1

An Overview of the Number and Operations Standard for School Mathematics? 2

3 Instructional programs from prekindergarten through grade 12 should enable all students to— Number & Operations Standard Understand numbers, ways of representing numbers, relationships among numbers, and number systems; Understand meanings of operations and how they relate to one another; Compute fluently and make reasonable estimates.

4 Number & Operations Standard for Grades 6 – 8.

5 Understand numbers, ways of representing numbers, relationships among numbers, and number systems Students should become facile in working with fractions, decimals, and percents; Students should consider the advantages and disadvantages of working with various representatives of quantities; Students should continue to work with whole numbers and develop a sense of magnitude of very large numbers; Students should work with whole numbers in their study of number theory.

6 Understand meanings of operations and how they relate to one another Students should continue to refine their understanding of addition, subtraction, multiplication and division as they use these operations with fractions, decimal, percents, and integers; Students understanding of operations can be enhanced as they examine the validity and utility of properties of operations such as commutative and associative properties; Students should continue their study of inverses with fractions, decimals and integers.

7 Compute fluently and make reasonable estimates. Students should acquire the ability to compute efficiently and accurately with fractions, decimals, and integers; Teachers should help students learn how to decide when exact answers or an estimate would be more appropriate; Students should develop and adapt procedures for mental calculations and computational estimation with fractions, decimals, and integers; Teachers should help students learn how to decide when and what technology to use in solving a problem.

8 Number & Operations Standard for Grades 9 – 12.

9 Understand numbers, ways of representing numbers, relationships among numbers, and number systems Students should become increasingly facile in dealing with very large and very small numbers; Students should become familiar with different representations of numbers including those of calculator representation; Students should understand the progression and the kinds of equations that can be solved in each number system; continued

10 Understand numbers, ways of representing numbers, relationships among numbers, and number systems Students should have an understanding of the system of real numbers; Students should use their understanding of numbers to explore new systems, such as vectors and matrices;

11 Understand meanings of operations and how they relate to one another Students should learn to consider operations in general ways rather than only with particular computations; Students should extend their understanding of operations to number systems that are new to them; Students should learn how to compute permutations and combinations without the use of organized list and tree diagrams.

12 Compute fluently and make reasonable estimates. Students should be able to decide whether a problem calls for a rough estimate, an approximation to an appropriate degree of precision, or an exact answer; Students should be able to select a suitable method of computing from among mental mathematics, paper and pencil calculations, and the use of calculators and computers and be proficient with each.

13 Working in groups (7-8, 9-10 and 11-12), develop a lesson for students in that band width that will illustrate at least one of the bullets in the number and operations standard. We will leave time at the end of the period to present your ideas. Use the format that we have been working with in this class. Pick a topic and develop the way in which you will present it so that at least one of the bullets is used. You are also expected to use bullets from the process standards.

14 Assignment Read: NCTM Principles and Standards p 67-71, , and