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This lesson emphasizes patterns, discovery, and vocabulary by focusing on the basic connections between graphs, tables, and symbolic representations for lines, parabolas, inverse models, and exponential functions. Students investigate various patterns and models using the graphing calculator.
This lesson emphasizes patterns, discovery, and vocabulary by focusing on the basic connections between graphs, tables, and symbolic representations for lines, parabolas, inverse models, and exponential functions. Students investigate various patterns and models using the graphing calculator. This lesson is designed for first-year algebra students and is an ideal follow-up to a unit on lines. 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. The 39-page pdf file includes several pages of nice applications of the models presented. The lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Getting Out of Line 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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| Adobe Acrobat Reader |
| This technology integrated lesson provides an opportunity for the introduction or reinforcement of the following technology skills: |
| Grades 9-12 |
| Explore Mathematical Concept |
structured activity
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| Mathematics Academic Content Standards |
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| Patterns, Functions and Algebra Standard | |
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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. |
| E. | Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros. |
| I. | Model and solve problem situations involving direct and inverse variation. |
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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. |
| 7. | Use symbolic algebra (equations and inequalities), graphs and tables to represent 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. |
| 16. | Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. |
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| Grade Level Indicators (Grade 9) |
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| 2. | Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations. |
| 3. | Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations. |
| 5. | Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum. |
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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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| 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. |
| E. | Use a variety of mathematical representations flexibly and appropriately to organize, record and communicate 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) |
| identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. |
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| Expectations (9 - 12) |
| understand relations and functions and select, convert flexibly among, and use various representations for them; |
| analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior; |
| understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions; |
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| Use mathematical models to represent and understand quantitative relationships |
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| Expectations (6 - 8) |
| identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. |
| model and solve contextualized problems using various representations, such as graphs, tables, and equations. |
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| Expectations (9 - 12) |
| understand relations and functions and select, convert flexibly among, and use various representations for them; |
| analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior; |
| understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions; |
| identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships; |
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| Connections Standard | |
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| Recognize and apply mathematics in contexts outside of mathematics |
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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 8 - 10 |
| TOPICS |
Mathematics --
Algebra;
Graphing;
Nonlinear functions;
Linear functions;
Connections, applications;
Representation;
Technology |
| FOUND IN |
| COR |
| KEYWORDS |
| graphing calculator |
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Publisher: Public Broadcasting Service
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