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Welcome to Math Level 6

Mr. Whalen

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Today’s topic is…

Problem-Solving Workshop:

Mixed Bag

Divisibility

Least Common Multiple

Greatest Common Factor

Ratios, Proportions and Rates

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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.

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Guided Practice

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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

Guided Practice

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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

Guided Practice

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3-

6 lbs. of potatoes cost $54. How much would 5 lbs. cost?Ratio &

Proportion

Guided Practice

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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

Guided Practice

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Blank video tapes can be purchased in packages of 3 for $4.99, or 10 for $15.49. Which is a better value?

Unit Price

Guided Practice

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Guided PracticeAnswers

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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

Guided Practice

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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.

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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

Guided Practice

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3-

6 lbs. of potatoes cost $54. How much would 5 lbs. cost?Ratio &

Rates

Guided Practice

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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

Guided Practice

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5-

Blank video tapes can be purchased in packages of 3 for $4.99, or 10 for $15.49. Which is a better value?

Unit Price

Guided Practice

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Independent Practice

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Independent Practice #1

15 kg of onions cost $120. How much would 44 kg cost?

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PROBLEM SOLVING

WORKSHOP II

Independent Practice #2

Juan and Freddie both travel for work. Juan visits New York every 18 days. Freddie visits NY once every 24 days.

Today, both men are in New York. How many days from now will both men be in New York again at the same time?

LCM

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Independent Practice #3

There are 126 students at school.

The music teacher wants to split the students up into equal groups for playing instruments.

Suggest three different ways that the teacher can split up the students.

Divisibility &

Factors

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Independent Practice #4

12 kg of wheat flour costs $36. How much would 15 kg cost?

Ratio & Proportion

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Independent Practice #5

Kim can buy a 64 ounce carton of orange juice for $2.49 or a 96 ounce carton for $3.29. Which is a better value?

(Round to the nearest cent

if necessary)

Unit Price

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Independent Practice #6

Jesse is setting out food for a party.

He has 6 avocado rolls and 18 cucumber rolls.

He wants each plate to be identical, with no rolls left over.

What is the greatest number of plates Jesse can create?

GCF

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PROBLEM SOLVING

WORKSHOP II

Independent Practice #7

A boat can travel 90 miles on 9 gallons of gasoline. How far can it travel on 4 gallons?Ratio &

Proportion

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PROBLEM SOLVING

WORKSHOP II

LCM

Independent Practice #8

John, Louise and Rita love to swim. John swims every 2 days, Louise swims every 3 days and Rita swims every 5 days.

If they all swim together on June 1st , when would be the next time they all swim on the same day?

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Independent Practice #9

A boat can travel 72 kilometers on 36 liters of gasoline. How much gasoline will it need to go 58 kilometers?

Ratio & Proportion

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PROBLEM SOLVING

WORKSHOP II

Independent Practice #10

A school has classes in French, Spanish and Chinese.

The French class has 29 students, Spanish has 27 students and Chinese has 23.

For which classes will the teacher have difficulty dividing the students into equal groups?

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Independent Practice Answers

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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 324 = 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.

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Divisibility

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Ratio & Proportion

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Ratio, Proportion and Rate

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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.

 

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7-  

Solution: You could set up a proportion. 

Since _9_ = _4_ 90 40 

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.

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8- LCMSince 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.)

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9- Set up a proportion: 

72 km = 58 km 36 l g

 

Cross multiply 

2088 = 72g 72 72

 

29 = g

The boat needs 29 liters to go 58km.

Ratio & Rate

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10- DIVISIBILITYOf 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.

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ConclusionMath 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.

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Assignments

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.

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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?

Problem Solving

Workshop

Assignment

#1

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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?

Problem Solving

Workshop

Assignment

#2

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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?

Problem Solving

Workshop

Assignment

#3

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

Problem Solving

Workshop

Assignment

#4

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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 $34.99.

a) Find the unit rate for base minutes for each plan.

b) Which company offers a lower rate for base minutes?

Problem Solving

Workshop

Assignment

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