1. Prime Numbers Eratosthenes’ Sieve
Unit 2 Algebraic Reasoning 5th grade Day 3

2. Eratosthenes (ehr-uh-TAHS-thuh-neez)
Eratosthenes was the librarian at
Alexandria, Egypt in 200 B.C.
Note every book was a scroll.
Unit 2 Algebraic Reasoning 5th grade Day 3

3. Eratosthenes (ehr-uh-TAHS-thuh-neez)
Eratosthenes was a Greek mathematician, astronomer, and geographer.
He invented a method for finding prime numbers that is still used today.
This method is called Eratosthenes’ Sieve.
Unit 2 Algebraic Reasoning 5th grade Day 3

4. Unit 2 Algebraic Reasoning 5th grade Day 3
Eratosthenes’ Sieve
A sieve has holes in it and is used to filter out the juice.
Eratosthenes’s sieve filters out numbers to find the prime numbers.
Unit 2 Algebraic Reasoning 5th grade Day 3

5. Unit 2 Algebraic Reasoning 5th grade Day 3
Definition
Factor – a number that is multiplied by another to give a product.
7 x 8 = 56
Factors
Unit 2 Algebraic Reasoning 5th grade Day 3

6. Unit 2 Algebraic Reasoning 5th grade Day 3
Definition
Factor – a number that divides evenly into another.
56 ÷ 8 = 7
Factor
Unit 2 Algebraic Reasoning 5th grade Day 3

7. 7 Definition 7 is prime because the only numbers
Prime Number – a number that has only two factors, itself and 1. 7
7 is prime because the only numbers
that will divide into it evenly are 1 and 7.
Unit 2 Algebraic Reasoning 5th grade Day 3

8. Unit 2 Algebraic Reasoning 5th grade Day 3
Hundreds Chart
On graph paper, make a chart of the numbers from 1 to 100, with 10 numbers in each row.
Unit 2 Algebraic Reasoning 5th grade Day 3

9. Unit 2 Algebraic Reasoning 5th grade Day 3
Hundreds 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
Unit 2 Algebraic Reasoning 5th grade Day 3

10. 1 – Cross out 1; it is not prime.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
Unit 2 Algebraic Reasoning 5th grade Day 3

11. Remember all numbers divisible by 2 are even numbers.
Hint For Next Step
Remember all numbers divisible by 2 are even numbers.
Unit 2 Algebraic Reasoning 5th grade Day 3

12. 2 – Leave 2; cross out multiples of 21 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
Unit 2 Algebraic Reasoning 5th grade Day 3

13. Unit 2 Algebraic Reasoning 5th grade Day 3
Hint For Next Step
To find multiples of 3, add the digits of a number; see if you can divide this number evenly by 3; then the number is a multiple of 3.
2 6 7
Total of digits = 15
3 divides evenly into 15
267 is a multiple of 3
Unit 2 Algebraic Reasoning 5th grade Day 3

14. 3– Leave 3; cross out multiples of 31 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
Unit 2 Algebraic Reasoning 5th grade Day 3

15. Unit 2 Algebraic Reasoning 5th grade Day 3
Hint For the Next Step
To find the multiples of 5 look for numbers that end with the digit 0 and 5.
385 is a multiple of 5
& 890 is a multiple of 5
because the last digit
ends with 0 or 5.
Unit 2 Algebraic Reasoning 5th grade Day 3

16. 4– Leave 5; cross out multiples of 51 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
Unit 2 Algebraic Reasoning 5th grade Day 3

17. Unit 2 Algebraic Reasoning 5th Grade Day 3
5– Leave 7; cross out multiples of 7 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
Unit 2 Algebraic Reasoning 5th grade Day 3

18. 6–Leave 11; cross out multiples of 112 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
Unit 2 Algebraic Reasoning 5th grade Day 3

19. All the numbers left are prime1 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
Unit 2 Algebraic Reasoning 5th grade Day 3

20. The Prime Numbers from 1 to 100 are as follows:
2,3,5,7,11,13,17,19,
23,31,37,41,43,47,
53,59,61,67,71,73,
79,83,89,97
Unit 2 Algebraic Reasoning 5th grade Day 3

21. Unit 2 Algebraic Reasoning 5th Grade Day 3
Credits
Clipart from “Microsoft Clip
Gallery” located on the Internet at
clipgallerylive/default.asp
Unit 2 Algebraic Reasoning 5th grade Day 3