Kids sometimes find it confusing to differentiate between multiples & factors. Here are a few visuals that I've found helpful:

Multiple: the product of a given number and another number.

We could show this on a number line:

To find the multiples of 3, we can start with our given number (3) and then multiply it by 2 (6), by 3 (9), by 4 (12), and so on...

We also see multiples represented by tile (Number Pieces):

1 group of 3 tile = 3

2 groups of 3 tile = 6

3 groups of 3 tile = 9

4 groups of 3 tile = 12

We can also use a visual model to investigate factors.

Factors: numbers that, when multiplied together, result in a product.

One of my favorite ways to do this? Lay out the product with tile (Number Pieces). Let's look at 12:

Use the 12 tile to form as many rectangular arrays as possible. The dimensions produce factors of the number. Here we can see arrays with dimensions of:

1 x 12

2 x 6

3 x 4

(Note: When using this visual model, prime numbers are also easy to distinguish: if it's prime, only one rectangular array--a 1 by the number--is possible.)

**Why Do We Care?**

My son is currently taking AP Calculus. He just popped in my office, saw what I was doing and said, "For us, finding factors is just one tiny step in a huge process. We do it all the time." Factors are a part of higher level math! And, at a slightly lower level, students frequently use factors when working with fractions...not to mention (!) multiplication.

**Additional Resources**

I just created Fold It!...Factors & Multiples, a new set of flap books (Venn Diagrams & Shutter Folds) for students to compare and contrast factors and multiples. When complete, pages make a nice addition to student math journals. Alternate versions (different number combinations as well as blank copies) are included to allow for many uses: differentiation, exit slips, homework, notebook pages, math stations, etc.

The new set is also available as part of a bundled Multiples & Factors Flap Pack that includes the popular Flap Books "Present" Multiples & Factors (pictured right).

As always, new products (& bundles) are introduced with a sale price.

**More Ideas**

Looking for more ideas? Here are some of my favorites from around the web:

- Flap Books & Online Games - in this blog entry, I share photos of flap books we made and link to a variety of games on the web
- Factor & Multiple Anchor Charts with Student-Made Posters from Young Teacher Love - both are awesome.
- Online Venn Diagram - create your own Venn Diagram to compare factors & multiples (example, right)
- Multiple Mummy - kids use adding machine tape to make multiple strips and turn their teacher into a mummy.