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In this lesson, students design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Using the data they gather in a table, students graph and write an equation for a line of best fit.
In this lesson, students design an experiment to model a leaky faucet and determine the amount of water wasted due to the leak. Using the data they gather in a table, students graph and write an equation for a line of best fit. They then use their derived equation to make predictions about the amount of water that would be wasted from one leak over a long period of time or the amount wasted by several leaks during a specific period of time. In addition to the lesson plan, the site includes ideas for teacher discussion, extensions of the lesson, additional resources, and a discussion of mathematical content. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Drip, Drop, Drip, Drop 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/sk)
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While this site is specified for grades 6-8, the lesson could easily be used in a high school classroom. Students in Manufacturing and Construction Technologies career fields can appreciate the central problem about water being wasted by plumbing or other mechanical system components.
While this site is specified for grades 6-8, the lesson could easily be used in a high school classroom. Students in Manufacturing and Construction Technologies career fields can appreciate the central problem about water being wasted by plumbing or other mechanical system components. The lesson is particularly appropriate for students studying plumbing and those interested in hydraulics. The skills involved include applying algebraic formulas, graphing, and charting techniques. The lesson suggests using a graphing calculator to model and predict results. Modeling and prediction are important skills that are applicable in all career-technical fields.
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computer
graphing calculator
Internet connection
timer/stopwatch |
| Adobe Acrobat Reader |
| This technology integrated lesson provides an opportunity for the introduction or reinforcement of the following technology skills: |
| Grades 6-8 |
| Gather and analyze data |
structured activity
website |
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| Mathematics Academic Content Standards |
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| Patterns, Functions and Algebra Standard | |
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| Benchmarks (5 - 7) |
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| B. | Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules. |
| E. | Use rules and variables to describe patterns, functions and other relationships |
| F. | Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships. |
| L. | Analyze functional relationships, and explain how a change in one quantity results in a change in the other. |
| M. | Approximate and interpret rates of change from graphical and numerical data. |
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| Benchmarks (8 - 10) |
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| B. | Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations. |
| C. | Translate information from one representation (words, table, graph or equation) to another representation of a relation or function. |
| D. | Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. |
| I. | Model and solve problem situations involving direct and inverse variation. |
| J. | Describe and interpret rates of change from graphical and numerical data. |
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| Grade Level Indicators (Grade 6) |
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| 1. | Represent and analyze patterns, rules and functions, using physical materials, tables and graphs. |
| 2. | Use words and symbols to describe numerical and geometric patterns, rules and functions. |
| 5. | Produce and interpret graphs that represent the relationship between two variables. |
| 8. | Use technology to analyze change; e.g., use computer applications or graphing calculators to display and interpret rate of change. |
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| Grade Level Indicators (Grade 7) |
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| 1. | Represent and analyze patterns, rules and functions with words, tables, graphs and simple variable expressions. |
| 3. | Recognize and explain when numerical patterns are linear or nonlinear progressions; e.g., 1,3,5,7... is linear and 1,3,4,8,16... is nonlinear. |
| 5. | Represent linear equations by plotting points in the coordinate plane. |
| 10. | Analyze linear and simple nonlinear relationships to explain how a change in one variable results in the change of another. |
| 11. | Use graphing calculators or computers to analyze change; e.g., distance-time relationships. |
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| Grade Level Indicators (Grade 8) |
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| 1. | Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. |
| 2. | Generalize patterns and sequences by describing how to find the nth term. |
| 4. | Extend the uses of variables to include covariants where y depends on x. |
| 6. | Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems. |
| 7. | Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. |
| 8. | Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. |
| 14. | Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation. |
| 15. | Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. |
| 16. | Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. |
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| Mathematical Processes Standard | |
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| Benchmarks (5 - 7) |
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| H. | Use representations to organize and communicate mathematical thinking and problem solutions. |
| I. | Select, apply, and translate among mathematical representations to solve problems; e.g., representing a number as a fraction, decimal or percent as appropriate for a problem. |
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| Benchmarks (8 - 10) |
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| E. | Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate mathematical ideas. |
| F. | Use precise mathematical language and notations to represent problem situations and mathematical ideas. |
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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 (6 - 8) |
| represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; |
| relate and compare different forms of representation for a relationship; |
| identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. |
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| Represent and analyze mathematical situations and structures using algebraic symbols |
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| Expectations (6 - 8) |
| represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; |
| relate and compare different forms of representation for a relationship; |
| identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. |
| explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; |
| use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; |
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| Use mathematical models to represent and understand quantitative relationships |
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| Expectations (6 - 8) |
| represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; |
| relate and compare different forms of representation for a relationship; |
| identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. |
| explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; |
| use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; |
| model and solve contextualized problems using various representations, such as graphs, tables, and equations. |
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| Analyze change in various contexts |
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| Expectations (6 - 8) |
| represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules; |
| relate and compare different forms of representation for a relationship; |
| identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. |
| explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; |
| use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; |
| model and solve contextualized problems using various representations, such as graphs, tables, and equations. |
| use graphs to analyze the nature of changes in quantities in linear relationships. |
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| Representation Standard | |
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| Create and use representations to organize, record, and communicate mathematical ideas |
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| Select, apply, and translate among mathematical representations to solve problems |
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| Use representations to model and interpret physical, social, and mathematical phenomena |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Best Practice |
| STANDARDS ALIGNMENT |
| Grades 6 - 8 |
| CAREER FIELDS |
Construction Technologies;
Manufacturing Technologies |
| TOPICS |
Mathematics --
Algebra;
Graphing;
Linear functions;
Measurement;
Volume;
Time;
Technology |
| FOUND IN |
COR
Standards First |
| KEYWORDS |
line of best fit;
variables;
TI-83 |
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Publisher: Public Broadcasting Service
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