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Stacking Cans & Cups Investigation

Stacking Cans & Cups Investigation. A Closer Look at the Cups. Let’s collect a more complete data set. Record the following four data points on your rough draft paper. 5 cups ? cm. 8 cups ? cm. 12 cups ? cm. 15 cups ? cm.

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Stacking Cans & Cups Investigation

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  1. Stacking Cans & Cups Investigation A Closer Look at the Cups

  2. Let’s collect a more completedata set.

  3. Record the following four data points on your rough draft paper.

  4. 5 cups ? cm

  5. 8 cups ? cm

  6. 12 cups ? cm

  7. 15 cups ? cm

  8. Analyze this data with words, tables, graphs, and equations.

  9. Rule of Four Multiple Representations of Mathematical Functions 1. Verbal representations:WORDS 2. Numerical representations:TABLES 3. Graphical representations:GRAPHS 4. Symbolic representations:EQUATIONS

  10. Explicit Formula h(c) = ? Recursive Formula h(0) = ? h(c) = ?

  11. Stacking Cans & Cups Investigation Extension

  12. Extension:Use your data from this task to compute the height of theEmpire State Buildingin: CANS CUPS

  13. A debrief of the data from one kind of coffee cup. (Your data might be different)

  14. y = 1.62x + 9.39

  15. y = 1.62x + 9.39

  16. Formalizing the Mathematics … y=1.62x+ 9.39 x = the number of cups y = the height of the stack (cm) rate of change = 1.62 cm/cup y-intercept = 9.39 cm UNITS MATTER! Zero Cups ? (0, 0) or (0, 9.39) ?

  17. y=1.62x+ 9.39 Zero Cups ? (0, 0) or (0, 9.39) ? DISCRETE DATA Explain the meaning of each ordered pair: real world vs. our model

  18. y=1.62x+ 9.39 Domain of the model: 1, 2, 3, 4, … Range of the model: 11.01, 12.63, 14.25, 15.87, …

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