10/22: 10/22 Exploration 4.1 4.3


Exploration 4.1: Exploration 4.1 So we don’t have time for this exploration, but this game is played in the schools. So I’ll leave them on the slides and you can look at on your own.


Rules: Rules The team crosses out a number. The taxman crosses out all the proper factors of that number. The team crosses out another number. A number can only be crossed out if one of its proper factors has not been crossed out. {At the end of the game the taxman gets all the remaining numbers. } Not going to do. To determine your score add up all the numbers your team crossed out.


Against me!: Against me! We won’t use the rule of the taxman getting the rest for this part: Factor Game 1. What are some strategies?


4.3: 4.3


A word problem: A word problem A florist has 36 roses and 27 tulips, she must use to create bouquets. What is the largest number of bouquets she can make without having any flowers left over, and with each bouquet having the same number of each flower? You can use any resource. Talk with your group.


1. Greatest common factor (GCF) [You might also see greatest common divisor, GCD]: 1. Greatest common factor (GCF) [You might also see greatest common divisor, GCD] If we have two numbers a and b, the GCF is the greatest number that divides both a and b. Notation: GCF(a, b) Can look for the GCF of more than 2 numbers, which we’ll get into later. What is the GCF(4,8)? GCF(2,8)? What can we say about the size of a GCF?


Slide10: Can the GCF of two numbers ever be one? Relatively Prime:


2. How to find the GCF: 2. How to find the GCF A. Use factorization and see what is the largest number in common to both. Factors of 24= Factors of 36= Common Factors=


Slide13: B. Use intuition or number sense You might already know the GCF. You try a factor and can keep going (common when you reduce fractions) 24=6∙4 24=12∙2 36=6∙6 36=12∙3


Slide14: C. Repeatedly divide by prime numbers (I’ve never seen this one before.)


Slide15: D. Prime Factorization. 24=2∙2∙2∙3=23∙3 36=2∙2∙3∙3=22∙33 Want what’s common in both prime factorizations. Look for smallest exponents.


Slide16: What is the GCF(12, 30, 75)? Find a pair of numbers above 50 whose GCF is 2.


Another Word Problem: Another Word Problem During the summer months, one ice cream truck visits Monica’s neighborhood every 4 days. A second ice cream truck visits her neighborhood every 5 days. If both trucks visited today, when is the next time that both trucks will visit on the same day? (You just have to say how many days from now)


3. The Least Common Multiple (LCM): 3. The Least Common Multiple (LCM) The LCM of two numbers a, and b is the smallest number that both a and b divide. Very important for fractions. Notation: LCM(a,b) What is the LCM(5,10)? LCM (7,3)? What can we say about the size of the LCM?


A variation of the word problem:: A variation of the word problem: What if the first ice cream truck came every 6 days, and the second every 8 days. When will be the next time they arrive on the same day?


4. Strategies to finding the LCM: 4. Strategies to finding the LCM A. Look at the multiples of each. Stop when you get one in common. Ex: Find the LCM(6,9) Multiples of 6= Multiples of 9=


Slide24: B. Use Prime Factorization. Ex: Find the LCM(24,36) 24=2∙2∙2∙3=23∙3 36=2∙2∙3∙3=22∙33 The LCM must contain all the factors of each number. Look for greatest exponent.


4. The Relationship Between the GCF and LCM: 4. The Relationship Between the GCF and LCM Fill in the following table: Do you notice a pattern?


Slide26: We then have that: Any ideas why? Find the LCM(24, 36) and LCM (27, 35)


Slide27: If the GCF of 45 and x is 9, and the LCM of 45 and x is 135, find x. Read your book as well!


Homework: Homework Due Friday: Assignment 10