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Warm Up MI­ 36

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Assignment

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Practice

713 77

A = bh7 x 1391

A = ½bh½(7 x 7)½(49)24.5

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Practice6

8

4

84

12

8

54

A=½bh6x824 A=bh

4x832

A=bh12x896

A=½h(b1 + b2)½(4)(8 + 5)½(4)(13)(2)(13)26

24 + 32 + 96 + 26 =

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Practice

246

A=bh24 x 6

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Practice

4410

A=bh44x10

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Stretch

5 5 10 10

12

30

Whole KiteA= bh12 x 30360

White KiteA= bh12 x 15180

Whole ­ White = 

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Stretch

5

55

RhombusA=bh5 x 420

TriangleA=½bh½(5 x 4)

10

TriangleA=½bh½(5 x 4)

10

20 + 10 + 10 =

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ReviewA=½h(b1 + b2)½(8)(15 + 6)½(8)(21)(4)(21)

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ReviewA=½bh½(4.5x4)½(18)

A=bh(4.5x20)

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Review14

14A=bh14x14

5(17 + 20) = 5 x 17 + 5 x 20

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learning goals

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M1: 1.4 Common Factors and Multiples

/ / #

Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

Factor Pairs: two natural numbers other than zero that are multiplied together to produce another number.

Distinct Factors: factors that appear only once in a list.

18

Rainbow

T- Chart

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MI ­40

12 15 16 20

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M1: 1.4 Common Factors and Multiples

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Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

Common Factor: a factor of 2 or more numbers.• numbers that share the same factors.

Greatest Common Factor (GCF): The greatest of 2 or more numbers in common.

The greatest amount of ways to divide something equally.

3 Ways:1. T-chart- list factors2. Tree3. Ladder

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MI ­40

12 15 16 201  122   63   4

1  153   5

1  162   84   4

1  202   104    5

Common Factors:1, 3

GCF: 3

Circle the common factors & find the GCF.

Common Factors:1, 2, 4GCF: 4

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M1: 1.4 Common Factors and Multiples

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Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

Prime:  2 factors, 1 and itself.Composite: more than 3 factors

3 = 1 x 3

8 = 1 x 88 = 2 x 4

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Sieves of Eratosthenes

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M1: 1.4 Common Factors and Multiples

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Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

Prime Factorization: long string of ONLY prime factors • Written as the product of primes.• Divide number until all prime numbers

are revealed.• DO NOT DIVIDE BY 1• Answer written in exponents

> 22 x 5

20

10 2

5 2Factor Tree

Ladder

20 Only divide by prime numbers.• 2, 3, 5, 7, 11• Until you get to 1• The numbers on the side of the ladder

are the prime factors.• Write them in exponent form.

> 22 x 5

2102551

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Find the prime factorization of using a tree.81 240

Find the prime factorization of using a ladder.56 42

9 9

3 3 3 3

34

24 10

2 5212

34

2 2

24 x 3 x 5

2282142771

2213771

2 x 3 x 723 x 7

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12 15 16 20

List the common factors comparing 2 numbers.

1  122   63   4

1  153   5

1  162   84   4

1  202   104    5

12 & 15 = _____________________________________

12 & 16 = _____________________________________

12 & 20 = _____________________________________

15 & 16 = _____________________________________

15 & 20 = _____________________________________

16 & 20 = _____________________________________

1, 31, 2, 41, 2, 411, 51, 2, 4

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MI ­40

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Find the prime factorization of 54 and 84 using a tree /ladder.

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M1: 1.4 Common Factors and Multiples

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Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

Greatest Common Factor (GCF): The largest factor two or more numbers have in common.• The greatest amount of ways to

divide something equally.

Relatively Prime: Two numbers that do not have any common factors other than 1.

20 and 35

1 202 104 5

1 355 7

Common Factors:1 & 5

GCF = 5

GCF & the distributive property

5 is the GCF of 20 and 35.

5(20 + 35) = 5 x 4 + 5 x 7

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Cycles

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M1: 1.4 Common Factors and Multiples

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Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

Common Multiple: A number that is a multiple of 2 or more numbers.

Least Common Multiple (LCM): Smallest product (other than zero) that two or more numbers have in common.

Commutative Property of Multiplication: States that for any numbers a and b, the product a b is equal to the product b a.

2: 2, 4, 6, 8, 10, 12

4: 4, 8, 12, 16, 20

LCM = 4

Multiple: shared products of numbers

a b = b a

2 4 = 4 2

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M1: 1.4 Common Factors and Multiples

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Examples: Notes:

Essential Question: How can you use shapes to see relationshipsbetween numbers?

LCM using the ladder.1. Divide by prime numbers.2. Go until the 2 numbers don't have any

more common factors.3. Multiply all the numbers on the

outside of the ladder together.

Ladder/ Hockey Sticks

28  24214  12     27  6

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Find the LCM of 24 & 16 using the ladder.

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18

56

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Remember!!