Math Concepts: Factors, multiples, division, and multiplication

What You Can Do: Students can learn about factors in a variety of ways. One method is to draw
a rectangle with a given area. The length and width of the rectangle are two factors of the area. If only one rectangle
can be drawn for a given area, then the number is prime. For instance, the only rectangle that can be drawn with
an area of 23 square units is a 1 × 23 rectangle. But in most cases, more than one rectangle can be drawn with the same
area, indicating that the number is not prime. For instance, there are four rectangles with an area of 24 square units:
1 × 24, 2 × 12, 3 × 8, and 4 × 6. All numbers used as the length or width of any of those rectangles is a factor of 24.

Another method for learning about factors is dividing a group of objects into equal piles. Just as an area of 24 square
units can be represented by a 3 × 8 rectangle, a group of 24 objects can be divided into 3 groups of 8 objects each. To
explore factors, ask your child to divide a deck of 52 cards into groups of equal size, or have your child find the number
of ways that a pack of 12 AAA batteries could be placed in equal-sized groups.

Given some number, a factor is a smaller number that evenly divides into the given number. On the other hand,
a multiple is a number into which the given number evenly divides. For instance, 1, 2, 3, 4, and 6 are factors
of 12, whereas 24, 36, 48, 60, and so on, are multiples of 12.

Multiples are a bit more prevalent than factors, and they form nice patterns. In addition, the words multiple and multiply have
the same root, and kids immediately understand that they are related. There are 2 tires on a bicycle. If another bike is
added, there are 4 tires. As the number of bikes increases, the number of tires increases to 6, 8, 10, 12, and so on. Kids
readily understand such patterns, so getting them to understand the concept of multiples often involves exposure to patterns
and using the word multiple in context.

Math in the Game: Players quickly learn that prime numbers don’t work so well in this game.
The only factor of a prime number other than the number itself is 1. On the first turn of the game, the number 1 will be
selected as a factor of whatever number is chosen, which means that it will no longer be available. Thereafter, a player
that chooses a prime number will lose a turn.

Related Resources:

Factorize

Students determine the factorizations for a number by creating all possible rectangles of a given area.

*Chocolate FACTORy: Finding Factors of Numbers 1 Through 36*

In this lesson students create rectangular arrays to represent sizes of chocolate boxes. They find all of the factors of each number up to 36 and learn the difference between prime and composite numbers.