Table of Contents for #45 Pi in the Sky:
Preparation and Support
Why teach TOPS? Welcome Standards Getting Ready Overview Photocopies
Activities and Lesson Notes
A. PI IS A CONSTANT
- 1. What's Pi, anyway?
- 2. Chop Circumferences into Equal Arc Lengths.
- 3. Approximate Pi Using a Paper Plate and String.
- 4. Make a Pi Graph.
- 5. Calculate Earth Distances.
- TOOLS: Millimeter Beads Pi Graph
B. RADIANS AND DEGREES
- 1. So What's a Radian?
- 2. Inscribe an Equilateral Triangle.
- 3. And What's a Pi Radian?
- 4. Divide a Circle Into Radian Wedges.
- 5. Calibrate a Protractor.
- 6. No Protractors Allowed!
- 7. Calibrate a Circle in Degrees and Radians.
- TOOLS: Snowman Protractor
C. COUNTING DIAMETERS
- 1. Make a Coin-Diameter Ruler.
- 2. Observe from the Plane of Your Table Top.
- 3. Arrange Coins to Have the Same Apparent Size.
- 4. Explore Angular Size Relationships Among Coins.
- 5. Make a Ruler from Paper Plates.
- 6. Does a Moon Ruler Correctly Scale the Real Thing?
- 7. Gaze at a Paper Plate Moon.
- 8. Test Your Moon Ruler on Family and Friends.
- TOOLS: Coin Ruler Moon Ruler Dime Ruler
D. VISUAL ACUITY
- 1. Test Your Visual Acuity with a 1 mm Dot.
- 2. Test Your Visual Acuity with Other Dot Diameters.
- 3. Compare Your Eyesight with GLAST and Hubble.
- 4. Can You See a Dime at 100 Meters?
- TOOL: Millimeter Dots
E. TIE YOUR KAMAL
- 1. Make a Paper Kamal and Try It Out.
- 2. Learn to Ride Your Kamal.
- 3. What's Your Apparent Shoe Size?
- 4. Knowing Height, Estimate Distance.
- 5. Knowing Distance, Estimate Height.
- 6. Lay Out Inner Solar System Plus Jupiter.
- 7. Do Other Planets Have Larger Moon-Rises?
- TOOLS: Kamal Triangle Planets to Scale
F. LOOK FROM HERE AND THERE
- 1. Estimate Diameter from a Distance.
- 2. Measure Something Tall Three Ways.
- 3. What's Parallax and How Do We Measure It?
- 4. Step Aside and Look Again.
- 5. How Far to Nearby Stars?
- 6. I Beg Your Parsec.
Complete Master List for #45 Pi in the Sky:
Starred* items may be purchased below.
- ruled notebook paper
- pencils with good erasers
- calculators (scientific calculators are optional)
- * paper plates, generic, 9 inch diameter
- * masking tape
- * clear tape
- meter sticks
- index cards
OCCASIONAL OR SINGLE USE
- metric ruler
- drawing compass
- * thread
- * straight pins
- size-D battery, dead or alive
- * straws
- * hand lenses
- coins (U.S. pennies, nickels, quarters)
- * clay
- dark construction paper (black, dark blue, etc.)
- standard hole punch
- corrugated cardboard
- current calendar with moon phases
- small jars or cans
- box or grocery bag to carry stuff
- packaging tape
- clip board for recording observations outside
- mirror (optional)
Solar Eclipse Viewing Glasses
CE Certified for solar viewing - use with book #40 The Earth Moon and Sun and #45 Pi in the Sky
Special offer for the 2014 partial solar eclipse on October 23rd. Most of North America will be able to see a partial eclipse, which will be especially dramatic in the northern states and Canada. While supplies last, get yours today!
Please remember that looking at a solar eclipse without proper eye protection can be very dangerous. Only look directly at the sun with solar eclipse viewing glasses.
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.
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.)
9-inch diameter, generic white
A classic ripple edge-design, with wide application in TOPS experiments. Buy these here for convenience, or for less at your local grocery store.
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.
Tape - masking
3/4 inch x 55 yd roll
A handy science supply used in most TOPS modules.
light duty, 25 yd spool
Just plain old thread. Used in many TOPS titles, especially in Pendulums #34.
Teaching Tips for #45 Pi in the Sky:
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 #45 Pi in the Sky:
These 37 labs 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 37 labs 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: Objects appear as large as the angle they subtend in your field of view. Thus, you can hide the Sun with your thumb.
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: Estimate the angular size of the moon in radians. Does it really seem that small?
Earth and Space Science (content standard D)
NSES Framework: Objects in the sky Changes in earth and sky Earth in the solar system
Core Content: Create simple instruments that measure the apparent angular size of distant objects. Estimate real size and real distance as astronomers do. Understand the geometry of subtended angles; the astronomy of apparent size.
History and Nature of Science (content standard G)
NSES Framework: Science as a human endeavor History of science
Core Content: Ancient Arabian navigators sailed north or south until their Kamal (a rectangle of wood on a knotted string) fit perfectly between Polaris and their horizon. Then they "sailed their latitude" to home port.