My 4th graders used to struggle with the difference between factors and multiples. (Heck, there are plenty of adults who still do, based on watching my students trying to teach their parents when they do their student-led conferences in January...but I digress.)
The Common Core for 4th Grade states that students should be able to “find all factor pairs for a whole number in the range of 1-100” … and “determine whether a given number in the range of 1-100 is prime or composite.”I don't know about your math program, but mine doesn't spend much time reinforcing the vocabulary of factor, multiple, prime, or composite. They assume that kids remember the difference after a couple of days of review. Doesn't work that way with my kiddos!
This Finding Factors Freebie is what I use to help my 4th graders learn how to find all the factors of “Today’s Number” which is a routine we do as part of my SMARTBoard Math Calendar. Today’s Number is always whatever day of school it is, and we make an organized factor list, starting with 1 and the number.
This is similar to divisibility rules, but because we are making an organized factor list, students use the idea of "doubles and halves as they go in order trying to see which number could be factors.
As an example, say that it is the 76th day of school. We would start with 1 and 76.
Since 76 is even, we know that 2 will be a factor. Half of 70 is 35 and half of 6 is 3. 35 + 3= 38.
(1, 2, 38, 76)
3 is not a factor because the digits add up to 13, which is not a multiple of 3.
I teach my kids to use "doubles and halves" to figure out if 4, 6, or 8 are factors.To see if 4 is a factor, we go back to 2 x 38. We can double the 2 to get a 4, and if the other factor is even, we can take half of it and the answer is the same. 38 is even, and half of it is 19, so 4 will be a factor.
(1, 2, 4, 19, 38, 76)
5 can't be a factor because 76 doesn't end in a 5 or 0.
6 can't be a factor because 3 wasn't.
There are no tricks for 7, but we would know that 10 x 7 is 70, and there is 6 left over, so it can't be a factor.
8 can't be a factor because the factor pair of 4 is odd.
9 can't be a factor, because the digits don't add up to 9 or a multiple of 9.
10 can't be a factor, because 76 doesn't end in a 0.
11 can't be a factor because the digits are not the same.
12 can't be a factor because 3 wasn't a factor.
So, our final factor list is (1, 2, 4, 19, 38, 76), and students tell me that the number is composite because it has more than 2 factors.
My students become experts on prime and composite numbers, as well as the difference between factors and multiples, thanks to this daily repetition. I reinforce the idea that "factors are few, but multiples are many".)
Click on the picture to get your freebie. There is a large one that can be projected via interactive white board, and a small version for students to cut out and put in their math notebooks.