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Today’s topic is… 2 Divisibility Least Common Multiple Greatest Common Factor Ratios, Proportions and Rates

OBJECTIVES: 1. Determine what is being asked. 2. Plan how to solve the problem. 3. Solve problems involving divisibility, greatest common factor, least common multiple, ratios and rates. 4. Check your answer. 5. Communicate the answer. 3

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PROBLEM SOLVING WORKSHOP II 1.Forty-eight students are going on a field trip. Their teacher wants to separate them into equal groups. Suggest five different ways that the teacher can do it. Divisibility 5

PROBLEM SOLVING WORKSHOP II 2- A lighthouse flashes its light every 12 seconds, another every 18 seconds, and a third every minute. At 6.30pm the three flash simultaneously. How long will it be until all three lighthouses flash again at the exact same time? LCM 6

3- 6 lbs. of potatoes cost $54. How much would 5 lbs. cost? Ratio & Proportion 7

4- Cameron is making bead necklaces. He has 90 red beads and 100 orange beads. What is the greatest number of identical necklaces he can make if he wants to use all of the beads? GCF

5- Blank video tapes can be purchased in packages of 3 for $4.99, or 10 for $ Which is a better value? 9 Unit Price

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PROBLEM SOLVING WORKSHOP II 1.Forty-eight students are going on a field trip. Their teacher wants to separate them into equal groups. Suggest five different ways that the teacher can do it. Divisibility 11

12 1- This is a divisibility question. What are the factors of 48? 1, 48, 2, 24, 3, 16, 4, 12, 6, 8 On a field trip, the number per group might depend on the how many chaperones are available or other considerations. But the teacher might choose to divide the class into groups of 3, 4, 6, 8 or 12.

PROBLEM SOLVING WORKSHOP II 2- A lighthouse flashes its light every 12 seconds, another every 18 seconds, and a third every minute. At 6.30pm the three flash simultaneously. How long will it be until all three lighthouses flash again at the exact same time? LCM 13

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3- 6 lbs. of potatoes cost $54. How much would 5 lbs. cost? Ratio & Rates 15

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4- Cameron is making bead necklaces. He has 90 red beads and 100 orange beads. What is the greatest number of identical necklaces he can make if he wants to use all of the beads? GCF

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5- Blank video tapes can be purchased in packages of 3 for $4.99, or 10 for $ Which is a better value? 19 Unit Price

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PROBLEM SOLVING WORKSHOP II LCM 23

24 Divisibility & Factors

25 Ratio & Proportion

26 Unit Price

GCF 27

PROBLEM SOLVING WORKSHOP II Ratio & Proportion 28

PROBLEM SOLVING WORKSHOP II LCM 29

30 Ratio & Proportion

PROBLEM SOLVING WORKSHOP II 31

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33 2- This question is a Least Common Multiple question. The most effective way to solve is to use prime factors. 18 = 2 x 3 x 3 24 = 2 x 2 x 2 x 3 The Least Common Multiple of these includes all the prime factors of either number. LCM= 2 x 2 x 2 x 3 x 3 = 72 In 72 days from today, both men will be back in New York at the same time.

34, Divisibility

35 Ratio & Proportion

36 Ratio, Proportion and Rate

6- This is a GCF question. Since 6 is a factor of itself and also of 18, it is the GCF. There can be only 6 plates. 37

38 7- Solution: You could set up a proportion. Since _9_ = _4_ But you might have noticed that 90 is a multiple of 10 and so the boat gets 10 miles per gallon. Thus is could travel 40 miles on 4 gallons.

39 8- LCM Since 2, 3, and 5 are all prime numbers the best solution is to multiply them together. 2 x 3 x 5 = 30 John, Louise and Rita will all swim again in exactly 30 days. (Although there will be days before that in which two of them would swim together.)

40 9- Set up a proportion: 72 km = 58 km 36 l g Cross multiply 2088 = 72g = g The boat needs 29 liters to go 58km. Ratio & Rate

DIVISIBILITY Of the three classes only French has a number of students which is a prime number. That means the students in the French class cannot be divided into equal groups.

Math skills are intended to be applied. We apply those skills by solving real world problems. Step one is recognizing which skills are most appropriate to finding the solution. Step two is applying the skill with accuracy. Step three is making sense of - communicating- the answer. 42

In your math notebook, complete the exercises that follow. Be sure to show all work. Make sense of the answer. Please write a sentence which explains the meaning of your answer. 43

Scribner's prints 6 books at a time. Penguin prints books in sets of 15. Both companies printed the same number of books last year. What is the smallest number of books that each company could have printed? 44

Destiny is sewing. She has two pieces of thread: one 18 feet long and the other 12 feet long. She needs to make as many pieces of thread as she can. All must be the same length. She wants no thread left over. What is the greatest length that she can make them? 45

The ratio of spheres to cubes spheres in a geometry box is 1 to 5. If there are 9 spheres in the geometry box then how many cubes and spheres are there altogether? 46

8 lbs. of apples cost $88. How much would 34 lbs. cost? 47

48 Company A cellular phone company offers a wireless phone plan that includes 250 base minutes for $24.99 per month. Company B has a plan that includes 325 base minutes for $ a)Find the unit rate for base minutes for each plan. b)Which company offers a lower rate for base minutes?