# 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!