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The major goal of this lesson is to collect data from a variety of experiments, determine what type of model best fits the data, and explain why. Students explore a variety of relationships using pennies, pressure, temperature, light, and pendulums to determine the algebraic equation that best represents the pattern modeled by the variables involved in each situation.
The major goal of this lesson is to collect data from a variety of experiments, determine what type of model best fits the data, and explain why. Students explore a variety of relationships using pennies, pressure, temperature, light, and pendulums to determine the algebraic equation that best represents the pattern modeled by the variables involved in each situation. The lesson begins with a review of the cooling curve and a discussion of the algebraic model that best represents those data. The students are then assigned five experiments: (1) distance and the number of pennies that can be balanced on the overhanging end of a ruler, (2) pressure and volume, (3) distance and light intensity, (4) mass and distance from the center in a see-saw situation, and (5) what determines the period of a pendulum. In addition to the lesson plan, the site includes ideas for assessment, teacher discussion, extensions of the lesson, additional resources, and a discussion of the mathematical content. This lesson is accompanied by video clips illustrating lesson procedures. Two of the five experiments are discussed in the video, but all five are included in the written lesson guide. The user should first locate the Pennies, Pressure, Temperature, and Light lesson and then access the appropriate video clips at the PBS TeacherSource website. The video player necessary to view the video clips can be downloaded for free from the site. (author/pk)
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This lesson offers an excellent way for students to demonstrate how the laws of physics relate to specific career pathways. Students work in groups, solve the given problem, and explain how the factors relate to their specific career-technical field.
This lesson offers an excellent way for students to demonstrate how the laws of physics relate to specific career pathways. Students work in groups, solve the given problem, and explain how the factors relate to their specific career-technical field. Newton's Law of Cooling applies to the measurement of the basic thermal properties in polymers, as well as in the fields of Transportation and Manufacturing Technologies. Boyle's Law is needed when studying hydraulics and pneumatics in the Engineering and Science Technologies career field. Boyle's Law can also be applied in problems of heat transfer and the harnessing of unused heat energy.
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computer data collection probe graphing calculator Internet connection |
| Adobe Acrobat Reader |
| This technology integrated lesson provides an opportunity for the introduction or reinforcement of the following technology skills: |
| Grades 9-12 |
Gather and analyze data. Explore Mathematical Concept |
| Data Collection Probes |
structured activity website |
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| Mathematics Academic Content Standards |
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| Measurement Standard |  |
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| Benchmarks (8 - 10) |
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| F. | Write and solve real-world, multi-step problems involving money, elapsed time and temperature, and verify reasonableness of solutions. |
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| Benchmarks (11 - 12) |
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| B. | Apply various measurement scales to describe phenomena and solve problems. |
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| Patterns, Functions and Algebra Standard |  |
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| Benchmarks (8 - 10) |
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| I. | Model and solve problem situations involving direct and inverse variation. |
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| Grade Level Indicators (Grade 10) |
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| 10. | Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions. |
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| Data Analysis and Probability Standard |  |
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| Benchmarks (11 - 12) |
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| A. | Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators. |
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| Grade Level Indicators (Grade 11) |
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| 4. | Create a scatterplot of bivariate data, identify trends, and find a function to model the data. |
| 5. | Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation. |
| 8. | Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. |
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| Mathematical Processes Standard |  |
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| Benchmarks (8 - 10) |
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| B. | Apply mathematical knowledge and skills routinely in other content areas and practical situations. |
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| Benchmarks (11 - 12) |
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| H. | Use formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations. |
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| Principles and Standards for School Mathematics |
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| Algebra Standard |  |
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| Understand patterns, relations, and functions |
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| Expectations (9 - 12) |
| understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions; |
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| Use mathematical models to represent and understand quantitative relationships |
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| Expectations (9 - 12) |
| understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions; |
| identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships; |
| draw reasonable conclusions about a situation being modeled. |
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| Measurement Standard |  |
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| Understand measurable attributes of objects and the units, systems, and processes of measurement |
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| Expectations (9 - 12) |
| make decisions about units and scales that are appropriate for problem situations involving measurement. |
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| Data Analysis and Probability Standard |  |
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| Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them |
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| Expectations (9 - 12) |
| understand histograms, parallel box plots, and scatterplots and use them to display data; |
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| Select and use appropriate statistical methods to analyze data |
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| Expectations (9 - 12) |
| understand histograms, parallel box plots, and scatterplots and use them to display data; |
| for bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools; |
| identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled. |
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| Connections Standard |  |
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| Recognize and apply mathematics in contexts outside of mathematics |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Best Practice |
| STANDARDS ALIGNMENT |
| Grades 10 - 12 |
| CAREER FIELDS |
Construction Technologies; Manufacturing Technologies; Transportation Systems |
| TOPICS |
Mathematics -- Algebra; Graphing; Nonlinear functions; Linear functions; Measurement; Length, distance; Volume; Time; Temperature; Weight, mass; Connections, applications; Statistics; Data display; Technology |
| FOUND IN |
COR Standards First |
| KEYWORDS |
inverse function; CBL; graphing calculator; curve of best fit; line of best fit |
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Publisher: Public Broadcasting Service
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