Graphing #03

(grades 6-10)
Soft-bound, 56 page book, 20 reproducible task cards, full teaching notes.

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Measure variables, generate date tables and plot graphs. Interpreted slopes and curves in terms of concrete reality – the stretch in a rubber band or the curve in a bottle. Be amazed by unusual coordinate systems and reflecting graphs.

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Table of Contents for #03 Graphing:

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. 1. Ordered Pairs (1)
  2. 2. Ordered Pairs (2)
  3. 3. Book Leaves (1)
  4. 4. Book Leaves (2)
  5. 5. Extrapolating Book Leaves
  6. 6. Container Curves (1)
  7. 7. Container Curves (2)
  8. 8. Container Curves (3)
  9. 9. Squares of Water
  10. 10. What's the Point?
  11. 11. Directly Proportional?
  12. 12. Pi Graph
  13. 13. Stretch Graph (1)
  14. 14. Stretch Graph (2)

  16. 15. Funny Flower
  17. 16. Crazy Graph
  18. 17. Circle Graph (1)
  19. 18. Circle Graph (2)
  20. 19. Double Grow Graph
  21. 20. A Family of Mice

Supplementary Pages

metric rulers • circular grid


Complete Master List for #03 Graphing:

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. 1/10/10: textbooks with a least 400 pages
  2. 2/20/20: index cards, 4x6 inches or larger
  3. 1/10/10: pairs of scissors
  4. * 1/1/1: spool of thread
  5. * 1/1/1: roll of masking tape
  6. 1/5/10: 100 mL graduated cylinders (or any narrow, straight sided container)
  7. 3/15/30: 100 mL beakers (or any wider, straight sided container)
  8. * 1/5/10: large test tubes
  9. * 1/5/10: drinking glasses with tapered sides
  10. 1/5/10: Erlenmeyer flasks, 100 mL or larger (or an oddly shaped container of similar capacity)

  11. * 0.3/1/3: cups oil-based clay
  12. * 1/5/10: small test tubes
  13. 4/20/40: cylinders of various sizes and kinds, including cans, bottles, and lids
  14. 1/1/1: roll string
  15. 1/5/10: calculators
  16. 1/5/10: soup cans or equivalent
  17. * 1/10/10: medium rubber band, about 2 1/2 inches long
  18. * 2/20/20: paper clips
  19. 1/10/10: sheets lined notebook paper
  20. 1/5/10: metric rulers
  21. 1/4/10: pieces chrome-plated pipe (or shiny mixing bowls)

Convenient Shopping:

Cups - plastic

9 or 10 ounce; clear, flexible, plastic

"Solo" brand or equivalent sold in grocery stores is suitable. Avoid brittle plastic. Used in #16 Pressure.

Tape - masking

3/4 inch x 55 yd roll

A handy science supply used in most TOPS modules.

Clay - modeling

oil-based, non-drying

Sold by the 100 gram stick, about 1/4 cup, in assorted colors (our choice). One stick serves a whole classroom for TOPS applications.

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.

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.

Test Tube - large disposable

36 mL capacity, 20 mm OD, 6 inch (150 mm) length

A lighter weight rimless Pyrex test tube made with thinner glass.

Test Tube - large reusable

34 mL capacity, 20 mm OD, 6 inch (150 mm) length

A tough Pyrex test tube made with rim and thicker glass. Has a white spot for labeling.

Test Tube - small disposable

6 mL capacity, 12 mm OD, 3 inch (75 mm) length

A lighter weight rimless Pyrex test tube made with thinner glass.

Test Tube - small reusable

9 mL capacity with 13 mm OD and 4 inch (100 mm) length

A tough Pyrex test tube made with rim and thicker glass. Has a white spot for labeling.


light duty, 25 yd spool

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

Teaching Tips for #03 Graphing:

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 #03 Graphing:

  1. Lesson 1: To practice plotting ordered pairs of whole numbers on a coordinate system.
  2. Lesson 2: To plot ordered pairs on coordinate systems with different scales. To practice estimating between graph lines when placing points.
  3. Lesson 3: To graph how the thickness of a book increases with its number of leaves.
  4. Lesson 4: To compare data that is read from a graph with actual measurements. To interpret the physical significance of the slope.
  5. Lesson 5: To extrapolate straight lines graphs. To check the validity of each extension mathematically.
  6. Lesson 6: To graph how the height of water in uniform cylinders changes with increasing volume.
  7. Lesson 7: To graph how the height of water in non-uniform cylinders changes with increasing volume.
  8. Lesson 8: To graph how the height of water in non-empty containers changes with increasing volume.
  9. Lesson 9: To summarize the physical significance of graph lines as they relate to containers of various sizes and shapes.
  10. Lesson 10: To discover that the ratio of coordinates (y/x) is constant for points that lie on any common straight line intersecting (0,0).
  11. Lesson 11: To decide by graphing whether two variables are directly proportional.
  12. Lesson 12: To graph how the diameter of a cylinder is related to its circumference.
  13. Lesson 13: To graph how a rubber band stretches with increasing weight.
  14. Lesson 14: To investigate how rubber bands stretch differently when paired in series and in parallel.
  15. Lesson 15: To map ordered pairs from one coordinate system onto another. To understand how the shape and size of a graph is altered by changing its scale.
  16. Lesson 16: To map ordered pairs onto a novel coordinate system of each student's own design. To appreciate how the shape of a graph is distorted by changing its coordinate system.
  17. Lesson 17: To map ordered pairs onto circular graph paper. To discover that a circular mirror transforms the circular figure back to rectangular dimensions.
  18. Lesson 18: To map simple geometric figures onto circular graph paper so their images, reflected from a circular mirror, appear normal.
  19. Lesson 19: To select suitable scales for a population graph. To appreciate how doubling population growth 'explodes' off the graph.
  20. Lesson 20: To graph birth rate and total population for a family of mice. To compare the environmental impact of mice with human beings.

National Science Education Standards (NRC 1996) for #03 Graphing:

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: 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 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
Core Concepts/Processes: Change can be measured and graphed to represent linear systems (straight lines) and nonlinear systems (curved lines).

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: Collect, organize, record, and plot data to relate graph shapes to physical shapes and dynamic systems. • Distort graph shapes by mapping ordered pairs onto novel grid systems.

Science in Personal and Social Perspectives (content standard F)

NSES Framework: Populations, resources and environments
Core Content: Track the explosive exponential growth of population curves. What are the implications for the quality of life on planet Earth?