Math Message 1.6 Please complete the following Math Message in
your Math notebooks and have your answers ready to share: Draw ALL
possible rectangular arrays for these numbers: 2, 4, 5, 10, 11, and
16
Slide 3
What exactly are prime numbers? A prime number has exactly two
factors- 1 and the number itself Important to know: the number 1 is
considered neither prime nor composite Lets look at some examples.
2 1 and 2 17 17 and 1 23 1 and 23
Slide 4
What are composite numbers? A composite number has more than
two factors Some examples of composite numbers: Number Factors 4 1,
2, 4 16 1, 2, 4, 8, 16 35 1, 5, 7, 35
Slide 5
September 4, 2013 1.7 Square Numbers
Slide 6
Math Message 1.7 1. Use coins, M & M candy, or any other
items that resemble counters. 2. Try and make a rectangular array
with an equal number of rows and columns for each of the following
numbers: 14 16 18 Which numbers make this kind of array? Show your
work for each array.
Slide 7
Answer to the Math Message: Of the three numbers, 16 is the
only one that can be represented equally 4 x 4 array * * * * * * *
*
Slide 8
How is a 4 x 4 array similar to a square? When an array has the
same number of rows and columns, it is shaped like a square and is
called a square array The number it represents is called a square
number Since 16 can be represented by a square array, the number 16
is a square number
Slide 9
Finding other Square Numbers How many objects are in the array?
9 How many rows are in the array set? 3 How many columns are in the
array set? 3 3-by-3 array
Slide 10
Square Numbers Any square number can be written as the product
of a number multiplied by itself 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x
4 = 16 A shorthand way of writing square numbers looks like this: 9
= 3 x 3 = 3 2 Lets work on MJ pg. 20
Slide 11
What are exponents? **You can read 3 2 as 3 times 3, 3 squared,
or 3 to the second power The raised 2 is called an exponent. It
tells you that 3 is used as a factor 2 times 3 2 = 3 x 3 = 9
Exponential Notation- numbers that are written with an exponent ex.
3 2
Slide 12
What is the difference between doubling a number and squaring a
number? What do you get when you double 10? 20 = 10 +10 or 10 x 2
What do you get when you square 10? 10 * 10 = 100 or 10 2
Slide 13
September 5, 2013 1.8 Unsquaring Numbers
Slide 14
1.8 Math Message Find the numbers that make these statements
true. Write out and complete each statement in your Math notebook.
1) ______ * ______ = 4 2) ______ 2 = 81
Slide 15
What numbers could the blank spaces in these problems
represent? Answers to the Math Message: 1) The factors of 1 and 4,
or 2 2) The factor 9 Now, lets replace the blank spaces with the
letter (the variable), N. What number is being represented by the
variable, N? N * N = 4 N = 2
Slide 16
What do you know about variables? A variable can only represent
one number if the number sentence is true. For example: m 2 = 81 m
squared equals 81 m * m = 81 What number is being represented by
the variable m to make the number sentence true? m = 9
Slide 17
Unsquaring Numbers When unsquaring a number, we need to undo
the operation If you square a number, you are multiplying it by
itself to get the product 4 * 4 = p When you are given the product,
you will need to undo the multiplication to identify the number
that was squared n * n = 16
Slide 18
Problems well complete in class.. What number, multiplied by
itself, is equal to 289? What strategies are you using? Lets
practice unsquaring numbers 1. 196 2. 10,000 3. 7,225 4. 441
Slide 19
Finding the Square Root of Numbers When you unsquare a number,
you have found the square root of the number What number squared is
64? 8 So, what is 64 squared? 8, because 8 * 8 = 64 What is the
square root of 64? 8
Slide 20
Testing our results using a calculator When using a calculator
to find the square root you will need to know the following: 1) If
the display shows a whole number, then the original number is a
square number. *For example: 576 is a square number because using
the square-root key displays a whole number, 24 2) If the display
shows a decimal, then the original number is not a square number. *
For example: 794 is not a square number because using the
square-root key displays a decimal--- 28.178006 (rounded to 6
decimal places)
Slide 21
September 6, 2013 1.9 Factor Strings and Prime
Factorizations
Slide 22
1.9 Math Message 8 + 8 and 4 * 4 are two names for the number
16. In your Math notebook, write at least five other names for 16.
Brainstorm the different ways and be prepared to share your answers
Name-Collection Box for 16
Slide 23
What are Factor Strings? A factor string is a multiplication
expression that has at least two factors that are greater than 1.
*In a factor string, the number 1 may NOT be used as a factor
Example of a factor string for the number, 24: 24 is 2 * 3 * 4 In
the factor string, you see three factors (2, 3, 4), this is called,
the length of the factor string *Now, lets find other factor
strings for 24
Slide 24
Lets practice(in class) 1) Find the factor string for 7 2) What
type of number is 7? A prime number The number 1 may not be used in
a factor string, so there are no factor strings for prime numbers
3) Lets find all possible factor strings for 36 Is 2 a factor of
36? Yes, 36 = 2 * 18 Is 2 a factor of 18? Yes, 36 = 2 * 2 * 9 Is 2
a factor of 9? No Is 3 a factor of 9? Yes, 36 = 2 * 2 * 3 * 3
Slide 25
Prime Factorization What kind of numbers are the factors in the
longest possible factor string for any number? Prime numbers The
longest factor string for a number is called the prime
factorization of the number For example: The prime factorization of
24 is 2 * 2 * 2 * 3
Slide 26
Using Factor Trees to find all the prime factors We will
practice creating a Factor Tree for 36 36 6 * 6 3 * 2 3 * 2 36 = 2
* 2 * 3 * 3 36 = 2 2 * 3 2
