Operations and Algebraic Thinking

Number Relationships:

Square Numbers:  When you multiply any number by itself you get a square number.  For example, multiplying 4 by itself gives the square number 16. 

The first ten square numbers are: 1, 4, 9, 16, 25, 36, 49, 81, 100. 

Powers:  A power tells you to multiply a number by itself.  (Another name for power is exponent.)  The value of the power shows you how many sets of the number to multiply.   For example, 43  means 4 to the power 3, which is 4 x 4 x 4.  

Factors:  A factor of a number is a whole number that divides exactly into it.  For example, you can divide 12 exactly by 3 (to get 4), so 3 is a factor of 12.   The factors of 12 are:  1,2,3,4,6,12

Number            Factors     

1                        1

2                        1,2

3                        1,3

4                        1,2,4

5                        1,5

6                        1,2,3,6                                                                            

7                        1,7

8                        1,2,4,8

9                        1,3,9

10                       1, 2,5,10

11                       1,11

12                       1,2,3,4,6,12

13                       1,13

14                       1, 2,7,14

15                       1,3,5,15

16                       1,2,4,8,16

17                       1,17

18                       1,2,3,6,9,18

19                       1,19

20                       1,2,4,5,10,20

Comparing signs: 

< means "less than."  For example, 4 < 10. 

> means "greater than."  For example, 15 > 10. 

The widest part of the > and < signs always points to the largest number. 

= means "equal to."  For example, 2 + 3 = 5 means 2 + 3 is equal to 5. 

ORDER OF OPERATIONS: To solve math problems with more than one operation ( +, -, x, /) remember this sentence for the correct order: 

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PLEASE EXCUSE MY DEAR AUNT SALLY  

Please = Parentheses

Excuxe = Exponents 

My = Multiply 

Dear = Divide

Aunt = Add

Sally = Subtract 

Do each operation from left to right.  First, do what's in parentheses.  Then, do the exponents.  Next, multiply and/ or then divide. Last, add and/ or then subtract. 

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Divisibility Rules: 

If you can divide a number by another one without leaving a remainder, it is divisible by the number. You can use these rules to see if a number is divisible by another.

Divisible by         Rule                                                 

2                        The last digit, is 0,2,4,6,8.

3                        You can divide the sum of the digits by 3.      

4                        The last two digits make a number you can divide by 4. 

5                        The last digit is 5 or 0.

6                        The last digit is even, and you can divide it by 3.                         

8                        The last three digits make a number you can divide by 8. 

9                        You can divide the sum of the digits by 9. 

10                       The last digit is 0. 

12                       You can divide the number by 3 and 4. 

25                       The last two digits are 00,25,50, or 75.

100                     The lat two digits are 00. 

Composite Numbers = has three or more factors.  For example, 10 has four factors; 1, 2, 5, and 10. 

Square Root = a factor of a number that you can multiply by itself to give that number.  For example, the square root of 16 is 4. The symbol for square root is √.

4 x 4 = 16

so, √16 = 4

Prime Number is a number that you can only divide by 1 and itself.  Primes only have two factors.  

The first ten positive prime numbers are:

2    3    5    7    11    13    17    19    23    29

Number Patterns: