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Odd and Even

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					                                      Odd and Even
Words for the Word Wall:
     Odd
     Even
     Sum

Materials:
      35 color tiles for each pair of students

Transparencies/Handouts:
      Hundred chart (one for each pair of students) (6C-7)
      Inch graph paper (6C-8)
      Odd and Even Recording Sheet (6C-9)
      Odd and Even Demonstration Cards (for presenter) (6C-10)

                Procedures                                           Notes
1. Remind students of a previous lesson            Hundred charts should be available for
   where the class found the multiples of          students to use.
   two patterns on a hundred chart. Have
   each pair share with their partner how to
   skip count by twos beginning with two
   and then how to skip count by twos
   beginning with one.
2. Model for students the procedure of             Rather than teaching students to memorize
   picking up a handful of tiles, counting         that numbers ending in 0, 2, 4, 6, and 8 are
   them, and sharing them equally with a           even, this activity develops the definition of
   partner. Ask your partner if he got his fair    even as “ a number that is divisible by two”
   share. If one tile is left over, give it to     by having two students try to share tiles
   your partner.                                   equally.
3. Using all of the tiles, demonstrate             Another way to determine if a number is odd
   working with a partner to try to arrange        or even is to take the total number of tiles
   the tiles into a rectangle that is two tiles    and try to build a rectangle that is two units
   wide. Use the inch graph paper to               wide.
   demonstrate how to color and cut out a
   record of the rectangle or non-rectangle
   that resulted from your attempt.




TEXTEAMS Rethinking Elementary School Mathematics Part II                          Day 6: Section C
Odd and Even                                                                               Page 51
4. Have students work with their partners          Sharing observations with a partner allows
   and repeat the procedure several times          all students to communicate their thinking.
   with different numbers of tiles. This will      Students may describe the even numbers as
   result in creating representations of a         numbers that can make two-tile wide
   variety of numbers, both odd and even.          rectangles and the odd numbers as having an
   Ask students to look at the shapes they         extra tile, a leftover tile, or needing one more
   drew and cut out from their graph paper.        tile to make a rectangle that is two tiles wide.
   Discuss with their partner about what
   they notice about the different numbers.
   How are they alike and how are they
   different? Have the class write a
   definition for odd numbers and even
   numbers.
5. Have students repeat the activity, this    This part of the activity is intended to give
   time recording their procedure and results students a visual way of distinguishing
   on the Odd and Even Recording Sheet.       between odd and even numbers. The time
                                              you spend on this part will depend on the
                                              level of your class.
6. Show students, using transparent
   Demonstration Cards (6C-10), that
   adding can be thought of as combining
   sets of tiles or areas of shapes.
   Demonstrate what happens when you
   combine the representations for two even
   numbers. Can the combined
   representations be formed into another
   rectangle with a width of two tiles?
   Again, using the Demonstration Cards,
   demonstrate what happens when you
   combine the representation of an odd
   number with the representation of an
   even number. (A rectangle, with a width
   of 2 units cannot be formed.) Now,
   demonstrate what happens when you
   combine the representations of two odd
   numbers. (If one of the odd number
   cards is rotated 90 degrees, it can be
   combined with another odd number card
   to form a rectangle with a width of 2
   tiles.) Continue the investigation with the
   students combining the representations of
   different numbers that they made in the
   first part of the activity. Ask them if their
   sums are odd or even.


TEXTEAMS Rethinking Elementary School Mathematics Part II                           Day 6: Section C
Odd and Even                                                                                Page 52
7. Tell the students they will be asked to         The number of examples and the size of the
   add some numbers. They need not give            numbers you use depend on your class.
   the answer, but simply predict whether          Young children need experiences visualizing
   the sum will be odd or even. Try sums           so they can eventually make generalizations
   like 7 + 3, 8 + 6, 13 + 6, etc.                 and then use the generalizations to make
                                                   predictions, all of which are important
                                                   components of algebraic reasoning. Be sure
                                                   to refer back to the odd and even patterns for
                                                   these numbers.
8. Have students discuss how knowing               Many questions both within and beyond
   about odd and even numbers can help us          mathematics require an understanding of odd
   solve problems, e.g. whether a house            and even to solve.
   number is odd or even is used to
   determine which side of the street the
   house is located.

Discussion:
Ask students to picture odd and even numbers in their minds as they reflect on their answers
to the following questions. Have them explain the reasons for their answers.

       If you add two odd numbers will the sum be even or odd?
       If you add two even numbers will the sum be even or odd?
       If you add an even and an odd number will the sum be even or odd?
       What happens when you add three odd numbers? Two odds and an even? Two evens
       and an odd? Five odds and one even?
       If a person has two coins but an odd number of cents in their pocket, what is the least
       amount of money they could have? (11 cents) What is the greatest amount of money
       they could have? (75 cents)

Similar questions can be investigated when subtracting numbers.

       Is the result odd or even when you subtract an odd number from an odd number?
       Is the result odd or even when you subtract an even number from an even number?
       Is the result odd or even when you subtract an odd number from an even number? Is
       the result odd or even when you subtract an even number from an odd number?




TEXTEAMS Rethinking Elementary School Mathematics Part II                          Day 6: Section C
Odd and Even                                                                               Page 53
                                                                 Transparency / Handout 6C-7



                                Hundred Chart

     1          2         3         4         5         6    7       8         9       10


   11         12        13        14        15        16    17     18        19        20


   21         22        23        24        25        26    27     28        29        30


   31         32        33        34        35        36    37     38        39        40


   41         42        43        44        45        46    47     48        49        50


   51         52        53        54        55        56    57     58        59        60


   61         62        63        64        65        66    67     68        69        70


   71         72        73        74        75        76    77     78        79        80


   81         82        83        84        85        86    87     88        89        90


   91         92        93        94        95        96    97     98        99      100




TEXTEAMS Rethinking Elementary School Mathematics Part II                   Day 6: Section C
Odd and Even                                                                        Page 54
1 Inch Graph Paper                                            Handout 6C-8




TEXTEAMS Rethinking Elementary School Mathematics Part II   Day 6: Section C
Odd and Even                                                        Page 55
                                                                       Transparency / Handout 6C-9



                       Odd and Even Recording Sheet
 What is the total         Do you and your          Do the tiles make a    Is the total number
number of tiles you        partner have the        rectangle that is two   of tiles odd or even?
   picked up?               same amount?                tiles wide?        How do you know?




TEXTEAMS Rethinking Elementary School Mathematics Part II                         Day 6: Section C
Odd and Even                                                                              Page 56
                                                                Transparency 6C-10



                         Demonstration Cards




                 2                                          3




                                                4



TEXTEAMS Rethinking Elementary School Mathematics Part II         Day 6: Section C
Odd and Even                                                              Page 57
                                                            Transparency 6C-10




                                                5




TEXTEAMS Rethinking Elementary School Mathematics Part II     Day 6: Section C
Odd and Even                                                          Page 58

				
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