1. Understanding Numbers

2. Lesson 1: Place Value

3. The all-time best selling book is Guinness World Records.
From October 1955 – June 2002 it sold, 94,767,083 copies
This number can be represented in a place-value chart
Hundred Millions
Ten Millions
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones 9 4  7  6 7  0   8 3 

4. Place Value
Information about a place value chart that you should know:
From Right to Left, each group of 3 place values is called a period
Within each period, the digits of a number are read as: hundreds, tens, ones
Millions Period
Thousands Period
Units Period
Hundred Millions
Ten Millions
(Ones)
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones

5. Place Value This place value chart shows the number 3 159 119
Here are some ways to represent this number:
Standard Form:
Expanded Form:
Number-Word Form: 3 million 159 thousand 119
Word Form: three million, one hundred fifty nine thousand one hundred nineteen
Hundred Millions
Ten Millions
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones 3 1 5 9

6. Lesson 2.1 Understanding Large Numbers
Space after hundreds
Lesson 2.1 Understanding Large Numbers
A Few Notes: When writing a number with 5+ digits, leave a space between the periods:
Space after thousands
Hundred Millions
Ten Millions
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones 3 1 5 9

7. Lesson 2.1 Understanding Large Numbers
A Few Notes:
When we read / say large numbers we say the period name after each period except the units period:
Three million
One hundred fifty-nine thousand
One hundred nineteen
Hundred Millions
Ten Millions
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones 3 1 5 9

8. Lesson 2:Multiples

9. Lesson 2: Multiples Explore (Partners)
On Thursday morning the local radio station held a call-in contest.
Every third caller to the station won a T- Shirt
Every seventh caller won a baseball hat
In 50 calls, which callers won a T-shirt? A baseball hat? Which numbers won both?

10. Lesson 2: Multiples In 50 calls, these callers won a T-shirt:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48
In 50 calls, these callers won a baseball hat:
7, 14, 21, 28, 35, 42, 49
In 50 calls, these callers won a won both:
21, 42

11. Lesson 2: Multiples The result of multiplying a number by a number
Example: multiples of 5 are 10, 15, 20
5 x 2 = 10
5 x 3 = 15
5 x 4 = 20

12. Lesson 2: Multiples A method for finding multiples
Use a chart. Start at the number and count by the number
The multiples of 6 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

13. Lesson 2: Multiples
A method for finding multiples Use multiplication: 5 x 1 = 5 5 x 2 = 10 (factor x factor = multiple) 5 x 3 = 15 5 x 4 = 20 5 x 5 = 25

14. Lesson 2: Multiples KEY PHRASES
5, 10, 15, and 20 are all multiples of 5.
5, 10, 15, and 20 are divisible by 5.
5 divides 5, 10, 15, and 20.

15. Lesson 2: Multiples A method for finding multiples Use a pattern rule:
Start at x. Add x each time
In this example X = 4
4,(+4 =) 8, (+4 =) 12, (+4 =) 16,(+4 =) 20,(+4 =)
The multiples of 4 are: 4, 8, 12, 16, 20, 24, …

16. Lesson 2: Multiples Here are the multiples of 2:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30
Here are the multiples of 5:
5, 10, 15, 20, 25, 30
Which multiples are in both lists?
10, 20, 30
These are common multiples of 5 and 2
10 is the least common multiple of 5 and 2

17. Solve This…
Wieners are sold in packages of 12. Hot dog buns are sold in packages of 8. Suppose you plan to sell about 75 hot dogs to raise money for charity. You do not want any wieners or buns left over. How many packages of each should you buy?

18. A Solution… Find the multiples of 8 8, 16, 24, 32, 40, 48, 60, 68. 72
12, 24, 36, 48, 60, 72, 84

19. A Solution… Identify the common multiples: 24, 48, 72
Since 72 is close to 75, you should buy 72 wieners and 72 buns.
You skip counted by eight 9 times to reach 72, so buy 9 packages of buns.
You skip counted by twelve 6 times to reach 72, so buy 6 packages of wieners.

20. Lesson 3: Factors

21. Factors Lesson 3: Factors
Factors are the numbers we multiply together to get another number:
Example: 5 x 3 = 15
5 is a factor
3 is a factor
15 is the product

22. Lesson 3: Factors A number can have many factors:
Example: factors of 12 are 1, 2, 3, 4, 6 and 12
2 × 6 = 12
4 × 3 = 12
1 × 12 = 12

23. Lesson 3: Factors Factors of 9 Factors of 15
Common Factors A number that is a factor of each of the given numbers Ex. List the Factors of 9 and 15 9: 1, 3, 9 15: 1, 3, 5, 15
Factors of 9
Factors of 15
Common Factors 1 3 9
5, 15
Greatest Common Factor = 3

24. Lesson 4:Prime and Composite Numbers

25. 2 x 8 = 16 Lesson 4: Prime Numbers
2 and 8 are factors of 16. What others can you name?
1, 4, 16
2 x 8 = 16
Factor
Factor
Product

26. Lesson 4: Prime Numbers Activity Cut out your squares
Use the squares to make all the different rectangles you can make using each number of squares
Complete the table to record your data

27. 1 x 6
3 x 2
2 x 3
6 x 1

28. Lesson 4: Prime Numbers Activity (Part 2)
use the information from the chart to complete the graph.

29. Lesson 4: Prime Numbers Activity (Part 3)
What observations can you make by looking at patterns in the graph you completed?

30. Lesson 4: Prime Numbers Explore: Which numbers have only 2 factors?
2, 3, 5, 7, 11, 13, 17, 19
What do you notice about these numbers?
All the numbers except 2 are odd numbers.
What do you notice about the factors of these numbers?
The factors of each number are 1 and the number itself.
Which numbers have more than 2 factors?
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20

31. Lesson 4: Prime Numbers
With 23 squares you can only make one rectangle 23 has two factors: 1, 23 A number with only two factors (1 and itself) is called a PRIME NUMBER 1 23

32. Lesson 4: Prime Numbers Simplify It…
When a number can not be divided evenly by another number
it must be a whole number greater than 1

33. Lesson 4: Composite Numbers3
With 24 Squares you can make 4 different rectangles 6 8 4
24 has eight factors: 1, 2, 3, 4, 6, 8, 12, 24 1 24 12
A number with more than two factors is called a
COMPOSITE NUMBER 2

34. Lesson 4: Composite Numbers
Simplify It…
When a number can be divided evenly by another number, it is a Composite Number

35. Brainpop: Prime Numbers
ndoperations/primenumbers/preview.wem l

36. Lesson 5: Prime Factorization

37. Lesson 5: Prime Factorization
All Composite Numbers are made up of Prime Numbers that have been multiplied together
It is like Prime Numbers are the building blocks of all numbers.

38. Lesson 5: Prime Factorizations
Prime Factors: factors that are Prime Numbers
Ex. 24 has eight factors:
1, 2, 3, 4, 6, 8, 12, 24
2, 3 are prime numbers therefore they are the prime factors of 24

39. Lesson 5: Prime Factorization
What are the prime factors of 12 ?
Method 1
Step 1 – Divide (It is best to start working from the smallest prime number)
12 ÷ 2 = 6
Yes, it divided evenly by 2. We have taken the first step!
12 = 2 x 6

40. Lesson 5: Prime Factorization
What are the prime factors of 12 ?
Method 1
Step 2 – Keep and Divide (keep all prime numbers and divide the rest)
12 = 2 x 6
6 is not a prime number, so we need to divide again
6 ÷ 2 = 3

41. Lesson 5: Prime Factorization
What are the prime factors of 12 ?
Method 1
Step 3 – Keep and Divide (keep all prime numbers and divide the rest)
12 = 2 x 2 x 3
2 and 3 are both prime numbers, so our factor phrase is:
12 = 2 × 2 × 3

42. Lesson 5: Prime Factorization
Try These:
What is the prime factorization of 48 ?
What is the prime factorization of 17?
What is the prime factorization of 147 ?

43. Lesson 2.5: Prime Factorization
Method 2: The Factor Tree

44. Lesson 2.5: Prime Factorization
Method 2: The Factor Tree

45. Lesson 5: Prime Factorization
Try These:
What is the prime factorization of 48 ?
What is the prime factorization of 17?
What is the prime factorization of 147 ?

46. Lesson 6: Order of Operations

47. Vocabulary Expression:
A mathematical statement with numbers and operations
A math question without an answer
Example:
2×3 =
4x – 7 =
10 x ÷ 5 =
𝜋 𝑟 2 =

48. Lesson 2.7: Order of Operations
When you solve a problem that uses more than one operation, the answer depends on the order in which you perform the operations.
Evaluate the expression: x 4
If you add first, you get: 9 x 4 = 36
If you multiply first, you get: = 27

49. Lesson 2.7: Order of Operations
To avoid getting two answers, there is a rule that multiplication is done before addition.
So, x 4 =
27, which is the correct answer

50. Lesson 2.7: Order of Operations
We use brackets if we want certain operations carried out first.
To make sure everyone gets the same answer when evaluating an expression, we use this order of operations:
Do the operations in brackets.
Multiply or divide, in order, from left to right.
Then add or subtract, in order, from left to right.

51. Lesson 2.7: Order of Operations
Evaluate: =
= 8 + 6
= 14

52. Lesson 2.7: Order of Operations
Evaluate: ÷ 2 =
÷ 2
= 16 – 7
= 9

53. Lesson 2.7: Order of Operations
Evaluate: 7 x (4 + 8)
7 x (4 + 8)
= 7 x 12
= 84

54. Lesson 2.7: Order of Operations
The order of operations is :
Brackets
Multiply / Divide (from left to right)
Add / Subtract (from left to right)

55. https://www.brainpop.com/math/numbersandoperations /orderofoperations/preview.weml