Compare fractions_ decimals and percents around the benchmark by lanyuehua

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									Compare fractions, decimals and percents around the benchmark
numbers


In mathematics, number sense refers to the understanding of numbers, their
magnitude, the relationship between numbers, and how they are affected when
performing mathematical operations. Number sense also encompasses the ability to
compute operations mentally and to compare numbers correctly. Students who possess
good number sense are proficient in performing mental calculations, computational
estimation, judging the magnitude of numbers as fractions, decimals and percents and
problem-solving using fractions, decimals and percents.

Students who lack good number sense:

      Do not recognize that proper fractions are numbers greater than zero and less
       than one
      Do not recognize that improper fractions are numbers greater than one
      Do not understand what the term “percent” means
      Cannot locate numbers as fractions, decimals and percents on a number line
      Cannot convert numbers between fractions, decimals and percents
      Cannot perform basic operations using fractions, decimals and percents
      Cannot perform problems within applications when fractions, decimals and
       percents are used
      Cannot recognize the reasonableness of answers to problems when the answers
       are fractions, decimals or percents

A number sense game using the snow board model would require students to:

   1. Compare a fraction to a benchmark fraction. Benchmark fractions should be
      fractions whose denominators are 2, 3, 4, 5 or 10. Each progressive level of the
      game should require students to perform higher level skills.
          o Example: The flag has ¾ printed on it. The snowboarder is carrying the
             fraction ¼. Direct the snowboarder to the left of the flag if ¼ is less than
             ¾ and to the right of the flag if it is greater than ¾.
          o Example: The flag has ¾ printed on it and the snowboarder is carrying
             another fraction with a different denominator. Direct the snowboarder to
             the left or right correctly.
          o Example: The flag has 5/4 printed on it. The snowboarder is carrying 4/3.
             Direct the snowboarder to the left or right of the flag correctly.
2. Compare decimals to other decimals in the same way the comparisons are made
   in #1.
3. Compare a fraction to two given benchmark fractions.
       o Example: Two flags are given, the one on the left has ½ printed on it and
          the one on the right has ¾ printed on it. The snowboarder is carrying the
          fraction 3/5. Direct the snowboarder to the left, in between or to the right
          of the two given flags to show the location of 3/5 in comparison to ½ and
          ¾.
       o Example: Two flags are given, the one closest to the left has 2/5 printed
          on it and the one on the right has 17/10 printed on it. The snowboarder is
          carrying the fraction 3/2. Direct the snowboarder to show the location in
          comparison to the given fractions.
4. Compare a decimal to two given decimals in the same way the comparison is
   made in #4.
5. Compare a percent to two given percents in the same way the comparison is
   made in #4.
6. Compare fractions, decimals and percents. Each progressive level of the game
   should require students to perform higher level skills.
       o Example: One flag is given with the decimal 0.45 printed on it. The
          snowboarder is carrying the fraction 4/5. Direct the snowboarder to the
          left of the flag if 4/5 is less than 0.45 and to the right of the flag if 4/5 is
          greater than 0.45.
       o Example: Two flags are given, one with ¼ on it and the other with 60%
          on it. The snowboarder is carrying 0.75. Direct the snowboarder to the
          left, in between or to the right of the two flags to show the location of
          0.75 in comparison to ¼ and 60%.
Test Questions


2. Write each decimal as a simplified fraction or mixed number:
      2a) 0.005
      2b) 2.45
      2c) 15.028

3. Write each fraction or mixed number as a decimal:
            15
      3a)
           100
               3
      3b) 12
              125
           17
      3c)
            8

4. Write the following decimals as percents:
      4a) 0.35
      4b) 1.05
      4c) 0.001
                                          1              3
5. Given the set of numbers:      0.32, 3 , 5 , 175%, 
                                          4              2
      5a) Locate the numbers on the given number line:




      5b) Order the numbers from least to greatest:

								
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