PRIME OR COMPOSITE
Performance Standard 6B.E
Determine prime and composite numbers from one to 100 and arrange a composite number’s factors in a rainbow
pattern accordingly:
• Mathematical knowledge: Identify prime and composite numbers and know and use divisibility rules.
• Strategic knowledge: Use strategies appropriately to determine prime and composite numbers and to arrange a
composite number’s factors in a rainbow pattern.
• Explanation: Explain completely and clearly what was done and why it was done.
Procedures
1.
2.
3.
In order to investigate, represent, and solve problems using number facts, operations and their properties,
algorithms, and relationships (6B), students should experience sufficient learning opportunities to develop the
following:
• Determine whether a number is prime or composite.
• Identify all the whole number factors of a composite number.
• Explore and use divisibility rules.
Provide each student with a copy of the two “Prime or Composite” recording sheets and the rubric. Have
students review and discuss the task to be completed and how the rubric will be used to evaluate it.
Review the divisibility rules with the students and have them complete the “Divisibility Rules” table.
Number
540
346
621
2,690
5,211
4,002
6,732
9,017
10,950
12,579
4.
5.
by
4
yes
no
no
no
no
no
yes
no
no
no
5
yes
no
no
yes
no
no
no
no
yes
no
6
yes
no
no
no
no
yes
yes
no
yes
no
9
yes
no
yes
no
yes
no
yes
no
no
no
10
yes
no
no
yes
no
no
no
no
yes
no
Ask students to shade all composite numbers on the 100 chart and leave prime numbers blank. Composite
numbers may be determined using knowledge of multiples, divisibility rules, and a calculator, as well as
drawings of arrays on graph paper or making arrays with available manipulatives such as square tiles.
Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
One is a factor of all numbers and is not considered prime. Two is the only even prime number. There are 25
prime numbers from 1 to 100.
Ask each student to pick a number greater than 40 and produce a rainbow pattern using its factors.
EXAMPLE: 48
6.
Divisible
3
yes
no
yes
no
yes
yes
yes
no
yes
yes
2
yes
yes
no
yes
no
yes
yes
no
yes
no
1
2
3
4
6
8 12 16
24
48
During the second class period, ask each student to find one three-digit prime number and justify in writing how
s/he determined it is prime. (Each student needs to find one three-digit composite number and show it is a
composite number by using a rainbow pattern and divisibility rules. Example: 359 is a prime number. The
way to find out is to find the square root of the number. Then divide the three-digit number by all the prime
numbers lower than its square root. If none divide evenly; then, the number is prime. The square root of 359 is
18.9. Divide 359 by 2, 3, 5, 7, 11, 13, and 17. All composite numbers can be factored into its prime
components. So, if a number is not divisible by the primes lower than its square root, it can’t be factored and is,
therefore, prime.)
ASSESSMENT 6B.E
7.
Evaluate each student’s work using the rubric and use the guide on the rubric to determine the performance
level. Students should show a clear understanding of what makes a prime number prime and differentiate a
prime from composite number using a drawing of an array or making an array from manipulatives. They should
be able to determine all the factors of a composite number using divisibility rules. They should be able to use
the organizational technique called a “rainbow pattern” to display all the factors of a composite number.
Examples of Student Work follow
•
•
Resources
Copies of the “Prime or Composite” recording
sheets (100 chart and divisibility rules)
Mathematics Rubric
Time Requirements
• Two class periods
ASSESSMENT 6B.E
NAME _______________________________________________ DATE _______________________________
PRIME OR COMPOSITE
100 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
ASSESSMENT 6B.E
Answer Key
PRIME OR COMPOSITE
100 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
Composite numbers are shaded. Prime numbers are not shaded. One is neither composite nor prime. There are 25
prime numbers from 1 to 100.
ASSESSMENT 6B.E
NAME _______________________________________________ DATE _______________________________
Divisibility Rules
Complete the table. Write Y (yes) or N (no).
Number
540
346
621
2690
5211
4002
6732
9017
10950
12579
ASSESSMENT 6B.E
2
3
4
Divisible by
5
6
9
10
"Meets" (page 1)
"Meets" (page 2)
"Meets" (page 3)
"Exceeds" (page 1)
"Exceeds" (page 2)
"Exceeds" (page 3)
"Exceeds" (page 4)