Divisibility Rules of 11, 12 and 13

Duration: 11 min

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Inside: a video lesson and guided study material.

Module outline

  1. Child Development and Pedagogy / बाल विकास एवं शिक्षाशास्त्र: Concept of Development / विकास की अवधारणा, Psychological Theories of Development / विकास के मनोवैज्ञानिक सिद्धांत, Individual Differences, Personality and Gender / व्यक्तिगत भिन्नताएँ, व्यक्तित्व एवं जेंडर, Intelligence and Creativity / बुद्धि एवं सृजनात्मकता, Learning and Its Theories / अधिगम एवं इसके सिद्धांत, How Children Think and Learn / बालक कैसे सोचते एवं सीखते हैं, Emotion, Motivation, Mental Health and Guidance / संवेग, अभिप्रेरणा, मानसिक स्वास्थ्य एवं निर्देशन, Inclusive Education / समावेशी शिक्षा, Teaching-Learning Process / शिक्षण-अधिगम प्रक्रिया, Teaching Methods and Strategies / शिक्षण विधियाँ एवं रणनीतियाँ, Assessment and Evaluation / आकलन एवं मूल्यांकन, Lesson Planning and Teaching Skills / पाठ योजना और शिक्षण कौशल, Teaching Resources and Educational Technology / शिक्षण संसाधन और शैक्षिक प्रौद्योगिकी, Classroom Management and Communication / कक्षा प्रबंधन और सम्प्रेषण, Teacher Identity and Professional Development / शिक्षक पहचान और व्यावसायिक विकास, Educational Thinkers, Aims and National Policies / शैक्षिक विचारक, उद्देश्य एवं राष्ट्रीय नीतियाँ, Life Skills, Values, Peace and Environmental Education / जीवन कौशल, मूल्य, शांति एवं पर्यावरण शिक्षा, Social Science Pedagogy / सामाजिक विज्ञान शिक्षणशास्त्र, Social and Political Life / सामाजिक एवं राजनीतिक जीवन, Science Pedagogy / विज्ञान शिक्षण शास्त्र
  2. Language I — हिंदी / Hindi: भाषा, लिपि और वर्ण-विचार, संधि, शब्द-स्रोत और शब्द-रचना, समास, शब्द-भेद: विकारी और अविकारी, लिंग, वचन, कारक, काल और वाच्य, वाक्य-विचार और शुद्ध लेखन, शब्द-भंडार, रस, छंद, अलंकार और शब्द-शक्ति, हिंदी साहित्य, अपठित बोध, हिंदी शिक्षणशास्त्र, ICT in Education / शिक्षा में ICT
  3. Language II — English: Sounds, Spelling and Word Formation, Parts of Speech, Nouns and Pronouns, Articles, Determiners and Adjectives, Verbs and Modals, Tenses and Subject–Verb Agreement, Adverbs, Prepositions and Conjunctions, Sentence Structure, Voice and Narration, Vocabulary, Sentence Correction and Writing Skills, Poetry and English Literature, Reading Comprehension, Pedagogy of English Language
  4. Language II — اردو / Urdu: رسم الخط، املا اور تلفظ, ذخیرۂ الفاظ, قواعد, محاورے اور ضرب الامثال, شعر و سخن, اردو ادب کی تاریخ, تفہیمِ عبارت, اردو کی تدریس
  5. Language II — संस्कृत / Sanskrit: वर्णविचारः एवं संज्ञाप्रकरणम्, सन्धिप्रकरणम्, शब्दरूपाणि, धातुरूपाणि, कारकाणि एवं विभक्तयः, उपसर्गाः एवं अव्ययानि, प्रत्ययप्रकरणम्, समासप्रकरणम्, वाच्यप्रकरणम्, संख्याज्ञानम्, शब्दज्ञानम् एवं अनुवादः, अपठितावबोधनम्, संस्कृतसाहित्यम् एवं काव्यशास्त्रम्, संस्कृतशिक्षणशास्त्रम्
  6. Mathematics / गणित: Number System & Place Value / संख्या पद्धति एवं स्थानीय मान, Basic Operations, Simplification & Patterns / मूलभूत संक्रियाएँ, सरलीकरण एवं पैटर्न, Factors, Divisibility, HCF & LCM / गुणनखंड, विभाज्यता, म.स.प. एवं ल.स.प., Fractions & Decimals / भिन्न एवं दशमलव, Squares, Cubes, Exponents & Surds / वर्ग, घन, घातांक एवं करणी, Measurement: Length, Mass, Capacity, Time & Money / मापन: लंबाई, भार, धारिता, समय एवं मुद्रा, Algebra / बीजगणित, Ratio, Proportion, Average & Ages / अनुपात, समानुपात, औसत एवं आयु, Percentage, Profit–Loss & Interest / प्रतिशत, लाभ-हानि एवं ब्याज, Time & Work and Speed–Distance / समय-कार्य एवं चाल-दूरी, Lines, Angles, Shapes & Coordinates / रेखाएँ, कोण, आकृतियाँ एवं निर्देशांक, Triangles, Quadrilaterals, Circles & Trigonometry / त्रिभुज, चतुर्भुज, वृत्त एवं त्रिकोणमिति, Mensuration: Perimeter, Area & Volume / क्षेत्रमिति: परिमाप, क्षेत्रफल एवं आयतन, Data Handling, Statistics & Probability / आँकड़ा प्रबंधन, सांख्यिकी एवं प्रायिकता, Mathematics Pedagogy / गणित शिक्षणशास्त्र, Mathematical Operations & Arithmetical Reasoning / गणितीय संक्रियाएँ एवं अंकगणितीय तर्क
  7. Environmental Studies / पर्यावरण अध्ययन: Family, Friends and Community / परिवार, मित्र और समुदाय, Plants / पौधे, Animals / जंतु, Farming and Animal Husbandry / खेती और पशुपालन, Food and Nutrition / भोजन और पोषण, Body and Health / शरीर और स्वास्थ्य, Water / जल, Shelter / आवास, Travel, Transport and Communication / यात्रा, परिवहन और संचार, Maps, Directions and India / मानचित्र, दिशाएँ और भारत, Things We Make and Do / हम क्या बनाते और करते हैं, Earth, Sky and Disasters / पृथ्वी, आकाश और आपदाएँ, Environment, Ecology and Wildlife / पर्यावरण, पारिस्थितिकी और वन्यजीव, Natural Resources, Pollution and Climate Change / प्राकृतिक संसाधन, प्रदूषण और जलवायु परिवर्तन, Pedagogy of Environmental Studies / पर्यावरण अध्ययन का शिक्षणशास्त्र, Ancient Indian History / प्राचीन भारत का इतिहास, Earth, Globe and Maps / पृथ्वी, ग्लोब एवं मानचित्र, Physical Geography / भौतिक भूगोल, Natural Vegetation, Wildlife and World Regions / प्राकृतिक वनस्पति, वन्य जीवन एवं विश्व के प्रदेश, Geography of India / भारत का भूगोल, Resources and Development / संसाधन एवं विकास, Indian Constitution / भारतीय संविधान, Government: Union, State and Local / सरकार: केंद्र, राज्य एवं स्थानीय, Force, Pressure, Work and Energy / बल, दाब, कार्य एवं ऊर्जा, Heat and Sound / ऊष्मा एवं ध्वनि, Light / प्रकाश, Universe and Natural Phenomena / ब्रह्मांड एवं प्राकृतिक परिघटनाएँ, Matter and Its Structure / पदार्थ एवं उसकी संरचना, Metals, Non-metals and Materials of Daily Use / धातु, अधातु एवं दैनिक उपयोग की सामग्री, Living World: Classification, Cell and Tissues / सजीव जगत: वर्गीकरण, कोशिका एवं ऊतक, Human Body and Organ Systems / मानव शरीर एवं अंग तंत्र, Food, Nutrition and Health / भोजन, पोषण एवं स्वास्थ्य, Environment and Ecology / पर्यावरण एवं पारिस्थितिकी, Uttar Pradesh GK / उत्तर प्रदेश सामान्य ज्ञान, Plants: Nutrition, Transport and Reproduction / पादपों में पोषण, परिवहन एवं जनन, Sports / खेल जगत, International Relations & Organisations / अंतरराष्ट्रीय संबंध एवं संगठन, Key Appointments & Office Holders / प्रमुख नियुक्तियाँ एवं पदधारक
  8. Extra Practice (beyond syllabus) / अतिरिक्त अभ्यास (पाठ्यक्रम से बाहर): Indian Economy: Data & Current Affairs / भारतीय अर्थव्यवस्था: आँकड़े एवं समसामयिकी, Indian Art & Culture / भारतीय कला एवं संस्कृति, Science & Technology / विज्ञान एवं प्रौद्योगिकी, Environment & Climate Affairs / पर्यावरण एवं जलवायु समसामयिकी, Defence & Security / रक्षा एवं सुरक्षा, Static General Knowledge / स्थिर सामान्य ज्ञान, Government Schemes, Governance & Infrastructure / सरकारी योजनाएँ, शासन एवं आधारभूत संरचना, Ranking, Seating Arrangement & Puzzles / क्रम, बैठक व्यवस्था एवं पहेली, Calendar & Clock / कैलेंडर एवं घड़ी, Dice & Cubes / पासा एवं घन, Medieval Indian History / मध्यकालीन भारत का इतिहास, Colonial India and Social Reform / औपनिवेशिक भारत एवं समाज सुधार, Indian National Movement and Independent India / भारतीय राष्ट्रीय आंदोलन एवं स्वतंत्र भारत, Technology, Measurement and Motion / प्रौद्योगिकी, मापन एवं गति, Chemical Reactions, Acids, Bases and Salts / रासायनिक अभिक्रियाएँ, अम्ल, क्षार एवं लवण, Economics and Indian Economy / अर्थशास्त्र एवं भारतीय अर्थव्यवस्था, Electricity and Magnetism / विद्युत एवं चुंबकत्व, Bihar GK / बिहार सामान्य ज्ञान, Rajasthan GK / राजस्थान सामान्य ज्ञान, Curriculum and School Activities / पाठ्यचर्या और विद्यालयी गतिविधियाँ, Computer Hardware and Peripherals / कंप्यूटर हार्डवेयर एवं परिधीय उपकरण
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This educational video provides a comprehensive overview of divisibility rules for numbers 2 through 13, presented by an instructor in a screen recording format. The lecture begins with a colorful, hand-drawn wheel diagram that visually organizes the rules for divisibility by 2, 3, 4, 5, 6, 9, and 10, using examples and key phrases like 'ends in' and 'sum of the digits'. The presentation then transitions to a more formal slide format, where the instructor explains the rule for divisibility by 11, which involves subtracting the last digit from the number formed by the remaining digits, and demonstrates this with examples like 286 and 14641. The video continues with the rule for divisibility by 12, which is based on the principle that a number is divisible by 12 if it is divisible by both 3 and 4, illustrated with the numbers 648 and 524. A key concept introduced is that if a number is divisible by a composite number, it is also divisible by all of its factors, with examples for 6 and 12. The final segment covers the rule for divisibility by 13, which requires adding four times the last digit to the remaining number, demonstrated with the example 5061. The video concludes with a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide displaying 'DIVISIBILITY RULES' over a background of scattered numbers. It then transitions to a colorful, hand-drawn circular diagram titled 'DIVISIBILITY RULES'. This diagram is divided into sections for different numbers, each explaining a rule. For example, the rule for 2 is 'is an even number', for 5 it's 'ends in 0 or 5', and for 9 it's 'the sum of the digits is divisible by 9'. The instructor, Yash Jain Sir, is visible in a small window, explaining the concepts. The diagram also includes a section for 6, stating it is 'divisible by 2 AND 3'. The visual style is highly illustrative and engaging, using bright colors and arrows to connect concepts.

  2. 2:00 – 5:00 02:00-05:00

    The video shifts to a new slide titled 'Another Rule For 11'. The rule is stated as: 'Subtract the last digit from a number made by the other digits.' The instructor demonstrates this with the example 286: 28 - 6 = 22, and since 22 is divisible by 11, 286 is also divisible by 11. He then applies the rule to 14641: 1464 - 1 = 1463, then 146 - 3 = 143, then 14 - 3 = 11, and since 11 is divisible by 11, 14641 is also divisible by 11. The instructor uses red ink to write out the steps on the slide, emphasizing the process of repeated application.

  3. 5:00 – 10:00 05:00-10:00

    The next slide, titled '12', explains that a number is divisible by 12 if it passes both the divisibility rules for 3 and 4. The instructor demonstrates this with the number 648: the sum of its digits (6+4+8=18) is divisible by 3, and the last two digits (48) form a number divisible by 4, so 648 is divisible by 12. For 524, the sum of digits (5+2+4=11) is not divisible by 3, so 524 is not divisible by 12. The video then introduces a new concept: 'Factors Can Be Useful'. It explains that if a number is divisible by a composite number, it is also divisible by each of its factors. For example, if a number is divisible by 12, it is also divisible by 2, 3, 4, and 6. The instructor writes the factors of 12 as {1, 2, 3, 4, 6, 12}.

  4. 10:00 – 11:06 10:00-11:06

    The final topic is the divisibility rule for 13. The rule is to 'Add four times the last digit to the remaining leading truncated number.' The instructor demonstrates this with the number 5061: 506 + (1*4) = 510, then 51 + (0*4) = 51, then 5 + (1*4) = 9. Since 9 is not divisible by 13, 5061 is not divisible by 13. The instructor then corrects the example, showing that for 5061, the correct calculation is 506 + (1*4) = 510, then 51 + (0*4) = 51, then 5 + (1*4) = 9, which is not divisible by 13. The video ends with a 'THANKS FOR WATCHING' screen.

The video presents a structured and progressive lesson on divisibility rules, moving from a visually engaging overview to detailed, step-by-step demonstrations. It begins with a comprehensive diagram for basic rules (2, 3, 4, 5, 6, 9, 10), establishing a foundation. The core of the lesson focuses on more complex rules for 11 and 13, using a consistent method of explanation: stating the rule, providing a clear example, and showing the calculation process. A key pedagogical point is the introduction of the concept that divisibility by a composite number implies divisibility by its factors, which is a powerful shortcut for students. The instructor's use of a screen recording with on-screen annotations allows for a clear, focused presentation of the mathematical logic, making the content accessible for revision and learning.

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