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This lesson integrates ideas from geometry, measurement, and algebra. Students measure the length and width of a rectangle using at least six different standard and nonstandard units of measure.
This lesson integrates ideas from geometry, measurement, and algebra. Students measure the length and width of a rectangle using at least six different standard and nonstandard units of measure. Then they plot the (length, width) ordered pairs on the usual coordinate axes. Their challenge is to discover that the ordered pairs fall along a straight line whose slope represents the constant ratio of width to length regardless of the unit of measure. An activity sheet, discussion questions, suggestions for assessment, lesson extensions, and questions for teacher reflection are included. (sw)
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This best practice lesson can be useful to the mathematics teacher working with career-technical students because it combines concepts from geometry, measurement, and algebra that have real world applications. The lesson allows students to use a hand-on approach to measurement with both standard and non-standard units and to explore the meaning of slope and constant ratio as displayed on a graph.
This best practice lesson can be useful to the mathematics teacher working with career-technical students because it combines concepts from geometry, measurement, and algebra that have real world applications. The lesson allows students to use a hand-on approach to measurement with both standard and non-standard units and to explore the meaning of slope and constant ratio as displayed on a graph. (jrs)
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| Mathematics Academic Content Standards |
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| Measurement Standard |  |
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| Benchmarks (5 - 7) |
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| D. | Select a tool and measure accurately to a specified level of precision. |
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| Grade Level Indicators (Grade 7) |
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| 3. | Estimate a measurement to a greater degree of precision than the tool provides. |
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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. |
| F. | Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships. |
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| Benchmarks (8 - 10) |
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| D. | Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations. |
| J. | Describe and interpret rates of change from graphical and numerical data. |
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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. |
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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. |
| 5. | Produce and interpret graphs that represent the relationship between two variables. |
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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; |
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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; |
| 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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| 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; |
| 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; |
| use graphs to analyze the nature of changes in quantities in linear relationships. |
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| Measurement Standard | |
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| Apply appropriate techniques, tools, and formulas to determine measurements. |
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| Expectations (6 - 8) |
| select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision; |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Best Practice |
| STANDARDS ALIGNMENT |
| Grades 5 - 8 |
| CAREER FIELDS |
| General Career Skills |
| TOPICS |
Mathematics --
Algebra;
Linear functions;
Connections, applications |
| FOUND IN |
| Standards First |
| KEYWORDS |
| slope |
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Author: Kristen Chandler
Publisher: National Council of Teachers of Mathematics
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