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This site focuses on the genre of problems in which successive fractional parts of a set are removed, and the size of the original set is determined from the final remainder. Four ways of solving such problems are illustrated and discussed.
This site focuses on the genre of problems in which successive fractional parts of a set are removed, and the size of the original set is determined from the final remainder. Four ways of solving such problems are illustrated and discussed. Students work in groups to solve the "mangoes problem" and the "sailors and coconuts problem" with an eye toward communicating and appreciating different approaches to solving the problems. This lesson plan was adapted from an article that appeared in the November-December 1994 issue of Mathematics Teaching in the Middle School. (author/sw)
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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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| 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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| Grade Level Indicators (Grade 5) |
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| 12. | Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. |
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| Grade Level Indicators (Grade 6) |
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| 11. | Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning. |
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| Mathematical Processes Standard |  |
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| Benchmarks (5 - 7) |
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| A. | Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives. |
| B. | Apply and adapt problem-solving strategies to solve a variety of problems, including unfamiliar and non-routine problem situations. |
| C. | Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods. |
| J. | Communicate mathematical thinking to others and analyze the mathematical thinking and strategies of others. |
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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) |
| work flexibly with fractions, decimals, and percents to solve problems; |
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| Compute fluently and make reasonable estimates |
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| Expectations (3 - 5) |
| use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; |
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| Expectations (6 - 8) |
| work flexibly with fractions, decimals, and percents to solve problems; |
| select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods; |
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| Problem Solving Standard |  |
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| Solve problems that arise in mathematics and in other contexts |
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| Apply and adapt a variety of appropriate strategies to solve problems |
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| Monitor and reflect on the process of mathematical problem solving |
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| Communication Standard |  |
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| Organize and consolidate their mathematical thinking through communication |
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| Communicate their mathematical thinking coherently and clearly to peers, teachers, and others |
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| Analyze and evaluate the mathematical thinking and strategies of others; |
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| RESOURCE TYPE |
| Instructional Resource |
| PRACTICE LEVEL |
| Best Practice |
| STANDARDS ALIGNMENT |
| Grades 5 - 8 |
| TOPICS |
Mathematics -- Numbers and Operations; Fractions; Communication; Problem Solving |
| KEYWORDS |
| Chinese Remainder Theorem |
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Author: Jerry Stonewater Publisher: National Council of Teachers of Mathematics
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