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This lesson features three activities to promote number sense with large numbers, fractions, and decimal operations. In the first activity, students use proportional reasoning to determine whether $1 million in $1 bills would fit in a suitcase and how much it would weigh.
This lesson features three activities to promote number sense with large numbers, fractions, and decimal operations. In the first activity, students use proportional reasoning to determine whether $1 million in $1 bills would fit in a suitcase and how much it would weigh. In the second activity, students use circular regions to develop their sense of the relative sizes of fractions between 0 and 1. In the third activity, students play a game that develops their sense of the effect that operations with decimal numbers have on the size of the answer. The website includes a lengthy and detailed discussion of the various kinds of number sense students need to develop, complete with specific examples of different levels of understanding. Activity sheets are included. (sw)
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Number sense is a particularly important skill in most career technical fields, since students need to understand if and when a particular answer is logical and reasonable. Practical, on-the-job applications of mathematical concepts almost always begin with estimation and proceed to precise calculation.
Number sense is a particularly important skill in most career technical fields, since students need to understand if and when a particular answer is logical and reasonable. Practical, on-the-job applications of mathematical concepts almost always begin with estimation and proceed to precise calculation. Students need extensive practice in comparing their estimated answer with the precise calculation. While this lesson is not specific to a particular career field, the instructor can craft similar lessons which use the elements of the field. The suitcase example can be re-written as a shipping problem while the comparison of fractions activity and the decimal game can be can be incorporated into lessons on measurement and tolerances.
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| Mathematics Academic Content Standards |
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| Number, Number Sense and Operations Standard |  |
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| Benchmarks (5 - 7) |
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| B. | Compare, order and convert among fractions, decimals and percents. |
| I. | Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents. |
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| Benchmarks (8 - 10) |
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| F. | Explain the effects of operations on the magnitude of quantities. |
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| Grade Level Indicators (Grade 5) |
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| 13. | Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. |
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| Grade Level Indicators (Grade 6) |
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| 10. | Recognize that a quotient may be larger than the dividend when the divisor is a fraction; e.g., 6 divided by 1/2 = 12. |
| 13. | Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., 7/8 + 12/13 = 2 and 4.23 x 5.8 25. |
| 14. | Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions. |
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| Grade Level Indicators (Grade 9) |
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| 3. | Explain the effects of operations such as multiplication or division, and of computing powers and roots on the magnitude of quantities. |
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| Measurement Standard |  |
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| Benchmarks (5 - 7) |
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| 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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| Grade Level Indicators (Grade 7) |
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| 4. | Solve problems involving proportional relationships and scale factors; e.g., scale models that require unit conversions within the same measurement system. |
| 5. | Analyze problem situations involving measurement concepts, select appropriate strategies, and use an organized approach to solve narrative and increasingly complex problems. |
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| Principles and Standards for School Mathematics |
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| Number and Operations Standard |  |
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| Understand numbers, ways of representing numbers, relationships among numbers, and number systems |
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| Expectations (6 - 8) |
| compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line; |
| understand and use ratios and proportions to represent quantitative relationships; |
| develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation; |
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| Understand meanings of operations and how they relate to one another |
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| Expectations (6 - 8) |
| compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line; |
| understand and use ratios and proportions to represent quantitative relationships; |
| develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation; |
| understand the meaning and effects of arithmetic operations with fractions, decimals, and integers; |
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| Compute fluently and make reasonable estimates |
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| Expectations (6 - 8) |
| compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line; |
| understand and use ratios and proportions to represent quantitative relationships; |
| develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation; |
| understand the meaning and effects of arithmetic operations with fractions, decimals, and integers; |
| develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results; |
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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) |
| solve problems involving scale factors, using ratio and proportion; |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Best Practice |
| STANDARDS ALIGNMENT |
| Grades 5 - 9 |
| CAREER FIELDS |
| General Career Skills |
| TOPICS |
Mathematics -- Numbers and Operations; Decimals; Fractions; Whole numbers; Number sense |
| FOUND IN |
| Standards First |
| KEYWORDS |
| game |
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Author: Barbara J. Reys et al. Publisher: National Council of Teachers of Mathematics
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