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19 Cards in this Set
- Front
- Back
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Numeration system
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consists of a set of symbols and the rules for combining these symbols. Is a means of communicating.
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Numeral
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symbols or any appropriate combination of them. Names of numbers.
Connect abstract thought with the real world. |
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Number -
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- an abstract idea used in counting and measuring. A symbol which represents a number is called a numeral,
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Digit -
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a symbol (a number symbol, e.g. "3" or "7") used in numerals (combinations of symbols, e.g. "37"), to represent numbers
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What is the purpose of a numeration system?
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• To have a way to communicate
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We teach place value so that children learn
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the way number systems work.
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• Research says that almost all of the errors that children make in arithmetic are
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directly related to poorly developed place value concepts (ideas)
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For 496 we can explain:
400 + 90 + 6 (4 x 100) + (9 x 10) + (6 x 1) or (4x102)+(9x101)+(6x100) All of these representations mean the same thing. They are all called |
expanded notation.
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To interpret the numeral we depend upon
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exponentials.
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What is a code?
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-Write code means write numeral
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Any digit in base 10 has 3 values.
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They are face value, place value, and total value.
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Face value
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is the cardinality of the family of sets that is associated with a digit. It is stable. (no matter what it appears the same.)
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Place value
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is the value of the position the digit occupies. It is stable.
(Ex. 425 place value of 4 is 100) |
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Total value
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is face value x place value. It is variable.
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Base –Ten Place Value Numeration system
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is a set of symbols and the rules for combining these symbols.
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• Nonstandard interpretations enable teachers and students to
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think flexibly about place value ideas and make important connections between place value and arithmetic concepts they must learn.
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• Place value system evolved with these very important features:
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- There were only ten symbols or digits to be remembered
- The system had a zero, an important feature that most earlier systems lacked - The placement of a digit in a numeral had special numerical meaning |
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• The U.S. Bureau of Standards recommends omitting
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the commas in numerals with four digits or more.
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• An instructional sequence for Key Concepts
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1. Learning to regroup
2. Learning the significance of 10 3. Learning the place value significance of numbers greater than 19. 4. Stressing Regrouping 5. Counting by tens and ordering numbers 6. Avoiding reversals 7. Reading and writing numerals 8. Finding the nearest ten 9. Communicating 100 |
