Common Factors and Common Factors and MultiplesMultiples

There are many things in the world that happen There are many things in the world that happen over and over again in set cycles. Sometimes we over and over again in set cycles. Sometimes we want to know when two things will happen at the want to know when two things will happen at the

same time.same time.

Riding Ferris WheelsRiding Ferris Wheels You and your little sister You and your little sister

go to a carnival that has go to a carnival that has both a large and a small both a large and a small Ferris wheel. Ferris wheel.

You get on the Ferris You get on the Ferris wheel at the same time wheel at the same time your sister gets on the your sister gets on the small Ferris wheel. small Ferris wheel.

The rides begin as soon as The rides begin as soon as you are both buckled into you are both buckled into your seats. your seats.

Determine the number of seconds that will pass before you Determine the number of seconds that will pass before you and your sister are both at the bottom again.and your sister are both at the bottom again.

Also how many times will each Ferris wheel go around?Also how many times will each Ferris wheel go around?If the large wheel makes one If the large wheel makes one revolution in 60 seconds and the revolution in 60 seconds and the small makes one revolution in 20 small makes one revolution in 20 seconds.seconds.

If the large wheel makes one If the large wheel makes one revolution in 50 seconds and the revolution in 50 seconds and the small makes one revolution in 30 small makes one revolution in 30 secondsseconds

If the large wheel makes one If the large wheel makes one revolution in 10 seconds and the revolution in 10 seconds and the small makes one revolution in 7 small makes one revolution in 7 seconds.seconds.

Looking at Cicada CyclesLooking at Cicada Cycles

Cicadas spend most of their lives underground. Cicadas spend most of their lives underground.

Some populations of cicadas come above Some populations of cicadas come above ground every 13 yearsground every 13 years

Others come up every 17 years.Others come up every 17 years. The emergence of the cicadas are their key to The emergence of the cicadas are their key to

survival. survival. (may be up to 1.5 million per acre)(may be up to 1.5 million per acre)

So….what’s the bad news?So….what’s the bad news?

There has been at least one terrible year when There has been at least one terrible year when the cicadas laid so many eggs in trees that they the cicadas laid so many eggs in trees that they wrecked all the buds in the young trees.wrecked all the buds in the young trees.

What might have happened to cause such a What might have happened to cause such a mess?mess?

How many years until this happens again?How many years until this happens again?

Bagging SnacksBagging Snacks

Jane and her friends are going on a hiking trip.Jane and her friends are going on a hiking trip. Jane wants to make snacks of apples and trail Jane wants to make snacks of apples and trail

mix to take on the trip.mix to take on the trip. She has 24 apples and 36 bags of trail mix.She has 24 apples and 36 bags of trail mix.

Sharing…..Sharing…..

What is the greatest number of snack packs What is the greatest number of snack packs Jane can make if each pack must have exactly Jane can make if each pack must have exactly the same number of apples and mixes? (the same number of apples and mixes? (assume assume

none leftover)none leftover)

Could Jane make a different number of snack Could Jane make a different number of snack packs so that the treats are equally shared? packs so that the treats are equally shared?

Planning a PicnicPlanning a Picnic Miriam’s uncle donated 120 cans of Miriam’s uncle donated 120 cans of

juice and 90 packs of cheese crackers juice and 90 packs of cheese crackers for the school picnic. for the school picnic.

Each student is to receive the same Each student is to receive the same number of cans of juice and the same number of cans of juice and the same number of crackers.number of crackers.

What is the largest number of students What is the largest number of students that can come to the picnic and share that can come to the picnic and share the food equally?the food equally?

How many cans of juice and how many How many cans of juice and how many packs of crackers will each student packs of crackers will each student receive?receive?

Explain how you got your answers.Explain how you got your answers.

Class Party!!Class Party!! There are 23 students in your class and There are 23 students in your class and

1 teacher.1 teacher. Hot dogs come in packages of 8 and Hot dogs come in packages of 8 and

buns come in packages of 6.buns come in packages of 6. Everyone needs to get an equal number Everyone needs to get an equal number

of hot dogs and buns.of hot dogs and buns. What is the least amount of buns and What is the least amount of buns and

hot dogs you can buy so the food is hot dogs you can buy so the food is FAIR?FAIR?

How many packages of buns will you How many packages of buns will you buy?buy?

How many packages of hot dogs will How many packages of hot dogs will you buy?you buy?

More Party Goers!!More Party Goers!! Six guests decided to come to your Six guests decided to come to your

party. party. Same rules apply – be fair with your Same rules apply – be fair with your

food (buns-6, hot dogs-8).food (buns-6, hot dogs-8). What is the least amount of buns and What is the least amount of buns and

hot dogs you can buy so everyone gets hot dogs you can buy so everyone gets an equal amount?an equal amount?

How many packages of buns will you How many packages of buns will you need to buy?need to buy?

How many packages of hot dogs will How many packages of hot dogs will you need to buy?you need to buy?

More Picnic DilemmasMore Picnic Dilemmas Miriam’s uncle got hungry and Miriam’s uncle got hungry and

ate two packs of the crackers.ate two packs of the crackers. What is the largest number of What is the largest number of

students that can come to the students that can come to the picnic now and share the food picnic now and share the food equally?equally?

How many cans of juice and How many cans of juice and how many packs of crackers how many packs of crackers will each receive?will each receive?