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In this lesson, students explore how variations in the shape, color, and other characteristics of solar collectors affect the energy absorbed. Students make rectangular prisms that have the same volume but different linear dimensions.
In this lesson, students explore how variations in the shape, color, and other characteristics of solar collectors affect the energy absorbed. Students make rectangular prisms that have the same volume but different linear dimensions. After measuring the volume of several boxes with unit cubes, they develop the formula for the volume of a rectangular prism. They consider several other factors besides shape in experimenting to see what kind of solar collector is most efficient. This lesson is a nice integration of mathematics and science. (author/sw)
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Career-technical teachers will find this lesson has a lot to offer students in any field that uses measurements in the development of a product. The lesson integrates mathematics and science topics as students investigate what makes solar collectors effective and explore how prisms with different dimensions can have the same volume.
Career-technical teachers will find this lesson has a lot to offer students in any field that uses measurements in the development of a product. The lesson integrates mathematics and science topics as students investigate what makes solar collectors effective and explore how prisms with different dimensions can have the same volume. Although the lesson can be used with little modification in the high school career-tech setting, learning could be enriched by having students examine in depth the functioning of solar collectors and evaluate their impact on the environment. (jrs)
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| Mathematics Academic Content Standards |
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| Measurement Standard |  |
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| Benchmarks (3 - 4) |
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| D. | Identify appropriate tools and apply counting techniques for measuring side lengths, perimeter and area of squares, rectangles, and simple irregular two-dimensional shapes, volume of rectangular prisms, and time and temperature. |
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| Benchmarks (5 - 7) |
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| C. | Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders. |
| E. | Use problem solving techniques and technology as needed to solve problems involving length, weight, perimeter, area, volume, time and temperature. |
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| Benchmarks (8 - 10) |
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| B. | Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision. |
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| Grade Level Indicators (Grade 3) |
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| 5. | Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest 1/2 or 1/4 unit as appropriate. |
| 6. | Use appropriate measurement tools and techniques to construct a figure or approximate an amount of specified length, weight or volume (capacity); e.g., construct a rectangle with length 2-1/2 inches and width 3 inches, fill a measuring cup to the 3/4 cup mark. |
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| Grade Level Indicators (Grade 4) |
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| 2. | Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object. |
| 4. | Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume. |
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| Grade Level Indicators (Grade 5) |
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| 6. | Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. |
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| Grade Level Indicators (Grade 7) |
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| 5. | Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems. |
| 6. | Use strategies to develop formulas for finding area of trapezoids and volume of cylinders and prisms. |
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| Grade Level Indicators (Grade 8) |
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| 4. | Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find:
a. the surface area of a cylinder as a function of its height and radius; and
b. that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height. |
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| Principles and Standards for School Mathematics |
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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 (6 - 8) |
| understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. |
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| Apply appropriate techniques, tools, and formulas to determine measurements. |
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| Expectations (3 - 5) |
| select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles; |
| develop strategies to determine the surface areas and volumes of rectangular solids. |
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| Expectations (6 - 8) |
| understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume. |
| develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders; |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Best Practice |
| STANDARDS ALIGNMENT |
| Grades 3 - 8 |
| CAREER FIELDS |
Agricultural & Environmental Systems;
Construction Technologies;
Engineering & Science Technologies;
Manufacturing Technologies |
| TOPICS |
Mathematics --
Measurement;
Plane area;
Volume |
| FOUND IN |
| Standards First |
| KEYWORDS |
rectangular prism;
interdisciplinary;
solar collector |
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Publisher: National Council of Teachers of Mathematics
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