# #03 Graphing (grades 6-10)

Regular price $15.95

*Soft-bound, 56 page book, 20 reproducible task cards, full teaching notes.*

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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textbook with a least 400 pages, index cards, 4x6 inches or larger, pairs of scissors, spool of thread, roll of masking tape, 100 mL graduated cylinders (or any narrow, straight sided container), 100 mL beakers (or any wider, straight sided container), large test tubes, drinking glasses with tapered sides, Erlenmeyer flasks, 100 mL or larger (or an oddly shaped container of similar capacity), cups oil-based clay, small test tubes, cylinders of various sizes and kinds, including cans, bottles, and lids, string, calculators, soup cans or equivalent, medium rubber band, paper clips, sheets lined notebook paper, metric rulers, pieces chrome-plated pipe (or shiny mixing bowls)-
**Lesson 1:**To practice plotting ordered pairs of whole numbers on a coordinate system. -
**Lesson 2:**To plot ordered pairs on coordinate systems with different scales. To practice estimating between graph lines when placing points. -
**Lesson 3:**To graph how the thickness of a book increases with its number of leaves. -
**Lesson 4:**To compare data that is read from a graph with actual measurements. To interpret the physical significance of the slope. -
**Lesson 5:**To extrapolate straight lines graphs. To check the validity of each extension mathematically. -
**Lesson 6:**To graph how the height of water in uniform cylinders changes with increasing volume. -
**Lesson 7:**To graph how the height of water in non-uniform cylinders changes with increasing volume. -
**Lesson 8:**To graph how the height of water in non-empty containers changes with increasing volume. -
**Lesson 9:**To summarize the physical significance of graph lines as they relate to containers of various sizes and shapes. -
**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). -
**Lesson 11:**To decide by graphing whether two variables are directly proportional. -
**Lesson 12:**To graph how the diameter of a cylinder is related to its circumference. -
**Lesson 13:**To graph how a rubber band stretches with increasing weight. -
**Lesson 14:**To investigate how rubber bands stretch differently when paired in series and in parallel. -
**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. -
**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. -
**Lesson 17:**To map ordered pairs onto circular graph paper. To discover that a circular mirror transforms the circular figure back to rectangular dimensions. -
**Lesson 18:**To map simple geometric figures onto circular graph paper so their images, reflected from a circular mirror, appear normal. -
**Lesson 19:**To select suitable scales for a population graph. To appreciate how doubling population growth 'explodes' off the graph. -
**Lesson 20:**To graph birth rate and total population for a family of mice. To compare the environmental impact of mice with human beings.

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 customerservice@topscience.org.

National Science Education Standards (NRC 1996)

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)

• 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.

#### 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*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?