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Expectations from the Number and Operations Standard

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Palindromes. Choose another number and see how many steps it takes to form a palindrome. ... two-step, three step palindromes using different colors for each ... – PowerPoint PPT presentation

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Title: Expectations from the Number and Operations Standard


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
Three Aspects of Algebraic Thinking
  • Equality
  • Change
  • Generalizations

8
Types of Patterns
  • Repeating Patterns-have a core with a repeating
    element
  • ab-two repeating elements in core.
  • Growing Patterns-have a core with a growing
    element
  • YBBYYBBBYYYBBBB

9
Number Patterns
  • Circle 2 on your hundred board, then cover or
    mark out every multiple of 2 remaining 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.

10
Number Patterns (cont)
  • 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?

11
Consider the fractions 1 2 3 4 5 6
7 8 99 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.

12
  • 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?

13
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.

14
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.

15
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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