Download FactorGame

The Factor Game
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29
30
Game Board
1
6
11
16
21
26
2
7
12
17
22
27
3
8
13
18
23
28
4
9
14
19
24
29
5
10
15
20
25
30
4
9
14
19
24
29
5
10
15
20
25
30
4
9
14
19
24
29
5
10
15
20
25
30
Game Board
1
6
11
16
21
26
2
7
12
17
22
27
3
8
13
18
23
28
Game Board
1
6
11
16
21
26
2
7
12
17
22
27
3
8
13
18
23
28
Analyzing First Moves
FACTORS
1st
number
picked is
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Opponent Gets
FIRST MOVES
SUM
GOOD
NOT GOOD
Analyzing First Moves
FACTORS
1st
number
picked is
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Opponent Gets
FIRST MOVES
SUM
GOOD
NOT GOOD
Playing the Game
Review factors and divisors. A factor of a number is a number that when you
multiply it by another number, you get that number. For example, factors of 12
are 1, 2, 3, 4, 6, and 12. Another name for factor is divisor. When you divide a
number by one of its factors, it comes out even. You get another factor.
Materials
The Factor Game Board
Colored pencils, each player chooses a different color
Calculator
Procedure
Two people can play this game. The first player selects a number by circling it
and scores that number of points. The second player selects all the divisors of
the first player’s number and scores the sum of all the divisors.
The second player selects a number and the first player circles the factors. The
score is the sum of the numbers circled.
Illegal Moves – An illegal move is made when a person selects a number for
which there are no factors left. You may make an illegal move and et the number
in your score, but you lose your next turn. If you make an illegal move and your
partner right away makes an illegal move, then the game continues.
The game is over when there are no more legal moves left on the board.
The winner is the player with the larger score.
Analyzing First Moves
Materials
Analyzing First Moves recording sheet
Procedure
Suppose the first player chooses 26 on the first move. The first player scores 26
and the opponent scores the sum of the proper factors of 26, 1+2+13 = 16.
(Proper factors are all the factors that are less than the number.)
Is that a good first move? (Yes, you get 26 and your opponent gets less than 26,
namely 16).
Suppose the first player picks 18. What score does the opponent get?
(1+2+3+6+9= 21). Is 18 a good first move? (no).
Complete the Analyzing First Moves table as shown:
Factors
Number
Picked
.
.
.
18
.
26
First Moves
Opponent Gets
Sum
1,2,3,6,9
21
1,2,13
16
Good
Not Good
When 18 is the
first move, the
other player
gets 21.
18 - 21
26-16
When 26 is the
first move, the
other player
gets 16.
What first moves give the other player exactly 1 point?
(2,3,5,7,11,17,19,23,29)
What are these numbers called? (Prime Numbers)
A prime is a number that has exactly two factors, one and itself.
All the other numbers, except 1, are called composite numbers.
1 is neither prime nor a composite number. It is the only number with exactly one
factor.
Were all the prime numbers good first moves? (Yes)
Were all the composite numbers good first moves? (Some were good and some
were not)
What was the best first move? (29)
What was the worst first move? (24 or 30)
This game can be played on NCTMs Illumination website:
http://illuminations.nctm.org/ActivityDetail.aspx?ID=12