T1
Find the greatest common factor (GCF) of two whole numbers less than or equal to 100
NS.4
Lesson 1
BTC p107 Tax Collector
These are 12 envelopes, each one with some money in it. This is your money. I am just holding it for you. But, you can have any of these envelopes whenever you want. You just have to ask for it. So, which one do you want first? [They choose the 12]
OK. There you go. This envelope is now gone.
Right [snap fingers]. I forgot to tell you that we have to pay taxes on this money. And because you took the $12, the tax collector will take the 1, 2, 3, 4, and 6 envelopes [cross out the envelopes as you say the numbers]. Why does the tax collector take these envelopes?
Right! The tax collector takes the factors of whatever envelope you took. Ok, so which envelope do you want. [They choose 11]
Ok. But I forgot to mention that the tax collector always wants some taxes. So, when you choose an envelope there must always be at least one envelope for the tax collector to take -- one factor for the tax collector to take. So, can you take the $11?
[No.] So, which envelope can you take?
Ok. You take the $10. What does the tax collector take? [$5]
Ok. What next? [Nothing].
Ok. Now the tax collector is very kind and does not want to see anything go to waste, so they will take the rest of the envelopes [cross the rest out].
While working whole-class, you got $22 in total. You can get way more money! Your job is to work with your group to get more than $22.
Direct Instruction
Notes
Factors: the numbers you multiply together to get a specific product. (e.g. 1, 2, 3, 4, and 6 are all factors of 12). A factor is a number that divides another number evenly, with no remainder.
Common factors: Factors that are shared (e.x. the numbers 6 and 12 share a factor of 2)
Greatest Common Factor (GCF): the largest shared factor (e.x. the largest common factor between the numbers 6 and 12 is 6)
Prime number: a whole number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5, 7).
Use factor trees and prime numbers to find the GCF
Use The Ladder Method to find the GCF. Multiply ALL the numbers on the left side of the ladder. (Don't include the bottom numbers when multiplying.)
My Responsibilities
Due 11/12
1. CYUqs (do some with factor trees and some with the ladder method):
You are all going to do some of these. But, there are three things for you to keep in mind. First, do your own. Second, you choose where to start. Third, check your work with the students around you, and if you need help, get help. And if someone needs help, give help.
Check answers to make sure you are understanding:
2. Be sure that your notes are your notes are up to date:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
Lesson 2
Turn to your neighbor and describe what a factor is.
After completing the Check-your-understanding Questions, which were important for everyone to do?
What would you do if you were asked to find the GCF of 3 (or more numbers)?
Can we find the greatest common factor of 60, 24, and 48
On the blank side, write your first and last name and U5T1. Then, find the GCF of:
A. 24 and 30
B. 60 and 80
Lesson 1
BTC p107 Tax Collector
These are 12 envelopes, each one with some money in it. This is your money. I am just holding it for you. But, you can have any of these envelopes whenever you want. You just have to ask for it. So, which one do you want first? [They choose the 12]
OK. There you go. This envelope is now gone.
Right [snap fingers]. I forgot to tell you that we have to pay taxes on this money. And because you took the $12, the tax collector will take the 1, 2, 3, 4, and 6 envelopes [cross out the envelopes as you say the numbers]. Why does the tax collector take these envelopes?
Right! The tax collector takes the factors of whatever envelope you took. Ok, so which envelope do you want. [They choose 11]
Ok. But I forgot to mention that the tax collector always wants some taxes. So, when you choose an envelope there must always be at least one envelope for the tax collector to take -- one factor for the tax collector to take. So, can you take the $11?
[No.] So, which envelope can you take?
Ok. You take the $10. What does the tax collector take? [$5]
Ok. What next? [Nothing].
Ok. Now the tax collector is very kind and does not want to see anything go to waste, so they will take the rest of the envelopes [cross the rest out].
While working whole-class, you got $22 in total. You can get way more money! Your job is to work with your group to get more than $22.
Direct Instruction
Notes
Factors: the numbers you multiply together to get a specific product. (e.g. 1, 2, 3, 4, and 6 are all factors of 12). A factor is a number that divides another number evenly, with no remainder.
Common factors: Factors that are shared (e.x. the numbers 6 and 12 share a factor of 2)
Greatest Common Factor (GCF): the largest shared factor (e.x. the largest common factor between the numbers 6 and 12 is 6)
Prime number: a whole number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5, 7).
Use factor trees and prime numbers to find the GCF
Use The Ladder Method to find the GCF. Multiply ALL the numbers on the left side of the ladder. (Don't include the bottom numbers when multiplying.)
My Responsibilities
Due 11/12
1. CYUqs (do some with factor trees and some with the ladder method):
You are all going to do some of these. But, there are three things for you to keep in mind. First, do your own. Second, you choose where to start. Third, check your work with the students around you, and if you need help, get help. And if someone needs help, give help.
Check answers to make sure you are understanding:
2. Be sure that your notes are your notes are up to date:
3. Stuck? Choose to persevere: review your thinking, try different approaches, ask for help, search
Lesson 2
Turn to your neighbor and describe what a factor is.
After completing the Check-your-understanding Questions, which were important for everyone to do?
What would you do if you were asked to find the GCF of 3 (or more numbers)?
Can we find the greatest common factor of 60, 24, and 48
On the blank side, write your first and last name and U5T1. Then, find the GCF of:
A. 24 and 30
B. 60 and 80