Regular price \$17.95

Soft-bound, 48 page book, 16 reproducible task cards, full teaching notes.
Can you balance on one foot? (Impossible if the side of your foot is pressed against the wall.) Can you balance a card on a pin? (Easy if you curve the card so its center of gravity is located below the pin point.) Discover the mathematics of balancing with clever mobiles and cantilevers; apply your knowledge to art and engineering. This is a multidisciplinary delight!

4x6 inch index cards, meter sticks, straight pins, medium-sized cans, pennies, masking tape, thread, scissors, paper clips, newspaper, size-D batteries, dead or alive, wooden clothespins, plastic drinking straws, rubber bands, medium-sized nails, assorted coins: pennies, nickels, dimes, quarters, clear tape, waxed paper, 10 mL graduates, hand calculator, wood, hammer and nails to construct a stable ground-level see-saw, bathroom scales, gallon plastic milk cartons with handles and lids, feet of cord or thin rope, large bowl
• Lesson 1: To find the center of gravity (CG) of an index card. To understand why it shifts as mass is added to the card.
• Lesson 2: To use a plumb line to experimentally determine the CG of an irregular-shaped index card.
• Lesson 3: To observe that a standing object remains stable as long as its CG remains over its supporting base.
• Lesson 4: To feel your body lose stability as your CG shifts relative to your feet.
• Lesson 5: To define stable, unstable, and neutral equilibrium positions in terms of the displacement in an object's CG.
• Lesson 6: To observe how lowering the CG of an object below its pivot point stabilizes its equilibrium.
• Lesson 7: To construct an equal-arm balance beam. To use it to compare the relative masses of different coins.
• Lesson 8: To write mathematical equations that express a state of balance on a centered beam.
• Lesson 9: To increase the balance beam's sensitivity. To write more complex balance equations.
• Lesson 10: To develop a mass standard based on a 10 mL volume of water.
• Lesson 11: To use balance beam math to calculate the mass of unknown coins, based on the mass of known coins.
• Lesson 12: To construct a mobile and examine the mathematics of its design.
• Lesson 13: To experimentally determine the mass of the meter stick balance beam.
• Lesson 14: To cantilever beams beyond the edge of a support. To construct a mathematical series.
• Lesson 15: To calculate the weight of a friend on a balance beam, using your own weight as a standard of comparison.
• Lesson 16: To calculate your mass in kilograms using water jugs and a balance beam.
We encourage improvisation - it's one of the main goals of our hands-on approach! You and your students might invent a simpler, sturdier or more accurate system; might ask a better question; might design a better extension. Hooray for ingenuity! When this occurs, we'd love to hear about it and share it with other educators.
National Science Education Standards (NRC 1996)

#### TEACHING Standards

These 20 Activity Sheets promote excellence in science teaching by these NSES criteria:
Teachers of science...
A: ...plan an inquiry-based science program. (p. 30)
B: ...guide and facilitate learning. (p. 32)
C: ...engage in ongoing assessment of their teaching and of student learning. (p. 37)
D: ...design and manage learning environments that provide students with the time, space, and resources needed for learning science. (p. 43)

#### CONTENT Standards

These 20 Activity Sheets contain fundamental content as defined by these NSES guidelines (p. 109).
• Represent a central event or phenomenon in the natural world.
• Represent a central scientific idea and organizing principle.
• Have rich explanatory power.
• Guide fruitful investigations.
• Apply to situations and contexts common to everyday experiences.
• Can be linked to meaningful learning experiences.
• Are developmentally appropriate for students at the grade level specified.

#### Unifying Concepts and Processes

NSES Framework: Systems, order, and organization • Evidence, models and explanation • Constancy, change, and measurement • Evolution and equilibrium • Form and function
Core Concepts/Processes: A balance beam is a predictable, mathematical, equilibrium system: The sum of products (weight x pivot distance) on one side of a balance beam equals the sum of these products on the opposite side.

#### Science as Inquiry (content standard A)

NSES Framework: Identify questions that can be answered through scientific investigations. • Design and conduct a scientific investigation. • Use appropriate tools and techniques to gather, analyze, and interpret data. • Develop descriptions, explanations, predictions, and models using evidence. • Think critically and logically to connect evidence and explanations. • Communicate scientific procedures and explanations. • Use mathematics in all aspects of scientific inquiry.
Core Inquiries: Placing known weight on one side of a balance beam, calculate unknown weight on the opposite side.

#### Physical Science (content standard B)

NSES Framework: Properties and changes of properties in matter • Motions and forces
Core Content: Center of gravity • Plumb lines • Stable, unstable and neutral equilibrium • Cantilevers • Mobiles • Balance beams • Sensitivity • Grams and kilograms

#### Science and Technology (content standard E)

NSES Framework: Abilities of technological design • Understanding about science and technology
Core Content: Apply the mathematics of balance beams to cantilevers and mobiles.