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Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation, and the graphing calculator. The lesson starts with the presentation of the yo-yo problem.
Students explore linear patterns, write a pattern in symbolic form, and solve linear equations using algebra tiles, symbolic manipulation, and the graphing calculator. The lesson starts with the presentation of the yo-yo problem. Students then complete a hands-on design created with pennies that allows them to explore a linear pattern and express that pattern in symbolic form. Next, students solve a linear equation using algebra tiles. (Familiarity with the tiles is assumed.) Working from the concrete to the abstract is especially important for students who have difficulty with mathematics, and algebra tiles help students make this transition. In addition to using algebra tiles, students also use symbolic manipulation and the graphing calculator to solve the same linear equation. Finally, the students return to solve the yo-yo problem. A special feature of this lesson is the effective use of peer tutors in an inclusion classroom. 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 lesson plan is accompanied by video clips illustrating lesson procedures. The user should first locate the Yo-Yo Problem 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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algebra tiles
computer
graphing calculator
Internet connection
overhead display device |
| Adobe Acrobat Reader |
| This technology integrated lesson provides an opportunity for the introduction or reinforcement of the following technology skills: |
| Grades 6-8 |
| Use the internet to explore mathematical concept |
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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| A. | Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications. |
| B. | Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules. |
| C. | Use variables to create and solve equations and inequalities representing problem situations. |
| D. | Use symbolic algebra to represent and explain mathematical relationships. |
| 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. |
| H. | Solve linear equations and inequalities symbolically, graphically and numerically. |
| I. | Explain how inverse operations are used to solve linear equations. |
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| Benchmarks (8 - 10) |
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| A. | Generalize and explain patterns and sequences in order to find the next term and the nth term. |
| B. | Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations. |
| D. | Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. |
| F. | Solve and graph linear equations and inequalities. |
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| Grade Level Indicators (Grade 5) |
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| 1. | Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. |
| 3. | Use variables as unknown quantities in general rules when describing patterns and other relationships. |
| 4. | Create and interpret the meaning of equations and inequalities representing problem situations. |
| 5. | Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. |
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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. |
| 3. | Recognize and generate equivalent forms of algebraic expressions, and explain how the commutative, associative and distributive properties can be used to generate equivalent forms; e.g., perimeter as 2(1 + w) or 21 + 2w. |
| 4. | Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs. |
| 5. | Produce and interpret graphs that represent the relationship between two variables. |
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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. |
| 2. | Generalize patterns by describing in words how to find the next term. |
| 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. |
| 4. | Create visual representations of equation-solving processes that model the use of inverse operations. |
| 5. | Represent linear equations by plotting points in the coordinate plane. |
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| Grade Level Indicators (Grade 8) |
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| 2. | Generalize patterns and sequences by describing how to find the nth term. |
| 3. | Identify functions as linear or nonlinear based on information given in a table, graph or equation. |
| 5. | Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. |
| 7. | Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. |
| 9. | Solve linear equations and inequalities graphically, symbolically and using technology. |
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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. |
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| Principles and Standards for School Mathematics |
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| Number and Operations Standard | |
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| Understand meanings of operations and how they relate to one another |
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| Expectations (6 - 8) |
| understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems. |
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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. |
| develop an initial conceptual understanding of different uses of variables; |
| use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; |
| recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. |
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| Expectations (9 - 12) |
| write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases; |
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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. |
| develop an initial conceptual understanding of different uses of variables; |
| use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; |
| recognize and generate equivalent forms for simple algebraic expressions and solve linear equations. |
| model and solve contextualized problems using various representations, such as graphs, tables, and equations. |
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| Expectations (9 - 12) |
| write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency—mentally or with paper and pencil in simple cases and using technology in all cases; |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Promising Practice |
| STANDARDS ALIGNMENT |
| Grades 5 - 9 |
| TOPICS |
Mathematics --
Algebra;
Linear equations;
Patterns, sequences;
Communication;
Representation;
Technology |
| FOUND IN |
| COR |
| KEYWORDS |
algebra tiles;
graphing calculator;
peer tutoring |
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Publisher: Public Broadcasting Service
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