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

Riding Ferris Wheels You and your little sister go to a carnival that has both a large and a small Ferris wheel. You and your little sister go to a carnival that has both a large and a small Ferris wheel. You get on the Ferris wheel at the same time your sister gets on the small Ferris wheel. You get on the Ferris wheel at the same time your sister gets on the small Ferris wheel. The rides begin as soon as you are both buckled into your seats. The rides begin as soon as you are both buckled into your seats.

Determine the number of seconds that will pass before you and your sister are both at the bottom again. Also how many times will each Ferris wheel go around? If the large wheel makes one revolution in 60 seconds and the small makes one revolution in 20 seconds. If the large wheel makes one revolution in 50 seconds and the small makes one revolution in 30 seconds If the large wheel makes one revolution in 10 seconds and the small makes one revolution in 7 seconds.

Looking at Cicada Cycles Cicadas spend most of their lives underground. Cicadas spend most of their lives underground. Some populations of cicadas come above ground every 13 years Some populations of cicadas come above ground every 13 years Others come up every 17 years. Others come up every 17 years. The emergence of the cicadas are their key to survival. (may be up to 1.5 million per acre) The emergence of the cicadas are their key to survival. (may be up to 1.5 million per acre)

So….what’s the bad news? There has been at least one terrible year when the cicadas laid so many eggs in trees that they wrecked all the buds in the young trees. There has been at least one terrible year when the cicadas laid so many eggs in trees that they wrecked all the buds in the young trees. What might have happened to cause such a mess? What might have happened to cause such a mess? How many years until this happens again? How many years until this happens again?

Bagging 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 mix to take on the trip. Jane wants to make snacks of apples and trail 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….. What is the greatest number of snack packs Jane can make if each pack must have exactly the same number of apples and mixes? ( assume none leftover) What is the greatest number of snack packs Jane can make if each pack must have exactly the same number of apples and mixes? ( assume none leftover) Could Jane make a different number of snack packs so that the treats are equally shared? Could Jane make a different number of snack packs so that the treats are equally shared?

Planning a Picnic Miriam’s uncle donated 120 cans of juice and 90 packs of cheese crackers for the school picnic. Miriam’s uncle donated 120 cans of juice and 90 packs of cheese crackers for the school picnic. Each student is to receive the same number of cans of juice and the same number of crackers. Each student is to receive the same number of cans of juice and the same number of crackers. What is the largest number of students that can come to the picnic and share the food equally? What is the largest number of students that can come to the picnic and share the food equally? How many cans of juice and how many packs of crackers will each student receive? How many cans of juice and how many packs of crackers will each student receive? Explain how you got your answers. Explain how you got your answers.

Class Party!! There are 23 students in your class and 1 teacher. There are 23 students in your class and 1 teacher. Hot dogs come in packages of 8 and buns come in packages of 6. Hot dogs come in packages of 8 and buns come in packages of 6. Everyone needs to get an equal number of hot dogs and buns. Everyone needs to get an equal number of hot dogs and buns. What is the least amount of buns and hot dogs you can buy so the food is FAIR? What is the least amount of buns and hot dogs you can buy so the food is FAIR? How many packages of buns will you buy? How many packages of buns will you buy? How many packages of hot dogs will you buy? How many packages of hot dogs will you buy?

More Party Goers!! Six guests decided to come to your party. Six guests decided to come to your party. Same rules apply – be fair with your food (buns-6, hot dogs-8). Same rules apply – be fair with your food (buns-6, hot dogs-8). What is the least amount of buns and hot dogs you can buy so everyone gets an equal amount? What is the least amount of buns and hot dogs you can buy so everyone gets an equal amount? How many packages of buns will you need to buy? How many packages of buns will you need to buy? How many packages of hot dogs will you need to buy? How many packages of hot dogs will you need to buy?

More Picnic Dilemmas Miriam’s uncle got hungry and ate two packs of the crackers. Miriam’s uncle got hungry and ate two packs of the crackers. What is the largest number of students that can come to the picnic now and share the food equally? What is the largest number of students that can come to the picnic now and share the food equally? How many cans of juice and how many packs of crackers will each receive? How many cans of juice and how many packs of crackers will each receive?