1. Big Idea 2 – Fractions & Decimal Operations

2. Associative Property of Addition – the property that
states when the grouping of addends is changed, the
sums is the same Example: (2 + 5) +7 = 2 + (5 + 7)
Common Factor – a number that is a factor of two or
more numbers Example: factors of 4: 1, 2, 4 factors of 6: 1,
2, 3, 6 - 1 & 2 are the common factors
Commutative Property of Addition – the property that
states that when the order of two or more addends is
changes, the sum is the same Example: 4 + 6 = 6 + 4

3. Composite number – a whole number having more
than two numbers Example: 2 (1,2)
Divisible – a number is divisible by another number if
the quotient is a whole number and the remainder is
zero
Factor Tree – a diagram that shows the prime factors
of a number

4. Greatest Common Factor (GCF) – the greatest factor
that two or more numbers have in common
Example: 2 – (1, 2)
4 – (1. 2. 4)
6 – (1, 2, 3, 6)
2 is the GCF of 2, 4 & 6
Ladder Diagram – a diagram that shows the steps of
repeatedly dividing by a prime number until the
quotient is 1
Prime Factorization – a number written as the product
of all its prime factors

5. 6.1 Addition
with Like
Denominator
s
Complete
Investigate pg. 231
with a partner
Materials needed:
pattern blocks

6. Explain how the sum is related to the number of
same-shaped pattern blocks.
Explain how you could add fractions that have the
same denominator without using the model?
Analyze in the Investigate, you modeled 5/6 + 3/6 =
8/6 using pattern blocks. Use blue quadrilaterals and
two yellow hexagons to model a different equation
with an equivalent sum. What is your equation?
Explain why you can use different-shaped pattern
blocks to model the same sum.

7. 6.1 Addition
with Like
Denominators
Use a number line
to add fractions.
?

8. 6.1 Addition
with Like
Denominators
Complete Problem
Solving pg. 234
Sense or Nonsense?

9. How can you use models
to add fractions with like
denominators?

10. 6.2 Subtraction
with Like
Denominators
Complete
Investigate with a
partner (pg. 235)
Materials: pattern
blocks

11. Explain how you subtracted in the take-away
model.
Explain how you subtracted in the
comparison model.
Analyze How is the comparison model
different from the take-away model?
Explain how you could subtract fractions that
have like denominators without using models.

12. 6.2 Subtraction
with Like
Denominators
Use a number line
to subtract
fractions.

14. How can you use
models to subtract
fractions with like
denominators?

15. A number is divisible by: Example Your Example
2 – if the last number is even 96
3 – if the sum of the digits is 96 (9+6 =15)
divisible by 3 15 ÷ 3 = 5
4 – if the last two digits form 128
a number divisible by 4 28 ÷ 4 = 7
5 – if the last digit is 0 or 5 355
6 – if the number is divisible 96
by 2 and 3 6 is even (9+6=15) 15÷3
9 – if the sum of the digits is 396 (3+9+6=18)
divisible by 9 18 ÷ 9 = 2
10 – if the last digit is 0. 550

17. 6.3 Problem
Solving pg.
16. Dirk bought a set of
stamps that has fewer 242
stamps than the set for
Germany. The number
Use the table to
of stamps in the set he solve 16 – 19
bought is divisible by 2,
3, 5, 6 and 10. Which
set is it?
17. The number of stamps in one set is divisible only by 5.
Which set is it?
18.Tina collects stamps. She wants to purchase two different
sets of stamps so that she can put 9 stamps on a page in her
collector’s notebook and not have any stamps left over.
Which two sets of stamps should she purchase?
19. Geri wants to put 10 stamps on some pages
in her stamp book and 9 stamps on other pages. Explain
how she could do this with the stamp set for Japan.

18. How can you tell if a
number is divisible by 2, 3,
4, 5, 6, 9 or 10?

20. Prime numbers – a whole number greater than 1 that
has exactly two factors, 1 and itself
Example: factors of 13: 1, 13
Composite numbers – a whole number greater than 1
that has more than two factors
Example: factors of 12: 1, 2, 3, 4, 6, 12

21. Prime
Numbers
Step 1: Cross out 1,
because it is not a prime
number (it has only one
factor)
Step 2: Circle 2, since it is
prime (factors: 1,2) Cross
out all other multiples of
2.
Step 3: Circle the next
number that is not
crossed out & then cross
out all of multiples of that
number.
Step 4: Repeat Step 3 until
every number is either
circled or crossed out.

23. How can you tell whether
a number is prime or
composite?

24. E very composite number can be written as a product
of factors that are all prime numbers.
A factor tree can be used – a diagram that shows the
prime factors of a number
There are two ways to begin a factor tree – using basic
facts of the number or divisibility rules
 Which ever strategy you use continue with it until the
only factors remaining are prime numbers

25. Brain Pop Video - Factors

26. 4 + 8 = 12 (12 is divisible by 3 therefore
Basic fact: 6 x 8 = 48
48 is also)

27. Ladder
Diagram
Start by choosing
a prime factor by
which the
number is
divisible. Then
divide.
Continue dividing
by a prime factor
until the quotient
is 1.

28. 21. The 4-digit code number is made up of the prime
factors of 140. The factors are entered in order from Problem
greatest to least. What is the code number? Solving pg. 250
22. This 5-digit code is made up the prime factors of Use the information
108. The factors are entered in order from least to below to solve 21-24
greatest. What is the code number?
Each customer of a
23. This 6 –digit code number is made up of the prime bank must enter a 4 –
factors of 900. Each factor repeats twice, and the 6 digit code number
to use his or her cash
numbers are entered in order from greatest to least.
card at an ATM
What is the code? machine.
24. This 6-digit code number is made up of the prime
Suppose the code
factors of 1260. The factors are entered in order number is made up of
from least to greatest. What is the code number? prime factors that
are part of the
25. Find the prime factorization of 240. Write your account number.
answer as an expression using exponents.
26. Which shows the prime factorization of 144?

29. How can you find all the
prime factors of a number?

30. A common factor is a number that is a factor of two
or more numbers.
Factors of 6: 1, 2, 3, 6
Factors of 9: 1, 3, 9
The common factors are 1 and 3.
Greatest Common Factor is the greatest factor that
two or more numbers have in common.
Greatest Common Factor (GCF) of 6 & 9 is 3.

32. Common
Factors &
Simplest Form
Simplest form is
when the
numerator and
denominator both
have 1 as their only
common factor

33. 18. What fraction of the 50
states are part of the
Southeast region? Write
your answer in simplest
form.
19. What fraction of the 50
states are part of the
Northeast region? Write
your answer in simplest
form.

34. Maths Mansion: Show 25: Do the Same to the Bottom as th

35. 20. What fraction of the 50 states
are part of the West and
Southwest regions? Write your
answer in simplest form.
21. Florida borders both the
Atlantic Ocean and the Gulf of
Mexico . Thirteen states border
only the Atlantic Ocean. Four
other states border only the Gulf
of Mexico. Use simplest form to
write the fraction of the 50
states that border one or both of
these bodies of water.

37. How can you find the greatest
common factor of two or more
numbers?

44. How can you rename
fractions greater than 1 as
mixed numbers and rename
mixed numbers as fractions
greater than 1?

45. 6.9 Add &
Subtract
Fractions
***important
information***
before you can add
fractions the
denominators must
be the same!

46. 6.9 Add &
Subtract Like
Fractions
***important
information***
Before you can
subtract fractions
the denominators
MUST be the same!

48. 19. What fraction of the
students chose summer
or spring as their favorite
season? Write your
answer in simplest form.
20. What fraction of the
students chose fall or
winter as their favorite
season? Write your
answer in simplest form.

49. 21. What fraction of the
students chose summer or
winter as their favorite
season? Write your
answer in simplest form.
22. Which is greater, the
fraction of the students
whose favorite season is
summer, or the fraction of
the students combined
whose favorite season is
winter, spring, or fall
combined? By how much?

50. How can I add or subtract
fractions with like
denominators?

55. How can I add or subtract
mixed numbers with like
denominators?

57. Step 1 – rename the
mixed number as a
fraction greater than 1.
Step 2 – subtract the
mixed numbers. Write
the answer in simplest
form.

58. Step 1 – Rename both
mixed numbers as
fractions greater than 1.
Step 2 – Subtract the
fractions greater than 1.
Write the answer in
simplest form.

60. How can you rename a mixed
number to subtract a larger
fraction?

61. The commutative property of addition states that
when the order of two addends is changed, the sum is
the same. For example: 4 + 5 = 5 + 4
The associative property of addition states that when
the grouping of addends is changed, the sum is the
same. The grouping of addends is usually shown by
parentheses. For example: (5 + 8) + 4 = 5 + (8 + 4)

65. How can you add fractions
with like denominators using
the properties of addition?