Table of Contents for #07 Math Lab:
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
CORE CURRICULUM
- 1. Penny Play
- 2. General Term
- 3. The Fibonacci Sequence
- 4. Seashell Spiral
- 5. The Golden Mean
- 6. Circle Sequence
- 7. Pool Table Induction
- 8. To The Limit
- 9. Circle
- 10. Ellipse
- 11. Parabola
- 12. Cardioid
- 13. Interior Angles
- 14. Easy Addition
- 15. Prime Numbers
ENRICHMENT CURRICULUM
- 16. Logarithms
- 17. Slide and Jump
- 18. Mobius Twist
- 19. Postal Bar Codes
- 20. Jigsaw Puzzle
Supplementary Pages
golden rectangles • centimeter grid • number square • bar code • cardioid points • number sieve
Complete Master List for #07 Math Lab:
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.
- 1/10/10: rolls of pennies (or index-card paper punches)
- 6/180/180: sheets of lined notebook paper
- 1/30/30: sheets of copier paper
- 1/15/30: index cards
- 1/15/30: metric rulers
- 1/15/30: drawing compasses
- 1/20/30: scissors
- * 1/10/10: rolls clear tape
- 1/7/15: hand calculators
- 1/30/30: sheets dark construction paper
- 1/5/15: bottles white glue
- * 1/5/15: hand lenses (optional)
- 1/1/1: pencil sharpener
- 1/20/30: pieces 8 1/2 x 11 inch corrugated cardboard
- * 1/2/2: spools thread
- * 2/140/60: straight pins
- 1/20/30: dark crayons, wrappers removed
- 2/20/60: small styrofoam cups
- 1/5/15: short pieces pencil lead
- 4/120/120: sheets scratch paper
- * 1/1/1: roll masking tape
- * 1/2/2: boxes paper clips
- 1/1/1: roll adding machine tape
- 3/15/15: used envelopes with bar codes.
Convenient Shopping:
Magnifier - hand lens
3X clear plastic hand lens
You'll find many uses for this basic tool of scientific inquiry. Very nice quality for the price. Supports #17 Light, #23 Rocks and Minerals, and #42 Focus Pocus. (One 3X hand lens is also included in each #100 Triple Magnifier Kit.)
Paper Clips
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.
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.
Tape - masking
3/4 inch x 60 yd roll
A handy science supply used in most TOPS modules.
Tape - clear
3/4 inch x 1000 inch roll
Your standard desk tape with matte write-on surface.
Thread
light duty, 25 yd spool
Just plain old thread. Used in many TOPS titles, especially in Pendulums #34.
Teaching Tips for #07 Math Lab:
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 tops@canby.com.
National Science Education Standards (NRC 1996) for #07 Math Lab:
TEACHING Standards
These 20 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)
CONTENT Standards
These 20 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 • Evolution and equilibrium • Form and function
Core Concepts/Processes: Induction says that what is true for the particulars is true in general. Such claims, while reasonable, are never absolutely certain.
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: Recognize patterns • Think inductively • Generate nth terms • Ellipses • Parabolas • Cardioids • Prime numbers • Logarithms • Solve puzzles
History and Nature of Science (content standard G)
NSES Framework: k458912 Science as a human endeavor • Nature of science • History of science
Core Content: Explore patterns and shapes of historical significance - the Fibonnacci series, Mobius strips, ellipses, parabolas, and the golden mean.
