Table of Contents for #08 Probability:
Preparation and Support
A TOPS Model for Effective Science Teaching Getting Ready Gathering Materials Sequencing Task Cards Long Range Objectives Review / Test Questions
Activities and Lesson Notes
- 1. Heads Or Tails?
- 2. Even Odds
- 3. Uneven Odds
- 4. Permutations
- 5. Combinations
- 6. Bell-Shaped Curve
- 7. Pascal's Triangle
- 8. Penny Pinball
- 9. Biased or Fair?
- 10. Pinball Puzzles
- 11. More Pinball
- 12. Simple as ABC
- 13. Sample Space
- 14. Single, Double, Triple
- 15. Four Probabilities
- 16. Or / Not
- 17. And
- 18. The Lucky Dice
- 19. A Tacky Experiment
- 20. Spinner Speak
- 21. Tooth Tape
- 22. Pattern Search
- 23. Lead Changes
- 24. Do Run Run
- 25. Do Do Run Run
- 26. Hit or Miss?
- 27. Random Toothpicks
- 28. Average Angles
probability grid permutation tree bar graphs Pascal's triangle angle gauge letter circle toothpick protractor outcome sheet ABC circles number circles line grid
Complete Master List for #08 Probability:
Key: (1st/2nd/3rd) denote needed quantities: (1st) enough for 1 student doing all activities; (2nd) enough for 30 students working in 10 lab groups all self-paced; (3rd) enough for 30 students working in 10 lab groups, all doing the same lesson. Starred* items may be purchased below.
- 1/15/15: towels, sweaters or other fabric to muffle sound (optional)
- 7/105/150: pennies
- 1/15/15: hand calculators
- * 1/8/8: rolls masking tape
- * 1/15/15: bottle caps, unbent, all the same brand
- 1/15/15: empty cereal boxes, 32 ounce Grape-Nut boxes recommended
- 2/30/30: pieces corrugated cardboard, about 10x12 inches
- 1/4/8: heavy scissors (optional)
- 1/15/15: quarts package filler (paper "straw," styrofoam peanuts, or loosely wadded newspaper)
- * 1/4/4: rolls clear tape
- 1/15/15: index cards, 4x6 inch
- * 10/150/150: paper clips
- 1/10/15: size-D batteries, dead or alive
- * 1/10/15: thick rubber bands
- * 50/750/750: straight pins
- 1/5/15: metric rulers
- * 1/15/15: plastic drinking straws
- 1/15/15: scissors
- 1/4/4: wire cutters
- * 0.1/1/1: cups modeling clay
- 1/1/1: package pinto beans or equivalent
- 1/15/15: plastic sandwich bags or equivalent
- 4/60/60: jar lids or other shallow containers
- 2/10/30: dice
- 1/5/15: styrofoam cups
- 10/50/150: flat thumb tacks, all the same brand
- 1/1/5: recycled phone book with white pages
- * 1/1/1: roll black electrical tape
- 1/2/8: desk calculator with tape
- 10/150/150: flat wooden toothpicks
- 1/1/1: scientific calculator (trigonometry text with sine tables)
Ideal for counting, uniform weights, and mini-containers to hold small portions of chemicals. These unused caps flare more widely than recycled caps. Used bottle caps, if unbent/undamaged, are an excellent free alternative.
Product #1159 not available.
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.
Stopper - rubber
black rubber, size #6, no hole
Used in #09 Floating and Sinking, #14 Kinetic Model, and #22 Machines.
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
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.
Tape - clear
3/4 inch x 1000 inch roll
Your standard desk tape with matte write-on surface.
Product #1012 not available.
Tape - masking
3/4 inch x 55 yd roll
A handy science supply used in most TOPS modules.
Teaching Tips for #08 Probability:
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 firstname.lastname@example.org.
National Science Education Standards (NRC 1996) for #08 Probability:
These 28 task cards 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 28 task cards 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
Core Concepts/Processes: Sample spaces predict ideal frequency distributions, but only after many rolls of the dice.
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: Count permutations tally combinations plot frequency distributions calculate probabilities. Decide whether a tack landing "heads" or "tails" is fair or biased.
Science in Personal and Social Perspectives (content standard F)
NSES Framework: Risks and benefits Personal and community health
Core Content: A gambler claims that a pair of dice are "hot" or "cold." If the dice are fair, can this be true?
History and Nature of Science (content standard G)
NSES Framework: Science as a human endeavor History of science
Core Content: Develop a frequency distribution based on Pascal's triangle.