# Primetime by xiaopangnv

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```									                                             Unit 1
Prime Time
OBJECTIVES

•Understand relationships among factors, multiples, divisors and products
•Recognize and use properties of prime and composite numbers, even and odd numbers, and square
numbers
•Use rectangles to represent the factor pairs of numbers
•Develop strategies for finding factors and multiples, least common multiples, and greatest common
factors
•Recognize and use the fact that every whole number can be written in exactly one way as a product
of prime numbers
•Use factors and multiples to solve problems and to explain some numerical facts of everyday life
•Develop a variety of strategies for solving problems-building models, making lists and tables, drawing
diagrams, and solving simpler problems

Mrs. Carol Lange                                                                                         1
Unit 1
Prime Time
Big Ideas
Factors and Products
Whole Number Patterns and Relationships
Common Multiples and Factors
Factorizations: Searching for Factor Strings

Essential Questions
Will breaking a number into factors help me solve a problem?
What relationships are revealed with factors?
What do the factor and multiples of the numbers tell me about the situations?
How can I find the factors of the numbers?
How can I find the multiples?
What common factors and common multiples do the numbers have?

Mrs. Carol Lange                                                                2
Textbook page 4
Unit 1
Prime Time
UNIT PROJECT
Choose a whole number that you especially like:
•Your number must be between 10 and 100
•Explain why you chose that number
•List three or four connections you can make between your number and your world
•At the end of the unit you will be creating a project to highlight your number

Mrs. Carol Lange                                                                  3
Textbook page 5, 70
Unit 1
Prime Time
ESSENTIAL VOCABULARY
factor                common multiples
divisor               least common multiple
multiple              common factors
prime number          greatest common factor
composite number      factorizations
factor pair           prime factorizations
square numbers        exponent
even number           relatively prime
odd number            conjecture
Venn diagram

Mrs. Carol Lange                                            4
Textbook page 74-79
Unit 1
Prime Time
INVESTIGATION ONE
Factors and Products
•Factors are whole number divisors of numbers:
1,2,5,10 are factors of 10
Every number has a limited number of factors!
•Play The Factor Game to practice finding factors, and to see
relationships among numbers
http://www.PHSchool.com          webcode amd-1101
•Proper factors are all the factor of a number except the number itself:
1,2,5 are the proper factors of 10
•Multiples are the products of a whole number and another whole number: the
multiples of 5 are 5 (5x1), 10 (5x2), 15 (5x3), and so on. Every
number has an unlimited number of multiples.
•Play The Product Game to practice finding multiples, and to see
relationships among numbers
http://www.PHSchool.com          webcode amd-1103

Mrs. Carol Lange                                                              5
Textbook page 6-21
Unit 1
Prime Time
INVESTIGATION ONE
Factors and Products
•Prime Numbers are numbers that have exactly two factors:
3,5,7,11,13,17,19…are prime because the only divisors they have are
1 and the number itself
http://www.PHSchool.com       webcode ame-9031
•The number one is neither prime, nor composite
•Composite Numbers are numbers that have more than two factors:
2,4,6,8,9,10,12,14,15…are composite because they have more than
two factors (divisors)

Mrs. Carol Lange                                                               6
Textbook page 6-21
Unit 1
Prime Time                                  Always
support
your
with
examples!
APPLICATIONS:

5) What factor is paired with 6 to give it 54?
9, because 9 x 6 = 54

16) Why is the set of factors of a number not the same as the set of proper
factors of that number?
Factors are different than proper factors because they do not include
the number itself.
Factors of 9 are 1,3,and 9; proper factors of 9 are 1,3
Multiple-choice skills practice:
http://www.phschool.com webcode ama-1154

Mrs. Carol Lange                                                                     7
Textbook page 14-15
Unit 1
Prime Time                                      Always
support
your
with
examples!
CONNECTIONS:

33A) In developing the ways in which we calculate time,
astronomers divided an hour into 60 minutes. Why is 60 a good choice
(better than 59 or 61)?
60 is a good choice for calculating time, because it has many factors
(1,60; 2,30; 3,20; 4,15; 5,30; 6,10). 59 and 61 do not have as many
factors.
33B) If you could select another number to represent the number of
minutes in an hour, what would be a good choice? Why?
I’d pick a number like 100, because it has a lot of factors (1,100;
2, 50; 4,25; 5,20; 10,10)

Mrs. Carol Lange                                                                      8
Textbook page 18
Unit 1
Prime Time                                       Always
support
your
with
examples!
EXTENSIONS:

43) What is the best move (in the Factor Game) on a 49-board? Why?

47 is a good first move, because it is the greatest prime number. You
will get 47 points, and your opponent will get only 1.

Mrs. Carol Lange                                                                      9
Textbook page 19
Unit 1
Prime Time
INVESTIGATION TWO
Whole-Number Patterns and Relationships

•Factor Pairs are two whole numbers that are multiplied to get a product
factor pairs of 10 are 1,10 and 2,5
Remember: every number has a limited number of factors!
•Square Numbers are numbers that result from multiplying the same number
times itself. (4 x 4 = 16, 2 x 2 = 4)
•Odd Numbers are numbers that do not have two as a factor.
•Even Numbers are numbers that have two as a factor.
•A conjecture is a best guess or prediction based on an observed pattern
•A Venn diagram uses circles to group things that belong together

Mrs. Carol Lange                                                           10
Textbook page 22-36
Unit 1
Prime Time                                  Always
support
your
with
Sample ACE questions and answers:                 examples!
APPLICATIONS:

8) What type of number has an odd number of factors? Give
examples
Square numbers have an odd number of factors, because one factor
pair is always the same. (16: 1,2, 4, 8, 16)

15) How can you determine whether a sum of several numbers, such as
13 + 45 + 24 + 17 is even or odd?
If all the numbers in the ones place are even, or if there is an even
number of odd numbers, than the sum is even.
For example: The sum of 3 + 5 + 4 + 7 will be odd, because there are
Problem 15 help:
http://www.phschool.com webcode ama-1215

Mrs. Carol Lange                                                                     11
Textbook page 31
Unit 1
Prime Time                                        Always
support
your
with
examples!
CONNECTIONS:

28) Allie’s eccentric aunt, May Belle, hides \$10,000 in \$20 bills
under her mattress. If she spends one \$20 bill every day, how many days
will it take for her to run out of bills?
It will take 500 days. I made a chart for 5 days, and saw that it would
take 5 days to spend \$100. 100 goes into 10,000, 100 times, so 100
times 5 days equals 500 days.
Be sure to explain any strategy you use!

Mrs. Carol Lange                                                                         12
Textbook page 33
Unit 1
Prime Time                                     Always
support
your
with
examples!
EXTENSIONS:

37) For any three consecutive numbers, what can you say about
odd numbers and even numbers? Why?

For any three consecutive numbers, either two of the numbers are
odd (4,5,6) or two of the numbers are even (5,6,7). It depends on
what the first number is.

Mrs. Carol Lange                                                                    13
Textbook page 34
Unit 1
Prime Time
ORDER OF OPERATIONS
Order of Operations is a rule developed by mathematicians that
determines in what order you solve an equation.

1) Solve all operations in parentheses first.
2) Solve all exponents
3) Multiply/divide left to right
Do ALL multiplication before you add or subtract!
Solve these:
7+6–3x2=              7   (multiply 3 x 2 first, then add 7 + 6 , then subtract 6 from 13)

32 – 2 x 3 + 6=       9   (Solve 32 first to get 9, then multiply 2 x 3 to get 6; 9 – 6 + 6 = 9)

Mrs. Carol Lange                                                                                 14
Textbook page 26
Unit 1
Prime Time
INVESTIGATION THREE
Common Multiples and Common Factors

•Common Multiples are multiples that appear on the list of multiples for two (or
more) different numbers. Some multiples of 5 are 5, 10, 15, 20, and
some multiples of 10 are 10, 20, 30. Common multiples for 5 and 10
are 10, and 20 because they are on both lists. Numbers have an
infinite number of common multiples. The smallest number on both
lists is the Least Common Multiple.
•Common Factors are factors that appear on the list of factors for two (or
more) different numbers. Factors of 18 are 1,18; 2,9; 3,6 and the
factors of 12 are 1,12; 2, 6; 3,4 so common factors are 1, 2, 3, and 6.
the Greatest Common Factor is 6.

Mrs. Carol Lange                                                                   15
Textbook page 37-48
Unit 1
Prime Time                                  Always
support
your
with
examples!
APPLICATIONS:

6) List the common multiples from 1 to 100 for each pair of
numbers. Then find the least common multiple for each pair.

20 and 25

20: 20, 40, 60, 80, 100
25: 25, 50, 75, 100
The LCM is 100.
It is the smallest multiple on that appears on both lists.

Mrs. Carol Lange                                                                   16
Textbook page 42
Unit 1
Prime Time                 Always
support
your
with
Sample ACE questions and answers:   examples!
CONNECTIONS:

36) 3 x 5 x 7 = 105 Use this fact to find each product.
a) 9 x 5 x 7 =
105 x 3 ( 315) because 9 is 3 x 3.
You need to include one more factor of 3.
b) 3 x 5 x 14 =
105 x 2 (210) because 14 is 7 x 2.
You need to include one more factor of 2.
c) 3 x 50 x 7 =
105 x 10 (1050) because 50 is 10 x 5.
You need to include one more factor of 10.
d) 3 x 25 x 7 =
105 x 5 (525) because 25 is 5 x 5.
You need to include one more factor of 5.
Mrs. Carol Lange                                                       17
Textbook page 45
Unit 1
Prime Time                                        Always
support
your
with
Sample ACE questions and answers:                     examples!
EXTENSIONS:

38) Ms. Santiago has many pens in her desk drawer. She says that
if you divide the total number of pens by 2, 3, 4, 5, or 6, you get a
remainder of 1. What is the smallest number of pens that could be in
Ms. Santiago’s desk?

The smallest number of pens in Ms. Santiago’s desk is 61. You need
to find the least common multiple of 2, 3, 4, 5 and 6, and add 1 (the
remainder) to it.

Mrs. Carol Lange                                                                      18
Textbook page 45
Unit 1
Prime Time
INVESTIGATION FOUR
Factorizations: Searching for Factor Strings

•Factorizations are strings of factors of a number. All numbers can be written
as strings of factors. For example: 50 can be written as 2 x 25, or
2 x 5 x 5.
•All numbers are products of prime numbers. The strong of factors that is made
up of all prime numbers is called the Prime Factorization of a
number. Prime Factorizations can be found by dividing each factor by
a prime number, or by using a factor tree to identify factor pairs.
•Exponents tell you how many times a number is used as a factor.
For example, 2 x 2 x 2 is written in exponent form as 23.
•Number pairs whose greatest common factor is one, are called relatively
prime. Relatively prime numbers can be multiplied together
to find their least common multiple.
Mrs. Carol Lange                                                                 19
Textbook page 49-60
Unit 1
Prime Time                                    Always
support
your
with
Sample ACE questions and answers:                   examples!
APPLICATIONS:

13) To indicate multiplication, you can use a raised dot symbol.
For example, 3 x 5 = 3 . 5. Find the prime factorization of 312 using
raised dot symbols.
312

6         52

3       2    2     26

2    13
3 . 2 . 2 . 2 . 13 = 312   or 3 . 23 . 13 = 312

Mrs. Carol Lange                                                                    20
Textbook page 56
Unit 1
Prime Time                                          Always
support
your
with
Sample ACE questions and answers:                         examples!
CONNECTIONS:

32) What is my number?
a) My number is a multiple of 2 and 7.
Start by listing multiples of 2 and 7: 14, 28, 42, 56, 70, 84, 98
b) My number is less than 100 but greater than 50.
Using the list from question a, eliminate multiples less than 50:
56, 70, 84, 98
c) My number is the product of 3 different prime numbers.
Find the prime factorization of each of your multiples.
56 (2 x 2 x 2 x 7); 70 (2 x 5 x 7); 84 (2 x 2 x 3 x 7); 98 (2 x 7 x 7).
Only 70 is a product of three different prime numbers.

Mrs. Carol Lange                                                                           21
Textbook page 58
Unit 1
Prime Time
INVESTIGATION FIVE
THE LOCKER PROBLEM
Students in a school create a problem by opening 1000 lockers.
•student 1 runs down the row of lockers and opens every door.
•student 2 closes the doors of all the even number lockers.
•student 3 changes the state (opens or closes) the doors of the lockers of
multiples of 3.
•Student 4 changes the state of the doors of lockers that are multiples of 4.

•Student 5 changes the state of every 5th door.
When all the students have finished, which locker doors are opened?
Discuss strategies you can use to solve the problem.

NEED HELP? http://www.PHSchool.com                       webcode amd-1501

Mrs. Carol Lange                                                                22
Textbook page 61-64
Unit 1
Prime Time
Always be
able to
END OF UNIT REVIEW                         provide an
explanation
for your
For your Unit Test, know how to:                work!

•Find factors and factor pairs of a number
•Find common factors and the greatest common factor of two numbers
•Find multiples of a number and least common multiples of two or more numbers
•Use exponents and Order of Operations
•Find a factor string and prime factorization of a number

Use your study guide from the back of the parent letter!

Mrs. Carol Lange                                                                   23
Textbook page 6-60
Unit 1
Prime Time
SPECIAL NUMBER PROJECT
For your special number project you need to choose one of the following projects:
•Collage
•Comic strip
•Narrative story
In your project, you need to include as much information