Notation of Square numbers

This math lesson is designed for 6-12 years old children to help them learn the square numbers and notation of squares using Montessori bead bars.

In our previous video lesson, we learned about counting with bead bars. In this video, we will learn how to multiply and make square notations using Montessori bead bars.

Prerequisites of Finding Square Numbers

What is the notation of a square?

The notation for a square is usually a super-scripted 2, written after the number or variable representing the length of one of its sides. It is usually pronounced as “x squared”. For example, if the length of one side of a square is x, the notation for the area of the square is x^2.

How Notation of Squares are Introduced in a Montessori Classroom?

In a Montessori classroom, the notation of squares is introduced using the Montessori bead bar. As shown in the video, children can explore squares by creating them with bars. They can use bead bars of the same length to create squares of various sizes and use different combinations of bead bars to experiment with different shapes.

How to Find a Square of the Number or Square Notation in a Montessori Way?

This notation method is a simple yet effective way for children to understand and remember the concept of squares. To find the square of a number, follow the below steps:

  1. Invite the child to the table along with the Montessori bead bars.
  2. Tell them today, we will find the square of a number using Montessori bead bars.
  3. As shown in the video, take the 5 bead bars 5 times and arrange them together.
  4. Now ask the child to count the bead bars both vertically and horizontally.
  5. Note the numbers and present them as 5×5 in the notebook.
  6. Now, to notate a square, children can count the number of beads used to create the square either counting all the beads or skip counting. For example, if a child creates a square using five bead bars of the same length, they can notate it as 5². The superscript of 2 indicates that the shape is a square. 
  7. Ask the child to note the count answer as 25. 
  8. Encourage the child to try finding the square of a number and write its notation with different numbered bars.

Benefits of Finding Square of a Number or Notation of Square 

The use of Montessori bead bars in notating squares provides a fun and interactive learning experience for children. It helps them develop their fine motor skills, spatial awareness, and understanding of mathematical notation. Furthermore, it encourages exploration and creativity, allowing children to think outside the box and experiment with different shapes and sizes. Incorporating Montessori bead bars into math lessons at an early age can help children build a strong foundation for future learning and success.

List of Square Numbers

Here are the squares of numbers 1-20:

  • 1^2 = 1
  • 2^2 = 4
  • 3^2 = 9
  • 4^2 = 16
  • 5^2 = 25
  • 6^2 = 36
  • 7^2 = 49
  • 8^2 = 64
  • 9^2 = 81
  • 10^2 = 100
  • 11^2 = 121
  • 12^l2 = 144
  • 13^2 = 169
  • 14^2 = 196
  • 15^2 = 225
  • 16^2 = 256
  • 17^2 = 289
  • 18^2 = 324
  • 19^2 = 361
  • 20^2 = 400

Ask the child to write square notations as shown in the video, and help them get a better understanding of the concept with this fun and interactive method.

Related Video Resources

To watch more math resources, click here.

Video Created by: Justine McNeilly


  • What is the notation for a square?

The notation for a square is usually a super-scripted 2, written after the number or variable representing the length of one of its sides. It is usually pronounced as “x squared”.

  • What are Square Numbers?

A square number is a number that is the product of a number multiplied by itself. For example, 9 is a square number because it is the product of 3 multiplied by 3. The sequence of square numbers begins: 1, 4, 9, 16, 25, 36, 49, 64, 81, and so on.

  • What are the 5 properties of square numbers?

There are five properties of square numbers:

    1. They are non-negative integers (0, 1, 4, 9, 16, …)
    2. They are the result of multiplying an integer by itself.
    3. The square of an even number is an even number.
    4. The square of an odd number is an odd number.
    5. The sum of any two square numbers is also a square number.