# Fourth Grade Math: Factor Relationships

Fourth graders have been exploring factor ideas for the past couple of weeks. Through drawing arrays and listing factor pairs, students constructed some important concepts, such as:

- 1 is a factor of every number
- 2 is a factor of every even number
- Square numbers have one number that gets multiplied by itself, so the array can form a square

Further investigation uncovered other concepts. Did you know that when you double a number, all of the factors of the original number are in the doubled number? Also, you can find the rest by doubling the original factors. For example, factors of 9 are 1, 3, and 9. 18, which is 9 doubled, will have all the factors of 9 (1, 3, and 9). You can find the rest by doubling those factors. If I double 1, 3, and 9, I will get 2, 6, and 18, which are the rest of 18s factors.

Probably the most interesting thing we discovered was that when you have a multiplication expression, such as 4 x 16, if you double one factor and cut the other in half (divide by 2), you will get the same product. So, I can double 4 and halve 16 to create a new expression, 8 x 8, which will be equivalent to 4 x16. This can be really helpful with some messy problems. For example, if I want to multiply 1 ½ x 8, that can be difficult. However, if you use the idea of doubling and halving, You can create an equivalent problem of 3 x 4, which is much easier!

Reminder, there will be a test Monday covering all of these ideas. Students received a review sheet today, which is also posted on School Loop.

Have a great weekend!