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The National Council of Teachers of Mathematics (NCTM, 2000) has identified number and operations as a strand in its Principles and Standards for School Mathematics. In grades pre-K through 12, instructional programs should enable all students to do the following:
• | Understand numbers, ways of representing numbers, relationships among numbers, and number systems |
• | Understand the meaning of operations and how they relate to one another |
• | Compute fluently and make reasonable estimates |
In grades 6-8 classrooms, students are expected to do the following:
• | Develop, analyze, and explain methods for solving problems involving proportions |
• | Work flexibly with fractions, decimals, and percents to solve problems |
• | Compare and order fractions, decimals, and percents efficiently, and find their approximate locations on a number line |
• | Develop an understanding of large numbers, and recognize and appropriately use exponential, scientific, and calculator notation |
• | Develop meaning for integers, and use them to represent and compare quantities |
• | Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results |
"In the middle-grades mathematics classrooms, young adolescents should regularly engage in thoughtful activity tied to their emerging capabilities of finding and imposing structure, conjecturing and verifying, thinking hypothetically, comprehending cause and effect, and abstracting and generalizing" (NCTM, 2000, p. 211).
Watch another segment from Ms. Miles's class, and think about how the students are developing this understanding of number and operations.
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