M1 1.4 Common Factors_Multiples Compacted.notebook 1 August 15, 2018 Jun 2010:53 AM Warm Up MI 36 8 14 18
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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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MI 40
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!!