Factor Dazzle Directions

Object: To correctly identify the factors of a number and to pick numbers for which your opponent will need to identify the factors.

Set-Up: The game board contains the numbers 1-36 arranged in a 6 × 6 grid.

Play: Your opponent will choose a number on the board. He or she will earn points equal to that number. You will then find all the factors of that number on the board, and you will earn points equal to the sum of the factors you find. However, points will be deducted for any number you choose that is not a factor or for any factor that you fail to identify.

You will then choose a number on the board, and your opponent will find all the remaining factors of that number.

If you select a number that has no factors remaining on the game board, you lose your turn.

You and your opponent alternate turns until none of the unselected numbers have any remaining factors left on the game board. Several numbers contain Double Dazzlers. A Double Dazzler doubles the number of points you earn for picking that number. The numbers containing Double Dazzlers are randomly selected and change from game to game.

Winning the Game: The winner is the player with the most points when no number on the game board has any remaining factors.

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:
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.