## Fancy Factorials

Mathematics, Algebra and Function, Operations (+, -, x, /, etc.)

Grade 5- 8

### Objective

Students learn about and work with factorials.

### Directions

Facts and Reminders
Ordering Two Objects
Have students place one red crayon and one blue crayon on their desks. How many different ways can they arrange them?
There are two different ways. They can put the red crayon first and the blue second, or they can put the blue first and the red second.
Ordering Three Objects
Have students place a third crayon, green, on their desks. How many different ways can they arrange them?
There are six different ways. Have them use their crayons to see if any arrangement has been missed. Notice that red is first in two arrangements, second in two arrangements, and third in two arrangements. This is true for each of the other colors as well.
Factorials
These arrangements can be expressed by a math concept called a factorial. The two-color arrangement is expressed this way: 2! = 2 x 1 = 2
The three-color factorial is expressed this way: 3! = 3 x 2 x 1 = 6
The exclamation point (!) is the sign for a factorial. Factorials can be multiplied:
2! x 3! = 2 x 1 x 3 x 2 x 1 = 12
Factorials can be divided:
3! / 2! = (3 x 2 x 1) / (2 x 1)= 3 / 2
Distribute the activity sheets and have students use what they have learned to complete the problems.

### Resources

• red, blue, green, yellow, and orange crayons for each student
• pencils
• Fancy Factorials activity pages

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