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Expectations from the Number and Operations Standard

Expectations from the Number and Operations Standard . Principles and Standards for School Mathematics National Council of Teachers of Mathematics 2000. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Grades 3-5

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Expectations from the Number and Operations Standard

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  1. Expectations from the Number and Operations Standard Principles and Standards for School Mathematics National Council of Teachers of Mathematics 2000

  2. Understand numbers, ways of representing numbers, relationships among numbers, and number systems. Grades 3-5 • Describe classes of numbers according to characteristics such as the nature of their factors. Grades 6-8 • Use factors, multiples, prime factorization, and relatively prime numbers to solve problems. • Develop meaning for integers and represent and compare quantities with them.

  3. Understand meanings of operations and how they relate to one another. Grades 6-8 • Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

  4. The Algebra Standard Principles and Standards for School Mathematics National Council of Teachers of Mathematics 2000

  5. Instructional programs from pre-kindergarten through grade 12 should enable all students to: • Understand patterns, relations, and functions. • Represent and analyze mathematical situations and structures using algebraic symbols .

  6. Instructional programs from pre-kindergarten through grade 12 should enable all students to: • Use mathematical models to represent and understand quantitative relationships. • Analyze change in various contexts

  7. Number Patterns • Circle 2 on your hundred board, thencover or mark out every multiple of 2remaining on the board. • Circle 3 on your hundred board (the next unmarked number following 2). Cover or mark out every multiple of 3 on the board, noting some have already been marked during the first step.

  8. Number Patterns (con’t) • What is the next unmarked number at the top of your board? Cover or mark out the multiples on the board. • Continue the process until the entire board is circled or marked. • Is there a pattern in the circled numbers? What is it?

  9. Consider the fractions:1234567899 9 9 9 9 9 9 9 9 • Think of each fraction as a division problem and compute each quotient. • Do you observe anything of interest? • Suppose a different denominator had been selected, for example 11.

  10. Look at the fractions through 1/11 through 6/11 repeating the process outlined above. • Do you observe any patterns? • Can you predict 7 ÷ 11 from the information gathered?

  11. Palindromes • These are word palindromes: WOW TOOT NOON • Are the following number palindromes? 6556 1231 44 232 9887 • How would you define palindrome? Circle all palindromes on the hundred chart.

  12. Palindromes • Consider 57. Can we transform 57 to form a palindrome? • Start with 57 + 75 = 132 (not a palindrome) • Try 132 + 231 = 363 (Palindrome!) • We call 57 a two-step palindrome.

  13. Palindromes • Choose another number and see how many steps it takes to form a palindrome. • Investigate other numbers on the hundred board. Mark one-step, two-step, three step palindromes using different colors for each category. Is there a pattern?

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