Big Idea 2 – Fractions & Decimal Operations

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

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

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

Complete

Investigate pg.

231 with a

partner

Materials

needed: pattern

blocks

6.1 Addition with Like Denominators

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.

Use a number

line to add

fractions.

6.1 Addition with Like Denominators

?

Complete

Problem Solving

pg. 234

Sense or

Nonsense?

6.1 Addition with Like Denominators

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

Complete

Investigate with

a partner (pg.

235)

Materials:

pattern blocks

6.2 Subtraction with Like Denominators

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.

Use a number

line to subtract

fractions.

6.2 Subtraction with Like Denominators

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

A number is divisible by:

Example Your Example

2 – if the last number is even

96

3 – if the sum of the digits is divisible by 3

96 (9+6 =15)15 ÷ 3 = 5

4 – if the last two digits form a number divisible by 4

12828 ÷ 4 = 7

5 – if the last digit is 0 or 5

355

6 – if the number is divisible by 2 and 3

966 is even (9+6=15)

15÷3

9 – if the sum of the digits is divisible by 9

396 (3+9+6=18)18 ÷ 9 = 2

10 – if the last digit is 0. 550

Use the table

to solve 16 –

19

6.3 Problem

Solving pg. 242

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.

16. Dirk bought a set of stamps that has fewer stamps than the set for Germany. The number of stamps in the set he bought is divisible by 2, 3, 5, 6 and 10. Which set is it?

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

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

Prime NumbersStep 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.

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

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 rulesWhich ever strategy you use continue with it

until the only factors remaining are prime numbers

Brain Pop Video - Factors

Basic fact: 6 x 8 = 484 + 8 = 12 (12 is divisible by 3 therefore 48 is also)

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.

Ladder Diagram

21. The 4-digit code number is made up of the prime factors of 140. The factors are entered in order from greatest to least. What is the code number?

22. This 5-digit code is made up the prime factors of 108. The factors are entered in order from least to greatest. What is the code number?

23. This 6 –digit code number is made up of the prime factors of 900. Each factor repeats twice, and the numbers are entered in order from greatest to least. What is the code?

24. This 6-digit code number is made up of the prime factors of 1260. The factors are entered in order from least to greatest. What is the code number?

25. Find the prime factorization of 240. Write your answer as an expression using exponents.

26. Which shows the prime factorization of 144?

Use the information below to solve 21-24

Each customer of a bank must enter a 4 – 6 digit code number to use his or her cash card at an ATM machine.

Suppose the code number is made up of prime factors that are part of the account number.

Problem Solving pg. 250

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

A common factor is a number that is a factor of two or more numbers.

Factors of 6: 1, 2, 3, 6Factors of 9: 1, 3, 9The 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.

Simplest form is

when the

numerator and

denominator

both have 1 as

their only

common factor

Common Factors & Simplest Form

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.

Maths Mansion: Show 25: Do the Same to the Bottom as the Top

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.

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

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

***important

information***

before you can

add fractions the

denominators

must be the

same!

6.9 Add & Subtract Fractions

***important

information***

Before you can

subtract

fractions the

denominators

MUST be the

same!

6.9 Add & Subtract Like Fractions

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.

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?

How can I add or subtract fractions with like denominators?

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

Step 1 – rename the mixed number as a fraction greater than 1.

Step 2 – subtract the mixed numbers. Write the answer in simplest form.

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.

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

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)

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