✦ Educational Innovator & Creator

I craft engaging mathematical journeys and creative learning spaces students love.

A dedicated and disciplined Mathematics educator currently serving as TGT Mathematics at Sainik School Nalanda (Ministry of Defence). Passionate about bridging the gap between abstract concepts and joyful learning through interactive digital tools, NEP‑aligned live worksheets, and creative institutional publications.

Explore Mathematics → About Me

✦ Selected Work

Featured Hubs

Three spaces where mathematics, digital design, and student creativity meet.

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Interactive · NEP‑Aligned

Live Worksheets

Interactive, NEP‑aligned digital worksheets built for conceptual clarity, self‑paced practice, and instant feedback.

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Visual Learning

Digital TLMs

Virtual teaching‑learning models that transform abstract mathematical ideas into visuals cadets can see and manipulate.

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Publications

Editorial & Creativity

Institutional publications, magazines like Aao Ud Chalen, and calendars independently planned, structured, and designed.

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✦ My Process

From idea to impact.

A structured, student‑centered process I follow to turn a classroom gap into a working digital resource.

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1. Explore

Identifying student learning gaps and where a concept needs more clarity.

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2. Formulate

Crafting digital TLMs and NEP‑aligned worksheets around that gap.

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3. Execute

Implementing interactive, NEP 2020‑aligned methodologies in the classroom.

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4. Inspire

Achieving academic rigor and clarity that students genuinely enjoy.

✦ Gallery Highlights

Moments from the journey

A few highlights from teaching, editorial, and recognition moments.

Sainik School Nalanda

Principal Welcome & Induction

Award & Recognition

Best Teacher Award Of Mathematics at Roshani Public School

Chief Editor & Press

Unveiling of the school magazine Led as Chief Editor.

Organizing Events

Awarded for the Best School Performance at Ambe Mahotsav

✦ Let's Create Together

Have an innovative mathematical
project or idea in mind? Let's bring it to life!

✉ Send Me a Message

Quick Questions

What kind of worksheets do you design? +

I design interactive, NEP-aligned digital worksheets tailored for conceptual clarity, self-paced practice, and immediate feedback across middle and high school mathematics topics.

Can you build TLMs for my chapter? +

Yes! I specialize in creating digital Teaching-Learning Models (TLMs) and virtual visual tools that transform abstract mathematical concepts into interactive visuals.

How do you integrate visual aids and technology into math classrooms? +

I leverage ICT tools, interactive Live Worksheets, dynamic geometric models, and activity-based learning aligned with NEP 2020 and NCF frameworks to make abstract math tangible and engaging for cadets.

Can educators reach out to discuss innovative math teaching ideas? +

Absolutely! I am always happy to connect, share insights, and discuss innovative math pedagogy, digital TLM creation, and technology-driven teaching methodologies with fellow educators.

Class 9 Maths Chapter 3: The World of Numbers Concept Infographic (Ganita Manjari)

August 17, 2026

← Back to Class List

📖 Core Vocabulary

Rational Numbers (Q)
Expressible as p/q (q ≠ 0). Their decimals either terminate or repeat in a loop.

Irrational Numbers (I)
Numbers that cannot be written as simple fractions. They are non-terminating and non-repeating (e.g., π, √2).

Real Numbers (R)
The complete continuum. Uniting rational and irrational sets perfectly maps to every single point on the number line leaving no gaps.

📐 Constructing √2

Using the Baudhâyana-Pythagoras theorem on a number line:

Hypotenuse becomes exactly √2

🔄 Cyclic Magic (1/7)

Derived from 1/7, this sequence of digits simply shifts its position in a loop when multiplied.

        1/7 = 0.142857

        1 × ... = 142857

        2 × ... = 285714

        3 × ... = 428571

        4 × ... = 571428

        5 × ... = 714285

        6 × ... = 857142

⚖️ Brahmagupta's Laws & Density

The Arithmetic of Fortunes (+) & Debts (−):

Fortune × Fortune = Fortune (+ × + = +)
Debt × Debt = Fortune (− × − = +)
Fortune × Debt = Debt (+ × − = −)

The Density Average Formula:

To find a rational number strictly between any two given numbers a and b, simply calculate their average:
x = (a + b) / 2

⚙️ Decimal to Fraction Algorithm

Goal: Convert 0.45 (0.4545...) to p/q format.

Let x equal the decimal:
x = 0.4545...

Multiply by 100 (since 2 digits repeat):
100x = 45.4545...

Subtract Step 1 from Step 2:
100x − x = 45.45... − 0.45...
99x = 45

Simplify to p/q:
x = 45 / 99
x = 5 / 11

⚠️ Common Pitfalls & Exam Traps

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The "Infinite" Misconception

Not all infinite decimals are irrational. Repeating decimals like 0.333... are Rational (1/3). Only patternless, non-repeating infinite decimals are Irrational.

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The 0.999... vs 1 Debate

0.999... is exactly equal to 1. Proven algebraically: If x = 0.999..., then 10x = 9.999...; subtracting gives 9x = 9, meaning x = 1.

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The Non-Zero Denominator

Why can't 'q' be Zero? Division by zero is mathematically undefined. Therefore, in any rational fraction p/q, the integer q must never be 0 (p/0 = Error).

🚀 Loved this? Get more visual study materials at: www.akashmaths.online

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Akash Srivastva

I craft engaging mathematical journeys and creative learning spaces students love.