Warm Up MI 36 8 14 18 Jun 20 10:53 AM 1
Assignment Jun 20 12:36 PM 2
Practice 7 13 A = bh 7 x 13 91 7 7 A = ½bh ½(7 x 7) ½(49) 24.5 Jun 20 12:36 PM 3
Practice 6 4 8 A=½bh 4 6x8 24 A=bh 4x8 32 4 5 8 8 A=bh 12x8 96 12 A=½h(b1 + b2) ½(4)(8 + 5) ½(4)(13) (2)(13) 26 24 + 32 + 96 + 26 = Jun 20 12:36 PM 4
Practice 24 6 A=bh 24 x 6 Jun 20 12:36 PM 5
Practice 44 10 A=bh 44x10 Jun 20 12:36 PM 6
Stretch 12 5 5 10 10 30 Whole Kite A= bh 12 x 30 360 Whole White = White Kite A= bh 12 x 15 180 Jun 20 12:36 PM 7
Stretch Rhombus A=bh 5 x 4 20 5 5 Triangle A=½bh ½(5 x 4) 10 5 20 + 10 + 10 = Triangle A=½bh ½(5 x 4) 10 Jun 20 12:36 PM 8
Review A=½h(b1 + b2) ½(8)(15 + 6) ½(8)(21) (4)(21) Jun 20 12:36 PM 9
Review A=½bh ½(4.5x4) ½(18) A=bh (4.5x20) Jun 20 12:36 PM 10
A=bh 14x14 14 Review 14 5(17 + 20) = 5 x 17 + 5 x 20 Jun 20 12:36 PM 11
Jun 21 2:28 PM 12
learning goals Jun 20 10:53 AM 13
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 18 Rainbow Notes: 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. T- Chart Aug 13 12:24 PM 14
12 15 16 20 MI 40 Jun 21 2:38 PM 15
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: Notes: 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 factors 2. Tree 3. Ladder Aug 13 12:24 PM 16
MI 40 Circle the common factors & find the GCF. 12 15 16 20 1 12 2 6 3 4 1 15 3 5 1 16 2 8 4 4 1 20 2 10 4 5 Common Factors: 1, 3 GCF: 3 Common Factors: 1, 2, 4 GCF: 4 Jun 21 2:38 PM 17
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 3 = 1 x 3 8 = 1 x 8 8 = 2 x 4 Notes: Prime: 2 factors, 1 and itself. Composite: more than 3 factors Aug 13 12:24 PM 18
Jun 21 2:52 PM 19
Sieves of Eratosthenes Jun 21 2:52 PM 20
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 20 10 2 5 2 2 Factor Tree Notes: 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 Ladder > 2 2 x 5 20 Only divide by prime numbers. 2 10 5 5 1 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. > 2 2 x 5 Aug 13 12:24 PM 21
Find the prime factorization of using a tree. 81 240 9 9 3 3 3 3 24 10 12 2 2 5 3 4 4 3 2 2 2 4 x 3 x 5 Find the prime factorization of using a ladder. 2 56 2 42 2 28 3 21 2 14 7 7 7 7 1 1 2 3 x 7 2 x 3 x 7 Aug 14 10:07 PM 22
12 15 16 20 MI 40 1 12 2 6 3 4 1 15 3 5 1 16 2 8 4 4 1 20 2 10 4 5 List the common factors comparing 2 numbers. 1, 3 12 & 15 = 1, 2, 4 12 & 16 = 1, 2, 4 12 & 20 = 1 15 & 16 = 1, 5 15 & 20 = 1, 2, 4 16 & 20 = Jun 21 2:38 PM 23
MI 40 Jun 21 3:12 PM 24
Jun 21 2:53 PM 25
Find the prime factorization of 54 and 84 using a tree /ladder. Aug 14 10:26 PM 26
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 20 and 35 1 20 1 35 2 10 5 7 4 5 Common Factors: 1 & 5 GCF = 5 Notes: 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. GCF & the distributive property 5 is the GCF of 20 and 35. 5(20 + 35) = 5 x 4 + 5 x 7 Aug 13 12:24 PM 27
Jun 21 2:51 PM 28
Cycles Jun 21 3:06 PM 29
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: 2: 2, 4, 6, 8, 10, 12 4: 4, 8, 12, 16, 20 LCM = 4 a b = b a 2 4 = 4 2 Notes: Multiple: shared products of 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. Aug 13 12:24 PM 30
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Jun 21 2:44 PM 32
/ / # M1: 1.4 Common Factors and Multiples Essential Question: How can you use shapes to see relationships between numbers? Examples: Ladder/ Hockey Sticks 2 28 24 2 14 12 7 6 Notes: 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. Aug 13 12:24 PM 33
Find the LCM of 24 & 16 using the ladder. Aug 14 10:37 PM 34
18 56 Jun 21 2:44 PM 35
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Remember!! Jun 20 12:36 PM 39