Odd and Even

Document Sample

```					                                      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
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

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
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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