Teacher: Roberto, show me the multiples of 3 on the number line in Question 2.
Roberto: [points to the numbers while saying] 6, 9, 12, 15, 18, 21, 24, 27, 30.
Teacher: Did everyone have those same numbers? Is that all the multiples of 3 on the number line?
Ming: There is another one. Three.
Teacher: Another multiple of 3? Is 3 a multiple of 3?
Roberto: No, it's just the first number when you are skip counting.
Ming: He's wrong, 3 is a multiple of 3.
Teacher: Why do you say that, Ming?
Ming: Because you can write a number sentence: 3 × 1 = 3. So it's a multiple.
Teacher: What do you think about that Roberto?
Roberto: I didn't think about that. I guess it is a multiple, but it seems weird.
Teacher: Why does it seem weird to you, Roberto?
Roberto: When I think of “multiple,” it sounds to me like multiplying so I think it has to be bigger.
Teacher: I can see why you think that, Roberto. But Ming is right. Three is a multiple of 3 because you can write a multiplication number sentence, 3 × 1 = 3. Sometimes the product is not larger than the numbers you are multiplying.
Teacher: Now, if 3 is a multiple of 3, can someone tell me, is 3 also a factor of 3?
Nila: Yes, it is.
Teacher: Why do you say that?
Nila: For the same reason, because 3 times 1 equals 3. You can multiply 3 times a number and get 3.
Teacher: Is 3 a factor of any of the other multiples you wrote on the number line?
Nila: I think it is a factor of all of them.
Teacher: Why do you say so?
Nila: Partly because I just know my multiplication facts, so I can see that 3 will go into all of the numbers evenly.
Grace: But also, when you skip count by 3, you are adding three each time, so it seems like 3 will always go into each number that you have and not have any extra. I don't know why but I think it will.
Teacher: And if it goes into the number evenly, what name do we give it?
Roberto: It's a factor.
