Table of Contents for #31 Perfect Balance:
Preparation and Support
A TOPS Teaching Model Getting Ready Gathering Materials Sequencing Activities Gaining a Whole Perspective Review/Test Questions Why Teach TOPS?
Activities and Lesson Notes
- 1. Build a Math Balance (1)
- 2. Build a Math Balance (2)
- 3. Paper Clip Balancing
- 4. Balance Addition
- 5. Balance Multiplication
- 6. Balance Puzzles
- 7. More Balance Puzzles
- 8. Does it Balance?
- 9. Which Way?
- 10. Short n' Long Arm Balancing
- 11. Build a Paper Beam Balance (1)
- 12. Build a Paper Beam Balance (2)
- 13. Balance Equations
- 14. Paper Clip Weighing (1)
- 15. Paper Clip Weighing (2)
- 16. Paper Square Weights
- 17. Pinto Bean Statistics
- 18. Squares and Rectangles
- 19. Educated Guess
- 20. Mountain of Paper Clips
Supplementary Cut Outs
squares and rectangles
Complete Master List for #31 Perfect Balance:
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.
- 1/15/15 scissors
- * 1/1/1 roll, clear tape
- * 1/1/1 roll, masking tape
- * 1/15/15 spring-action clothespins
- 1/1/1 "pincushion" material (styrofoam or cardboard or cork or ...)
- * 1/1/1 package, straight pins
- 1/15/15 pop-top soda cans with attached finger tabs (may substitute small soda bottles or small milk cartons)
- * 3/30/30 boxes standard-sized paper clips, 1 brand only (only 3 boxes needed if you do the last activity as a teacher demonstration)
- 1/15/15 cups sand (may substitute gravel, beans, or other ballast material)
- * 1/1/1 lump modeling clay
- 1/4/15 index cards, standard 3x5 inch
- 10/40/150 thumbtacks (or pushpins) -- must be heavier than your paper clips
- 1/1/1 package each: pinto beans, popcorn, lentils and long-grained rice
- 1/10/15 calculators
- 1/4/15 objects to weigh: post-1982 pennies, nickels, notebook paper
- 1/4/15 other objects to weigh: such as nails, pencils, crayons, erasers, bottle caps, chalk, corks, rubber stoppers, cotton balls, marbles, beads, buttons, key chains, bobby pins, pen caps, packing peanuts, etc.
- 1/1/1 margarine tub or equivalent bowl
Clay - modeling
Sold by the 100 gram stick, about 1/4 cup, in assorted colors (our choice). One stick serves a whole classroom for TOPS applications.
These are handy lab items to keep in stock. We use them as bulb holders, tongs, clips, and more.
size #1, steel, box of 100
Paper clips have 1001 uses in TOPS experiments, and science in general. Feel free to use paper clips you already have, but be aware that different brands come in different sizes and weights. In experiments where uniformity is important, don't mix brands.
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.
Tape - clear
3/4 inch x 1000 inch roll
Your standard desk tape with matte write-on surface.
Tape - masking
3/4 inch x 60 yd roll
A handy science supply used in most TOPS modules.
Teaching Tips for #31 Perfect Balance:
This book presents great opportunities for cross-age teaching. Arrange for your most capable older students to take their balances and unmarked activity sheets into a lower grade and mentor younger children one-on-one.
As with many TOPS units, these activities give helpful practice in reading and following directions, thus encouraging independent study. Physical results give almost instant feedback, and quick success builds student focus, confidence and enthusiasm. Perfect Balance is a particularly good subject for students for whom English is not their native language.
Keep a couple of balances available in a corner workstation for students who finish tests early, or for constructive activity on rainy days. Consider extra credit for students who construct new math challenges for others to solve with the balances.
Because the constructed balance beams can easily be sent home upon completion of class activity, students can have fun inventing their own independent extension activities.
NOTE: 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 email@example.com.
National Science Education Standards (NRC 1996) for #31 Perfect Balance:
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)
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 math balance is a physical representation of an algebraic equation: The tilt of beam represents equality and inequality. Force times pivot distance on one side of a balanced beam equals force times distance on the opposite side. A balancing system is integrative, interconnected, predictable and rational. A balance beam may be kept in equilibrium with offsetting changes.
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. Recognize and analyze alternative explanations and predictions. Communicate scientific procedures and explanations. Use mathematics in all aspects of scientific inquiry.
Core Inquiries: Improvise an equal arm balance for serious inquiry into mass and weight.
Physical Science (content standard B)
NSES Framework: Position and motion of objects Properties and changes of properties in matter Motions and forces Conservation of mass.
Core Content: Explore the physics of math balances. Build equal-arm balances and develop a series of masses accurate to 0.01 grams. Experiment with different weighing units.
Science and Technology (content standard E)
NSES Framework: Abilities of technological design Understanding about science and technology
Core Content: Build an analog computer (a math balance). Construct a gram balance sensitive to 0.01grams. Invent a system of masses based on paper clips and paper squares.
Science in Personal and Social Perspectives (content standard F)
NSES Framework: Science and technology in local challenges
Core Content: Older students teach younger students in a cross-age learning context, experiencing learning from a teaching perspective.