Balancing #04

(grades 6-11)
Soft-bound, 48 page book, 16 reproducible task cards, full teaching notes.

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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!

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Table of Contents for #04 Balancing:

Preparation and Support

A TOPS Model for Effective Science Teaching • Getting Ready • Gathering Materials • Sequencing Task Cards • Gaining a Whole Perspective • Long Range Objectives • Review/Test Questions

Activities and Lesson Notes

  1. 1. Center of Gravity
  2. 2. Plumb Line
  3. 3. Tipsy
  4. 4. Against the Wall
  5. 5. Stable / Unstable / Neutral
  6. 6. Dancing on a Pinhead
  7. 7. Meter Stick Balance
  8. 8. Math in the Balance (1)
  9. 9. Math in the Balance (2)
  10. 10. Penny's Worth
  11. 11. Small Change

  13. 12. Beam Me Up!
  14. 13. Unequal Arms
  15. 14. Cantilever
  16. 15. Weigh a Friend
  17. 16. Your Mass in Kilograms

Supplementary Pages

tilt gauge • mobile strips


Complete Master List for #04 Balancing:

Key: (1st/2nd/3rd) denote needed quantities: (1st) enough for 1 student doing all activities; (2nd) enough for 30 students working in self-paced pairs; (3rd) enough for 30 students working in pairs on the same lesson. Starred* items may be purchased below.

  1. 3/25/30: 4x6 inch index cards
  2. 1/10/10: meter sticks
  3. * 2/10/20: straight pins
  4. 3/30/30: medium-sized cans
  5. 8/80/80: pennies
  6. * 1/5/5: rolls masking tape
  7. * 1/3/3: spools thread
  8. 1/10/10: scissors
  9. * 1/3/3: boxes paper clips
  10. 1/10/10: full sheets newspaper

  11. 2/20/20: size-D batteries, dead or alive
  12. * 3/12/30: wooden clothespins
  13. * 1/4/10: plastic drinking straws
  14. * 6/60/60: rubber bands
  15. * 1/10/10: medium-sized nails
  16. 1/10/10: each of assorted coins: pennies, nickels, dimes, quarters
  17. * 1/3/3: rolls clear tape
  18. 1/1/1: roll waxed paper
  19. * 1/3/10: 10 mL graduates
  20. 1/10/10: hand calculator

  21. 1/1/1: wood, hammer and nails to construct a stable ground-level see-saw
  22. 1/1/1: bathroom scales
  23. 2/6/20: gallon plastic milk cartons with handles and lids
  24. 2/6/20: feet of cord or thin rope

  25. 1/1/1: large bowl

Convenient Shopping:

Tape - clear

3/4 inch x 1000 inch roll

Your standard desk tape with matte write-on surface.


wooden, spring-action

These are handy lab items to keep in stock. We use them as bulb holders, tongs, clips, and more.

Graduated Cylinder - 10 mL

shatter resistant plastic on stable base

An important lab inquiry tool for measuring small liquid volumes.

Tape - masking

3/4 inch x 55 yd roll

A handy science supply used in most TOPS modules.

Nails - 2 1/2 inch

steel carpenter's flat-head nail, 10-penny

Used in some TOPS titles. A surprisingly handy scientific supply.

Product #12000 not available.

Rubber Bands - assorted

10 grams each of thin, medium and thick

You get 30 grams of soft, strong, durable rubber bands: thin #16 (about 50), medium #32 (about 20), and heavy-duty #64 (about 10). These sizes are specifically selected to work in most TOPS experiments.

Straight Pins

steel, one and 1/16 inch long

Used in many TOPS experiments. Sometimes required for their magnetic properties. Don't purchase aluminum straight pins by mistake.

Straws - straight

plastic, thin

Any length straw, between 0.20 and 0.25 inches in diameter is suitable. Grocery stores generally carry straws with flexible "elbows." You can use those if you cut off the bendable section before using.


light duty, 25 yd spool

Just plain old thread. Used in many TOPS titles, especially in Pendulums #34.

Teaching Tips for #04 Balancing:

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. Please send ideas and photos to

Lesson by Lesson Objectives for #04 Balancing:

  1. 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.
  2. Lesson 2: To use a plumb line to experimentally determine the CG of an irregular-shaped index card.
  3. Lesson 3: To observe that a standing object remains stable as long as its CG remains over its supporting base.
  4. Lesson 4: To feel your body lose stability as your CG shifts relative to your feet.
  5. Lesson 5: To define stable, unstable, and neutral equilibrium positions in terms of the displacement in an object's CG.
  6. Lesson 6: To observe how lowering the CG of an object below its pivot point stabilizes its equilibrium.
  7. Lesson 7: To construct an equal-arm balance beam. To use it to compare the relative masses of different coins.
  8. Lesson 8: To write mathematical equations that express a state of balance on a centered beam.
  9. Lesson 9: To increase the balance beam's sensitivity. To write more complex balance equations.
  10. Lesson 10: To develop a mass standard based on a 10 mL volume of water.
  11. Lesson 11: To use balance beam math to calculate the mass of unknown coins, based on the mass of known coins.
  12. Lesson 12: To construct a mobile and examine the mathematics of its design.
  13. Lesson 13: To experimentally determine the mass of the meter stick balance beam.
  14. Lesson 14: To cantilever beams beyond the edge of a support. To construct a mathematical series.
  15. Lesson 15: To calculate the weight of a friend on a balance beam, using your own weight as a standard of comparison.
  16. Lesson 16: To calculate your mass in kilograms using water jugs and a balance beam.

National Science Education Standards (NRC 1996) for #04 Balancing:

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: and facilitate learning. (p. 32)
C: ...engage in ongoing assessment of their teaching and of student learning. (p. 37)
D: 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.