How to Find Cube Numbers? | Cube Notations | Math Lesson

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

In our previous video lesson, we learned about how to find squares of a number using Montessori bead bars. In this video, we will learn how to multiply and make cube notations using Montessori bead bars.

Prerequisites of Finding Cube Numbers

What is the Notation of a Cube?

When a number is raised to the power of three, it is called the cube of that number. The notation used for a cube of a number is to write the number with a small 3 exponent to its upper right.

For example, if we want to find the cube of the number 2, we write it as 2³. This notation indicates that we are taking 2 and multiplying it by itself three times. The result is 8, which is the cube of 2.

Similarly, if we want to find the cube of any number ‘a’, we write it as ‘a³’. This notation helps to quickly identify the operation that needs to be performed to find the cube of a number.

Why are Cube Numbers called Cubed Numbers?

Cube numbers (or cubed numbers) are so called because they are used to calculate the volume of a cube. A cube is a three-dimensional shape with sides of equal length, width, and height. To calculate its volume, we multiply the side length by itself twice, or “cube” it.

For example, a cube with a side length of 2 cm has a volume of 8 cm³ (since 2³ = 8). If we knew a cube had a volume of 27 cm³, we could deduce that each side measures 3 cm (since 3³ = 27).

This connection between cube numbers and the volume of a cube is why they are called cube numbers.

How Notation of Cubes Are Introduced in a Montessori Classroom?

In a Montessori classroom, the notation of cubes is introduced using the Montessori bead bar. As shown in the video, children can explore cubes by creating them with bars. Bead bars of the same length can be used to make various-sized cubes.

How to Find a Cube 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:

Invite the child to the table along with the Montessori bead bars.
Tell them today we will find the cube of a number using Montessori bead bars.
As shown in the video, let’s take 3 bead bars string 3 times and arrange them together.
Now ask the child to count the bead bars both vertically and horizontally.
Note the numbers and present them as 3x3x3 in the notebook.
Now, to notate a cube, children can count the number of beads used to create the cube, 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 33. The superscript of 3 indicates that the shape is a cube.
Ask the child to note the count answer as 27.
Encourage the child to try finding the cube of a number and write its notation with different numbered bars.

Benefits of Finding Square of a Number or Notation of Square

Here are five benefits of finding the cubes of a number:

Simplifies algebraic equations: Notating cubes makes it easier to write and understand equations involving cube variables.
Helps in geometry: Cube numbers can be used to calculate the volume of a cube, which is a three-dimensional shape with sides of equal length, width, and height.
Fosters quick mental math: Knowing the cubes of small numbers can aid in quick calculations and mental math.
Useful in scientific calculations: Cubes can be used to determine distances between objects in space, among other things.
Aids in understanding exponents: Knowing cubes will help you understand squares and higher powers of exponents.

List of Square Numbers

Here are the squares of numbers 1-20:

1x1x1 = 1³ = 1
2x2x2 = 2³ = 8
3x3x3 = 3³ = 27
4x4x4 = 4³ = 64
5x5x5 = 5³ = 125
6x6x6 = 6³ = 216
7x7x7 = 7³ = 343
8x8x8 = 8³ = 512
9x9x9 = 9³ = 729
10x10x10 = 10³ = 1000
11x11x11 = 11³ = 1331
12x12x12 = 12³ = 1728
13x13x13 = 13³ = 2197
14x14x14 = 14³ = 2744
15x15x15 = 15³ = 3375
16x16x16 = 16³ = 4096
17x17x17 = 17³ = 4913
18x18x18 = 18³ = 5832
19x19x19 = 19³ = 6859
20x20x20 = 20³ = 8000

In algebra, cubing is an important operation that is used in many equations and formulas. By using the notation of cubes, it becomes easier to write and understand these equations.

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

FAQs

How do you write a cube in math?

The notation used for finding a cube of a number is to write the number with a small 3 exponent to its upper right. For example, the cube of 2 is written as 2³.

What are the benefits of finding the cubes of a number?

There are several benefits of finding the cubes of a number. It facilitates quick mental math, simplifies algebraic equations, and aids in geometry. In addition, cubes can be used to understand other exponents, such as squares and higher powers.

What is the formula of a cube?

The formula for finding the volume of a cube is given by: Volume of Cube = Side³. Where ‘Side’ is the length of one side of the cube. To use the formula, simply cube the length of any one side of the cube to find its volume.

How to Find Cube Numbers? (Cube Notations)