Math 104 - CooleyMath For Elementary Teachers I OCC
Activity #33 – Sieve of Eratosthenes
CaliforniaState Content Standard – Number Sense – Grade Four4.0Students know how to factor small whole numbers:
4.2 Know that numbers such as 2, 3, 5, 7, and 11 do not have any factors except 1 and themselves and that such numbers
are called prime numbers.
In-Class Exercise:
Purpose:Use a sieve to investigate primes, composites, multiples, and prime factorizations.
Materials:Orange, red, blue, green, yellow colored pencils or crayons.
Getting Started:Eratosthenes, a Greek mathematician, invented the sieve method for finding primes
about 2200 years ago. This activity explores a variation ofEratosthenes’ sieve.
We are going to be working with the following grid on the next page.
One is neither prime nor composite. To show this, mark an X through 1.
Since the next number, 2, does not have any corner colored, then 2 is the first prime number. Use orange to color the diamond in which 2 is located. Now, use red to color theupper-left corner of all squares containing multiples of 2. The squares containing only colored corner(s)“fell” through the sieve, hence these numbers are considered composite.
1)What was the first multiple of 2 that fell through the sieve? ______
The next uncolored number is 3. Color the diamond surrounding the 3 in orange. Use blue to color the
upper-right corner of all squares containingmultiples of 3.
2)What was the first multiple of 3 that fell through the sieve? ______
3)What was the first multiple of 3 that fell through the sieve, that didn’t previously fall? ______
Repeat this process for 5 and then 7, since these numbers are not colored. Color the diamonds surrounding the numbers in orange. Usegreen to colorthe lower-right corners of the squares containing multiples of 5. Use yellow to color thelower-left corners of the squares containing multiples of 7. Note the first multiples of 7that fall through the sieve, that didn’t fall from other numbers previously. These numbers tend to be the prime numbers that people are unfamiliar with.
Finally, use orange to color the diamond surrounding all the numbers in the grid that are in squares with no
corners colored. These numbers are all primes.
4)How do you know that 2, 3, 5, and 7, are prime numbers?
5)How can you tell this from the way the sieve is colored?
6)How can you identify composite numbers from the way the sieve is colored?
** IMPORTANT – DO NOT FILL ANYTHING OUT UNTIL ALL INSTRUCTIONS ARE UNDERSTOOD **
Red = Upper-Left Corner = multiples of 2 (not including 2 itself)
Blue = Upper-Right Corner = multiples of 3 (not including 3 itself)
Green = Lower-Right Corner = multiples of 5 (not including 5 itself)
Yellow = Lower-Left Corner = multiples of 7 (not including 7 itself)
Orange = Diamonds = Primes (two distinct numbers that are only divisible
by 1 and itself only)
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
In-Class Exercise:
You can also use the Sieve of Eratosthenes and find all prime numbers from 1 through 100 in under 30 seconds using an alternate grid.
1 / 2 / 3 / 4 / 5 / 67 / 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
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