NS.4 - Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
WARM-UP
MINI LESSON - INDEPENDENT WORK/SHARE OUT/DISCUSSION
1) Naila is making a dress from two different pieces of fabric. One piece is 72 inches long, and the other is 90 inches long. She wants to cut both pieces into strips of equal width, and she wants the strips to be as wide as possible. How wide should she cut the strips?
2) Micah and Joas are racing their bicycles around their neighborhood. Micah finishes a lap every 5 minutes. Joas finishes a lap every 6 minutes. How long will it be until Micah "laps" Joas?
3) Jamie has soccer practice every 4th day and baseball practice every 3rd day. If today is May 8, what is the next date that Jamie will have both practices on the same day?
4) I am planning a picnic. Hot dogs come in packs of 8 and buns come in packs of 12. How many PACKAGES of buns and hot dogs must I purchase to not have any leftovers?
5) There are 2 different sizes of Ferris Wheels at the fair. It takes 8 minutes for the small one to make one revolution and 12 minutes for the big one to make a revolution. If both were started at the same time and is not stopped, how many minutes will pass until they are both at the bottom at the same time?
2) Micah and Joas are racing their bicycles around their neighborhood. Micah finishes a lap every 5 minutes. Joas finishes a lap every 6 minutes. How long will it be until Micah "laps" Joas?
3) Jamie has soccer practice every 4th day and baseball practice every 3rd day. If today is May 8, what is the next date that Jamie will have both practices on the same day?
4) I am planning a picnic. Hot dogs come in packs of 8 and buns come in packs of 12. How many PACKAGES of buns and hot dogs must I purchase to not have any leftovers?
5) There are 2 different sizes of Ferris Wheels at the fair. It takes 8 minutes for the small one to make one revolution and 12 minutes for the big one to make a revolution. If both were started at the same time and is not stopped, how many minutes will pass until they are both at the bottom at the same time?
TEAM CHALLENGE
Factors and Common Factors
a. List all the factors of 48.
b. List all the factors of 64.
c. What are the common factors of 48 and 64?
d. What is the greatest common factor of 48 and 64?
Secret Number
Juanita has a secret number. Read her clues and then answer the questions that follow:
Juanita says, “Clue 1” My secret number is a factor of 60.”
1) Can you tell what Juanita’s secret number is? Explain your reasoning.
2) Daren said that Juanita’s number must also be a factor of 120. Do you agree or disagree with
Daren? Explain your reasoning.
3) Malcolm says that Juanita’s number must also be a factor of 15. Do you agree or disagree
with Malcolm? Explain your reasoning.
4) What is the smallest Juanita’s number could be? Explain.
5) What is the largest Juanita’s number could be. Explain.
Suppose for Juanita’s second clue she says, “Clue 2: My number is prime.”
6)Can the class guess her number and be certain? Explain your answer.
Suppose for Juanita’s third clue she says, “Clue 3: 15 is a multiple of my secret number.”
7) Now can you tell what her number is? Explain your reasoning.
Suppose for Juanita’s fourth clue she says, “Clue 4: My secret number is a factor of 20.”
8) What is Juanita’s secret number?
Back to School - Music
You and your friends have tickets to attend a music concert. While standing in line, the promoter states he will give a gift card for a free album download to each person that is a multiple of 2. He will also give a backstage pass to each fourth person and floor seats to each fifth person. Which person will receive the free album download, backstage pass, and floor seats? Explain the process you used to determine your answer.
School Supplies
The Parents Teachers Association (PTA) at your school donated school supplies to help increase student creativity and student success in the classroom. Your teacher would like you to create kits that include one package of colored pencils, one glue stick, and one ruler. When you receive the supplies, you notice the colored pencils are packaged 12 boxes to a case, the rulers are packaged 30 to a box, and glue sticks are packaged 4 to a box.
1) What is the smallest number of each supply you will need in order to make the kits and not have supplies left over? Explain your thought process.
2) How many packaged rulers, colored pencils, and glue sticks will you need in order to make the kits? Explain the process you used to determine how many packages are needed for each supply.
a. List all the factors of 48.
b. List all the factors of 64.
c. What are the common factors of 48 and 64?
d. What is the greatest common factor of 48 and 64?
Secret Number
Juanita has a secret number. Read her clues and then answer the questions that follow:
Juanita says, “Clue 1” My secret number is a factor of 60.”
1) Can you tell what Juanita’s secret number is? Explain your reasoning.
2) Daren said that Juanita’s number must also be a factor of 120. Do you agree or disagree with
Daren? Explain your reasoning.
3) Malcolm says that Juanita’s number must also be a factor of 15. Do you agree or disagree
with Malcolm? Explain your reasoning.
4) What is the smallest Juanita’s number could be? Explain.
5) What is the largest Juanita’s number could be. Explain.
Suppose for Juanita’s second clue she says, “Clue 2: My number is prime.”
6)Can the class guess her number and be certain? Explain your answer.
Suppose for Juanita’s third clue she says, “Clue 3: 15 is a multiple of my secret number.”
7) Now can you tell what her number is? Explain your reasoning.
Suppose for Juanita’s fourth clue she says, “Clue 4: My secret number is a factor of 20.”
8) What is Juanita’s secret number?
Back to School - Music
You and your friends have tickets to attend a music concert. While standing in line, the promoter states he will give a gift card for a free album download to each person that is a multiple of 2. He will also give a backstage pass to each fourth person and floor seats to each fifth person. Which person will receive the free album download, backstage pass, and floor seats? Explain the process you used to determine your answer.
School Supplies
The Parents Teachers Association (PTA) at your school donated school supplies to help increase student creativity and student success in the classroom. Your teacher would like you to create kits that include one package of colored pencils, one glue stick, and one ruler. When you receive the supplies, you notice the colored pencils are packaged 12 boxes to a case, the rulers are packaged 30 to a box, and glue sticks are packaged 4 to a box.
1) What is the smallest number of each supply you will need in order to make the kits and not have supplies left over? Explain your thought process.
2) How many packaged rulers, colored pencils, and glue sticks will you need in order to make the kits? Explain the process you used to determine how many packages are needed for each supply.