The document discusses tiling a bathroom and prime and composite numbers. It explains that 4 tiles and 6 tiles are composite numbers because they have more than two factors, while 3 tiles and 5 tiles are prime numbers because they only have two factors. The document then explains the Sieve of Eratosthenes algorithm for finding prime numbers and provides an assessment and homework on identifying prime and composite numbers.

1. Bathroom Tiling
Make possible ways to arrange the
tiles.

2. 1. Use 4 tiles

3. 2. Use 6 tiles

4. 3. Use 3 tiles

5. 4. Use 5 tiles

6. For 4 tiles and 6 tiles
the factors are more than two:
4 tiles – factors are 4, 2 and 1
6 tiles – factors are 6, 3 and 1
Numbers with more than 2 factors are called

7. For 3 tiles and 5 tiles
the factors are ONLY two:
3 tiles – factors are 3 and 1
5 tiles – factors are 5 and 1
Numbers with ONLY two factors are called

8. Sieve of Eratosthenes
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100

9. 48
64
22
85
39
2
42
14
12
74
63
56
21
15
17
70
57
42
20
63
16
18
62
59
83
37
22
12
42
84
42
60
39
21
31
53
30
43
43
13
60
15
72
46
11
62
31
72
53
29
13
13
2
41
17
73
22
86
8
12
28
25
66
3
80
38
71
11
3
73
42
81
61
26
42
7
12
50
61
8
33
11
83
83
7
57
19
5
38
25
74
60
84
30
22
43
80
49
55

10. Assessment:
Write C if the number is composite and P if it is prime.
1. 67 ___
2. 100 ___
3. 81 ___
4. 43 ___
5. 31 ___
Write true or false.
1. The least prime number is 3.
2. The product of two prime numbers is a prime number.
3. All even numbers greater than 2 are composite.
4. The sum of any two prime numbers is a composite number.
5. The only even prime number is 2.

11. Homework
A. Answer the following questions: (1/2 sheet of paper, crosswise)
1.
I am a three-digit number. I am the sum of the prime numbers
between 40 and 60. Who am I?
2. What is the sum of the first prime numbers?
3. List the twin primes between 1 to 100.
4. Name two composite numbers that are prime.
5. Name three consecutive odd prime numbers.
6. Which is the smallest prime number?
7. How many prime numbers are there between 1 and 100?
8. Is every odd number other than 1 a prime number?
9. Is every even number other than 2 a composite number?
10. What are the first 10 prime numbers?

12. See you all tomorrow!
Prepared by:
DEMOSTHENES O. CAJES
Teacher I, DCCES

13. Sieve of Eratosthenes
Eratosthenes (276-194 B.C.) was the third
librarian of the famous library in Alexandria
and an outstanding scholar all around. He is
remembered by his measurement of the
circumference of the Earth, estimates of the
distances to the sun and the moon, and, in
mathematics, for the invention of
an algorithm for collecting prime numbers.
The algorithm is known as the Sieve of
Eratosthenes.
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