Prime, Composite, and Square Numbers

Students often work on concepts like prime, composite, and square numbers by manipulating symbols only. Prime numbers are only divisible by themselves and one. Composites have other factors (e.g., 4 has 4 x 1 and 2 x 2). This lesson presents these concepts through the use of arrays, which are a good way for students to visualize factors in a number as well as understand the properties of prime, composite, and squared numbers. The concept of an array is explained in the classroom discussion section below.

Students can explore the concept of primes, composites, and squared numbers by coloring on graph paper or using the spreadsheet for what amounts to "electronic graph paper." Colored arrays are a quick way for students to examine patterns. Students can also gain computer skills by formatting tables and dragging within them.

One limitation of this exercise is that it does not show students all of the factors in some numbers. For example, 16 can be reduced to 2 x 2 x 2 x 2. This cannot be shown visually using arrays the way they are described in this lesson.

See Spreadsheet Basics section in table of contents to set up a spreadsheet as electronic graph paper.

Math Objective

Learn to visualize the prime numbers and the factors for composite numbers and square numbers.


Math outcomes

  • Identify prime and composite numbers
  • Recognize, describe, extend, and create mathematical patterns in order to represent and solve problems: multiples and diagrams


Spreadsheet Skills

  • build colored arrays
  • drag and rearrange
  • format cells with color and grid


What To Do

Files to Use

Download Info/Instructions

facprac.doc (student worksheet)

factor.xls (teacher spreadsheet)

Creating Arrays (math basics lesson)

Optional resources

graph paper, scissors, colored pens or pencils


Classroom Discussion and Activities

Computer Lab Activities


Classroom Discussion and Activities (Whole Group)

Teacher Note: You have two options in this lesson. Students can make arrays in small groups using graph paper or you can do it as a large class exercise using a spreadsheet. In the interest of time, exploring arrays on the spreadsheet should probably be a group lesson, and students can take turns creating, coloring, and manipulating the arrays. You will need to know how to adjust cell heights and widths to make the cells on the spreadsheet square, and you will need to know how to use borders and color the cells in your arrays. Whether this is done with graph paper or the spreadsheet, be sure to stress the patterns in prime numbers and squared numbers.


Option 1: Using Graph Paper and Scissors






Computer Lab Activities

Option 2: Using the Spreadsheet







Teacher Note: If you have students create arrays using different numbers, you may want to conclude the lesson by going through factor.xls. This is a concise way of showing all of the prime, composite, and squared arrays for the numbers 1 to 25. Again, make sure to discuss the patterns for each number.