, 9, 249--‐272. Carpenter T. P., Franke, M. L., & Levi. L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann. Marson, R. (2004). Perfect balance 31: Inquiry through science, math and technology. Canby, OR: TOPS Learning Systems.