Teaching Students About the Number 135: A Unique Method for Enhancing Mathematics Education


Mathematics education is essential in today’s fast-paced world of technology and innovation. One way to enhance the learning experience for students is by introducing unique and engaging methods that pique their interest and curiosity. This article will focus on an unconventional approach to teaching mathematics by exploring the number 135 and discussing various aspects of its significance in enhancing students’ understanding of numbers, patterns, and mathematical concepts.

The Significance of 135:

At first glance, 135 may seem like just another ordinary number. However, when delving deeper into its properties and characteristics, it quickly becomes evident that 135 is more than meets the eye.

1. Sum of Consecutive Integers: First and foremost, 135 can be expressed as a sum of consecutive integers. It can be represented as the sum of numbers from 1 to 24, excluding the number 10. This property serves as an excellent opportunity to teach students about series, summation, and patterns.

2. Multiplication Pattern: Secondly, when multiplying nine by any whole number between one and four (inclusive), then adding the resulting product’s digits until only a single digit remains, that digit will always be equal to 135’s digits’ sum (i.e., 1 + 3 + 5 = 9). This fascinating pattern offers a chance to engage students in discovering interesting relationships between numbers.

3. Divisibility Rule: Additionally, the number 135 is divisible by both three and five. The divisibility rule for three states that if a number’s digits add up to a multiple of three, then the original number is divisible by three. Similarly, if a number ends in a zero or five, it is divisible by five. Teaching about divisibility rules not only helps students become more efficient in arithmetic operations but also introduces them to the concept of multiples.

Incorporating 135 in the Classroom:

Here are some practical ideas for involving 135 in various math lessons.

1. Warm-up Exercises: Use 135 as a warm-up activity to begin a lesson on patterns or divisibility rules. Have students brainstorm various mathematical properties and characteristics of this unique number to encourage engagement and curiosity.

2. Exploratory Projects: Assign group projects that require students to investigate the different aspects of 135, such as its multiplicative relationships with other numbers, factors, and divisibility rules. This encourages collaboration and critical thinking.

3. Math Puzzles and Challenges: Incorporate 135 into math puzzles, problems, or challenges that allow students to exercise their problem-solving skills. These activities can strengthen their understanding of mathematical concepts while fostering a love for learning and exploration.


Teaching students about 135 provides an exceptional opportunity to introduce unique methods that go beyond the standard curriculum’s scope. By focusing on a single number with intriguing properties, students can truly appreciate the beauty and complexity of mathematics while developing a deeper understanding of its principles. Engaging students in activities centered around 135 can foster creativity, critical thinking skills, and a passion for mathematics that will last a lifetime.

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