Name: _________________________________________
Ratio Sequence: Divisibility Rules, Multiples (Common Factors)
Date: _________________________
Define
Divisibility Rules: __________________________________________________________
Even Numbers: ________________________
Odd Numbers: ___________________________
Discover the divisibility rules by examining a list of multiples of 2 (even numbers)
Multiples of 2: 2, 4, ___, 8, 10, ___, 14, 16, 18, ___, 22, 24, 26, 28, ____
What patterns do you notice in the multiples of 2? (hint: last digit) __________________________________________
Values are divisible by 2, when _______________________________________________________________
Test your theory on the following numbers, and circle the values divisible by 2 (that share 2 as a factor):
44
51
72
50
60
126
200
315
Discover the divisibility rules by examining a list of multiples of 5
Multiples of 5: 5, 10, ___, 20, 25, ___, 35, 40, 45, ___, 55, 60, 65, 70, ____
What patterns do you notice in the multiples of 5? (hint: last digit) __________________________________________
Values are divisible by 5, when _______________________________________________________________
Test your theory on the following numbers, and circle the values divisible by 5 (that share 5 as a factor):
44
51
72
50
60
126
200
315
Discover the divisibility rules by examining a list of multiples of 10
Multiples of 10: 10, 20, ___, 40, 50, ___, 70, 80, 90, ___, 110, 120, 130, 140, ____
What patterns do you notice in the multiples of 10? (hint: last digit) _________________________________________
Values are divisible by 10, when _______________________________________________________________
Test your theory on the following numbers. Circle the values divisible by 10 (that share 10 as a factor):
44
51
72
50
60
126
200
315
Discover the divisibility rules by examining a list of multiples of 3
Multiples of 3: 3, 6, ___, 12, 15, ___, 21, 24, 27, ___, 33, 36, 39, 42, ____
What patterns do you notice in the multiples of 3? (hint: sum of digits) ________________________________________
Values are divisible by 3, when ________________________________________________________________
Test your theory on the following numbers, and circle the values divisible by 3 (that share 3 as a factor):
44
51
72
50
60
126
200
315
Discover the divisibility rules by examining a list of multiples of 9
Multiples of 9: 9, 18, ___, 36, 45, ___, 63, 72, 81, ___, 99, 108, 117, 126, ____
What patterns do you notice in the multiples of 9? (hint: sum of digits) ________________________________________
Values are divisible by 9, when ________________________________________________________________
Test your theory on the following numbers, and circle the values divisible by 9 (that share 9 as a factor):
44
51
72
50
60
126
200
315
Use the following list of numbers to answer the questions below
312
220
135
450
90
4
3.1
3
4
1) Which values above are multiples of 2? ___________ How do you know? ___________________________________
2) Which values above are multiples of 3? ___________ How do you know? ___________________________________
3) Which values above are multiples of 5? ___________ How do you know? ___________________________________
4) Which values above are multiples of 9? ___________ How do you know? ___________________________________
5) Which values above are multiples of 10? ___________ How do you know? __________________________________
6) What values were not in any list? __________________ What can you say about these numbers? _______________
_________________________________________________________________________________
7) Create a list of new values that share 2 and 3 as a factor: ________________________________________________
8) What do you notice about this list? __________________________________________________________________
(pg.7) Ratio Sequence: Divisibility Rules, Multiples (Common Factors)
 Derive the divisibility rules by observing patterns in multiples
 Describe the patterns in multiples. Define divisibility, even numbers and odd numbers.