A STORY OF NUMBERS

बहुत अच्छा सवाल 👍
आपके भेजे गए फोटो में तीन प्रश्न हैं। मैं उनके सरल अर्थ (मतलब) बता देता हूँ — ताकि आपको समझने में आसानी हो:

Q1.

👉 "Suppose you are using the number system that uses sticks to represent numbers … give a method for adding, subtracting, multiplying and dividing two numbers or two collections of sticks."

अर्थ:
मान लो हम गिनती लिखने के लिए सिर्फ डंडियाँ (sticks) इस्तेमाल करते हैं। अब सवाल ये है कि बिना 1,2,3… या नाम (one, two, three) लिखे हम कैसे जोड़ (addition), घटाव (subtraction), गुणा (multiplication) और भाग (division) करेंगे? यानी सिर्फ डंडियों के सहारे ये सब क्रिया कैसे समझा सकते हैं?

Q2.

👉 "One way of extending the number system in Method 2 is by using strings with more than one letter—for example, we could use ‘aa’ for 27. How can you extend this system to represent all the numbers?"

अर्थ:
Method 2 में हम अक्षरों (a, b, c …) से गिनती दिखा रहे थे। एक अक्षर 1 से 26 तक के लिए ठीक है। पर 27 के बाद कैसे दिखाएँ? इसके लिए उदाहरण दिया है: 'aa' = 27।
अब सवाल है कि आप इस तरीके को कैसे आगे बढ़ाओगे ताकि हर बड़ी से बड़ी संख्या भी अक्षरों की string (जैसे aa, ab, ba…) से लिखी जा सके?

Q3.

👉 "Try making your own number system."

अर्थ:
अब आप खुद कोई नई गिनती बनाने की पद्धति सोचो। जैसे कोई अपने symbol चुन सकता है (जैसे ●, ★, △), या कोई base बदल सकता है (जैसे base-5, base-12)। आपको एक creative number system बनाना है और दिखाना है कि उससे कैसे संख्याएँ लिखी जा सकती हैं।

✅ यानी तीनों questions का सार ये है:

डंडियों से जोड़-घटाव-गुणा-भाग करना।
अक्षरों से गिनती को extend करना।
खुद का नया numbering system बनाना।

क्या आप चाहेंगे कि मैं इन तीनों का बहुत छोटा-सा नोट (summary style) बना दूँ, ताकि exam में सीधा लिख सकें?

ठीक है 👍 चलिए इस Figure it Out के तीनों प्रश्नों को अभी यहीं विस्तार से हल करते हैं:

1) Stick system में जोड़, घटाव, गुणा, भाग कैसे करेंगे?

मान लो हर stick (|) = 1 है।

जोड़ (Addition):
दोनो संग्रह (collections) की लकड़ियाँ साथ रखो, फिर गिनकर या बाँधकर कुल निकाल लो।
👉 Example: ||| (3) + |||| (4) = ||||||| (7).
घटाव (Subtraction):
पहले संग्रह से उतनी लकड़ियाँ हटा दो जितनी घटानी हैं।
👉 Example: ||||| (5) – || (2) = ||| (3).
अगर पर्याप्त लकड़ियाँ नहीं हों तो बड़े बंडल को खोलकर छोटा करो (जैसे उधार लेना)।
गुणा (Multiplication):
या तो बार-बार जोड़ो, या फिर rows बनाओ।
👉 Example: 3 × 4 = 3 rows, हर row में 4 sticks →
```
||||
||||
||||
```
कुल = 12 sticks.
भाग (Division):
संग्रह को बराबर-बराबर समूहों में बाँटो।
👉 Example: 12 ÷ 4 → 12 sticks को 4 बराबर groups में बाँटा = हर group में 3 sticks।

2) Method 2 को extend करना (letters से):

यह system letters की string पर आधारित है।

एक अक्षर = 1 से 26 तक (a=1, b=2 … z=26)।
27 से आगे = दो अक्षरों वाली string।
👉 Example: 'aa' = 27, 'ab' = 28 … 'az' = 52, 'ba' = 53 आदि।

इसे ऐसे समझो जैसे alphabetic base-26 (जैसे Excel में columns A, B … Z, AA, AB …)।

नियम: अगर string में n letters हैं, तो value = positional system की तरह।
👉 Example: 'aa' = 1×26 + 1 = 27.
👉 'zz' = 26×26 + 26 = 702.

इस तरह कोई भी संख्या represent की जा सकती है — बस letters की लंबाई बढ़ानी होगी।

3) अपना number system बनाना:

मान लो हम एक symbol-based base-5 system बनाते हैं।

Symbols तय कर लेते हैं:
○ = 0, | = 1, Δ = 2, □ = 3, ★ = 4.
Place value = base-5 (हर जगह का मान ×5 बढ़ता है)।

👉 Example:

|Δ = 1×5 + 2 = 7.
Δ★ = 2×5 + 4 = 14.
□○| = 3×25 + 0×5 + 1 = 76.

इस तरह इस system से हम हर संख्या को symbols में लिख सकते हैं।

✅ अब तीनों parts पूरे हो गए।

क्या आप चाहेंगे कि मैं आपके लिए stick method का एक छोटा चार्ट (जोड़-घटाव-गुणा-भाग के उदाहरणों का सारांश) बना दूँ, ताकि आप इसे exam में सीधा use कर सकें?

Nice — let’s solve each one clearly and with examples.

1) Sticks system (Method 1) — how to add, subtract, multiply, divide using sticks

Assume each stick | is 1 unit. To keep numbers tidy we use bundles (e.g. a bundle of 5 sticks written ||||| or shown as ⁞), but we never use Hindu numerals or number names — only sticks & bundles.

Addition (combine then regroup)

Place two collections of sticks together, then regroup into bundles.
Example: ||||| ||| (5 + 3). Put together → ||||| ||| = |||||||| → regroup into one bundle of 5 and 3 leftover → ||||| + ||| = 8 sticks.

If you want to show 12 + 9: show ||||| ||||| || (12 = two 5-bundles + 2) plus ||||| |||| (9 = one 5 + 4). Combine all sticks, then make as many 5-bundles as possible, count leftover sticks.

Subtraction (remove sticks / unbundle if needed)

To compute A − B, remove B sticks from A physically. If A doesn't have enough single sticks, unbundle one bundle into single sticks, then remove.
Example: from ||||| || (7) subtract ||| (3): remove 3 singles → left |||| (4).

Multiplication (arrays or repeated addition)
Two ways:

Repeated addition: add one collection repeatedly. (e.g., 4 × 3 = add |||| three times = |||| |||| |||| → regroup = 12).
Array/grid method: make 4 rows of 3 sticks (or vice-versa) and then count total by bundling rows/columns. This is visually faster.

Division (grouping / repeated subtraction)

Equal grouping: split the sticks into equal piles. Count how many sticks per pile or how many piles you can make.
Repeated subtraction: subtract the divisor repeatedly until remainder less than divisor. Remainder are leftover sticks.
Example: 13 ÷ 4: arrange 13 sticks and make groups of 4 → 3 full groups (4+4+4 =12), remainder 1 stick.

This is just tally arithmetic: combine/uncombine sticks and bundles, use arrays for multiplication, repeated subtraction or grouping for division.

2) Extending Method 2 with multiple-letter strings (example: `'aa' = 27`) — how to represent all numbers

This is basically making a positional (base) system with letters. Two common ways:

A. Bijective base-26 (like spreadsheet columns: A, B, …, Z, AA, AB, …)

Let letters a..z represent 1..26 (no zero digit).
Single-letter strings cover 1–26 (a=1, ..., z=26).
Two-letter strings begin at 27: 'aa' = 27, 'ab' = 28, ..., 'az' = 52, 'ba' = 53 and so on.
General rule: treat the string as digits in base-26 but with digits 1..26 and no zero. For a string of length n with letters (each letter value from 1..26), the value is


  \sum_{i=1}^{n} v(L_i)\times 26^{\,n-i}

Example: 'aa' →

B. Positional base-26 with zero (0..25)

Map a→0, b→1, …, z→25. Then treat strings as base-26 digits including zero.
'a' = 0, 'b' = 1, etc.; 'ba' = . This is a standard base conversion but a representing zero is sometimes confusing if you want the first symbol to mean 1.

Which to pick?

If you want continuous numbering with 'aa' = 27 and no symbol for zero, use bijective base-26 (option A).
If you prefer a standard base system with a zero symbol, use option B.

How to extend to all numbers: allow strings of arbitrarily large length. Length 1 gives first 26 numbers, length 2 next 26² numbers (or 26×26 depending on scheme), length 3 next chunk, etc. Use the positional rule above to convert to/from decimal.

3) Make your own number system — a simple original system (example)

I’ll design a compact, visual system and show rules & examples.

System name: ●▲♦ base-5 glyph system (base 5 with 5 glyphs)

Digits & glyphs:

● = 0
▲ = 1
♦ = 2
■ = 3
★ = 4

Place value: positional base-5 (each place is ×5). So a 3-glyph string X Y Z means .

Examples:

▲ = 1 (decimal 1)
■▲ = 3×5 + 1 = 16 (decimal 16)
♦★▲ = 2×25 + 4×5 + 1 = 50 + 20 + 1 = 71

Addition rule: add glyphs placewise like normal base arithmetic; if sum ≥5, carry to next place.

Multiplication: repeated addition or multiply placewise with carries (same as other bases).

Why this is nice: glyphs are short and visual (good for tallies on displays), you can teach children easily, and it’s a full positional system so it represents every nonnegative integer with finite strings.

If you’d like, I can:

show worked numeric examples (e.g., add 27 + 45 using sticks and using the letter system),
convert several numbers into the letter scheme (bijective base-26) and back, or
create a different creative system (balanced ternary, Roman-like but positional, Fibonacci coding, etc.).

Which follow-up would you like me to do?

ठीक है — हर संख्या को भाग-भाग करके रोमन अंक बना देते हैं (M=1000, D=500, C=100, L=50, X=10, V=5, I=1; और संयोजन: CM=900, CD=400, XC=90, XL=40, IX=9, IV=4).

(i) 1222 = 1000 + 200 + 20 + 2 = M + CC + XX + II = MCCXXII.

(ii) 2999 = 2000 + 900 + 90 + 9 = MM + CM + XC + IX = MMCMXCIX.

(iii) 302 = 300 + 2 = CCC + II = CCCII.

(iv) 715 = 500 + 200 + 10 + 5 = D + CC + X + V = DCCXV.

चाहो तो मैं इन्हें तस्वीर/स्टेप-बाय-स्टेप भी दिखा दूँ — बताओ कौन सा तरीका पसंद करोगे।

prashnon ka Arth batate hue ineh solve karo

यहाँ पर दिए गए प्रश्नों का अर्थ समझाते हुए उनके उत्तर दिए गए हैं:

***

### प्रश्न 1 का अर्थ और उत्तर

**अर्थ:**

प्रश्न है कि क्यों कुछ प्राचीन समुदाय अलग-अलग वस्तुएँ गिनने के लिए अलग-अलग संख्या शब्दों का उपयोग करते हैं?

**उत्तर:**

ऐसा इसलिए किया जाता है ताकि विभिन्न वस्तु-समूहों को गिनने में आसानी हो, जैसे कर्बी, सब्जी, जानवर इत्यादि। इससे यह सुनिश्चित होता है कि गिनते समय कोई भ्रम न हो और प्रत्येक प्रकार की वस्तु के लिए उपयुक्त संख्या शब्द अपनाया जा सके। अक्सर इसका कारण सांस्कृतिक या प्रायोगिक होता है — जैसे बच्चों के लिए छोटे समूह या जोड़ों/जोड़ियों को गिनना आसान बनाना, या वस्तुओं की प्रकृति के अनुसार विशेष शब्द इस्तेमाल करना[1][2]।

***

### प्रश्न 2 का अर्थ और हल

#### अर्थ:

Gumulgal संख्या-पद्धति में 2-2 जोड़कर संख्याएँ बनाई जाती हैं, (जैसे 2=ukasar, 3=ukasar-urapon, 4=ukasar-ukasar आदि)। इस पद्धति में संख्याओं के लिए जोड़, घटाव, गुणा व भाग करना है।

#### समाधान:

पहले इनके संख्यात्मक मान ज्ञात करें:

- urapon = 1

- ukasar = 2

- ukasar-urapon = 3 (2+1)

- ukasar-ukasar = 4 (2+2)

- ukasar-ukasar-urapon = 5 (2+2+1)

- ukasar-ukasar-ukasar = 6 (2+2+2)

अब दिए गए ऑपरेशन हल करते हैं:

**(i) (ukasar-ukasar-ukasar-ukasar-urapon) + (ukasar-ukasar-ukasar-urapon)**

- ukasar-ukasar-ukasar-ukasar-urapon = 2+2+2+2+1 = 9

- ukasar-ukasar-ukasar-urapon = 2+2+2+1 = 7

- 9 + 7 = 16

- Gumulgal पद्धति में 16 = 8 x ukasar = ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar

**उत्तर:**

ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar [3][4]

**(ii) (ukasar-ukasar-ukasar-ukasar-urapon) – (ukasar-ukasar-ukasar)**

- 9 - 6 = 3

- 3 = ukasar-urapon

**उत्तर:**

ukasar-urapon [3][4]

**(iii) (ukasar-ukasar-ukasar-ukasar-urapon) × (ukasar-ukasar)**

- 9 × 4 = 36

- 36 = 18 × ukasar = (ukasar को 18 बार दोहराएं)

**उत्तर:**

ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar [3]

**(iv) (ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar-ukasar) ÷ (ukasar-ukasar)**

- 8 x ukasar = 16

- 2 x ukasar = 4

- 16 ÷ 4 = 4

- 4 = ukasar-ukasar

**उत्तर:**

ukasar-ukasar [3]

***

### प्रश्न 3 का अर्थ और उत्तर

**अर्थ:**

हिंदू संख्या पद्धति की वे विशेषताएँ बताओ, जिनसे यह Roman संख्या पद्धति के मुकाबले अधिक कुशल है।

**उत्तर:**

- अंक का स्थान (Place Value) — प्रत्येक अंक का मूल्य उसकी स्थिति से तय होता है।

- शून्य (Zero) का समावेश — इससे संख्याएँ लिखना और गणना आसान होती है।

- आधार 10 (Base 10) — यही डेसीमल पद्यति है।

- बड़े अंक संक्षिप्त रूप में — बहुसंख्यकों को कम अंकों में लिखा जा सकता है।

- गणनाएँ आसान — जोड़, घटाव, गुणा, भाग सरलता से संभव[5][6][7]।

***

### प्रश्न 4 का अर्थ

**अर्थ:**

अब तक की चर्चा के आधार पर अपने बनाए गए संख्या-पद्धति मॉडल में सुधार करें।

(यह एक रचनात्मक अभ्यास है: प्रयोग करते समय जगह, संक्षिप्तता और गणना की सरलता नए सिस्टम में जोड़ें।)

***

## सारांश

इन सवालों के उत्तर क्रमशः संस्कृति, गणितीय लॉजिक, और संख्या पद्धतियों की तुलना से जुड़े हैं। प्रत्येक ऑपरेशन कर के Gumulgal system के उत्तर दिए गए हैं, तथा Hindu-Arabic system के गुण Roman system से तुलना कर बताए गए हैं[2][3][5][6][7]।

now solve it

These are questions based on the Egyptian numeral system. The Egyptian system uses specific symbols for 1, 10, 100, 1000, 10000, 100000, and 1000000, combining these symbols additively to form numbers. Here are step-by-step solutions:

## Egyptian Symbols Reference

- 1: Single vertical line

- 10: Arch/hobble (upside-down U shape)

- 100: Coiled rope (spiral)

- 1000: Lotus flower

- 10000: Pointing finger

- 100000: Tadpole or frog

- 1000000: Man with raised arms

### 1. Represent the following numbers in the Egyptian system

Given numbers: **10458, 1023, 2660, 784, 1111, 70707**

#### Representation strategy

Break each number into thousands, hundreds, tens, and units, then use the symbols accordingly.

#### Example: 10458

- 10000: 1 pointing finger

- 400: 4 coiled ropes

- 50: 5 arches

- 8: 8 vertical lines

So, 10458 will have:

- 1 pointing finger

- 4 coiled ropes

- 5 arches

- 8 vertical lines

**You can apply the same method for other numbers:**

| Number | Egyptian Symbols Breakdown |

|---------|-----------------------------------------------|

| 10458 | 1×10000, 4×100, 5×10, 8×1 |

| 1023 | 1×1000, 0×100, 2×10, 3×1 |

| 2660 | 2×1000, 6×100, 6×10, 0×1 |

| 784 | 7×100, 8×10, 4×1 |

| 1111 | 1×1000, 1×100, 1×10, 1×1 |

| 70707 | 7×10000, 0×1000, 7×100, 0×10, 7×1 |

[1][2][3]

***

### 2. What numbers do these numerals stand for?

The image presents two sets of Egyptian numerals to decode:

#### (i)

Symbols:

- 3 arches (10 each)

- 5 vertical lines (1 each)

Calculation:

- 3×10 = 30

- 5×1 = 5

- Total: 30 + 5 = **35**

#### (ii)

Symbols:

- 4 lotus flowers (1000 each)

- 4 arches (10 each)

- 2 coiled ropes (100 each)

- 2 vertical lines (1 each)

Calculation:

- 4×1000 = 4000

- 2×100 = 200

- 4×10 = 40

- 2×1 = 2

- Total: 4000 + 200 + 40 + 2 = **4242**

[1][4][3]

***

### Summary Table

| Problem | Answer |

|---------|--------|

| (i) | 35 |

| (ii) | 4242 |

All answers use the additive method by summing the values of the Egyptian symbols present in the numeral.[1][4][2][3]

Citations:

[1] Egyptian numerals - MacTutor History of Mathematics https://mathshistory.st-andrews.ac.uk/HistTopics/Egyptian_numerals/

[2] The Egyptian Numeration System https://math.ucr.edu/~res/math153-2021/week01unit01/egyptian-addition.pdf

[3] Egyptian Numerals | PDF https://www.scribd.com/document/230788846/Egyptian-Numerals

[4] Egyptian Mathematics Numbers Hieroglyphs https://discoveringegypt.com/egyptian-hieroglyphic-writing/egyptian-mathematics-numbers-hieroglyphs/

[5] 1000867454.jpg https://ppl-ai-file-upload.s3.amazonaws.com/web/direct-files/attachments/images/79095579/50451b34-cb3a-4d50-8e8d-274a7ce5b604/1000867454.jpg?AWSAccessKeyId=ASIA2F3EMEYESUYAJ2WX&Signature=5g6S4Yz0Taz2052fAzSO8xQ1RsY%3D&x-amz-security-token=IQoJb3JpZ2luX2VjECIaCXVzLWVhc3QtMSJHMEUCIG7iKmmGpuYwdDbtvKXHugAZob4vDEPc83tUv2W8R1yRAiEAv%2B9BzWLjc1tP5D2HqILidBqdz1KQ%2BafHpKgUPzSCXH0q%2BgQIq%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARABGgw2OTk3NTMzMDk3MDUiDAiBfULQIQGAdPxfHyrOBLTxmZkgT2WHKRY5vAO%2BI8hPawv4T1%2BdvFguLNoH8TSOcB0w1uoaLID1BvXuLEuFZCAm9VyuudePon9DZCAkeprgoa4Mv5lklBP6maYYWb1FvMGLlTYXhO1IHpUsLCsVR3B8gABZHUWRK9i9FCT1OtcNZ51o8K%2F0NtO9ymHsmZBcbbGjHNqHbiL8tIS62BtkX6TeRFylI59x8JzjEGzGqMLv5yoxW%2Blq7wGIPlio9u5EyaXgZYCg3Y0Ye8sNZXkmeIrm%2FPQNoY7jWt3%2BbEMERY%2BIPsB5pRFwbrxiwz9midSYRBV692QOCmFpUGKvDWFY2gBIlgtVSiHJQw7NpxwokE2n4PuRiNIsnKDcuLvZOTAapPLUeYNRs0qAzZu%2B4R7fgopTiSvoME2Os%2F5NYCWGj0Q0EnF0iSKO08a%2Br6NrxMU9QZv5Lr0Ik%2BQX7TyJ0cCEBis8okZS%2BexEIEMHrTtUG6mzPVbWDk19RrPOeJG8s2ia%2BXzZgCEUH2q9mAeQ5sHs%2FpHH4CyUlGk%2BiGqG%2FBbYEahyBNJ6oeLVUSSEu8IoaikQ9mRxMHtXoBCadAcrEVellMk66EX83mLwkhe%2B5pMX1V6BHcdL4HUOS1%2BQioMCHBVyjxQRsMFmQgI%2Fb%2BapgECdp2qLFGVa%2BjkETpayYAaHKp0RpR7bAGcNQlhqV1%2BJtp51F8sRw4VmxJu3g%2BdKTvK3jXc58ijOnCL4S%2BFvfhJRC5Csk50ZdpIcexU%2Feqgvnwh%2BCYAu%2FOjvLsdaP6jMBBXfHLArusLCdnr6K1%2Fs%2BKKLMPi94MYGOpoBfNciJBN%2FJOYl1Kf2xIpSNn2ewaYJBQsA5wrUJjM5FkpV4hEGtrkj2W7AWB1Wtn1pxQ2PYC0USGgAlNzHjmoHCmG2oAZr%2BmBDKCwXuygEQpmuZ41ynulMk5rkLEy2tHUxJUwJBhOPRMQpUTLMPLjgRKFzqX%2BDQyv7AwShLdd05sXh5puPmjeqAUAEJlH%2BxwcDGe1jo1oNwcE1sQ%3D%3D&Expires=1758994833

[6] Egyptian numerals https://en.wikipedia.org/wiki/Egyptian_numerals

[7] The Hindu—Arabic Number System, Egyptian Numerals ... https://courses.lumenlearning.com/tulsacc-math1473/chapter/the-hindu-arabic-number-system/

[8] Egyptian Multiplication https://www.cs.drexel.edu/~popyack/Courses/CSP/Fa17/notes/04.1_Binary/Egyptian.html?CurrentSlide=11

[9] Ancient Egyptian Numbers https://ballycarrickmaddyps.org/wordpress/wp-content/uploads/2020/05/Ancient-Egyptian-numbers.pdf

[10] Egyptian Numeration System https://www.youtube.com/watch?v=rWs1cMO4V9s

[11] Ancient Egyptian Numbers https://bookunitsteacher.com/ancient_egypt/egyptian_numbers.htm

[12] Egyptian Numerals Conversions https://www.101computing.net/egyptian-numerals-conversions/

[13] A History of Mathematical Notations/Volume 1/Egyptians https://en.wikisource.org/wiki/A_History_of_Mathematical_Notations/Volume_1/Egyptians

[14] Ancient Egyptian Numerals https://teachinglondoncomputing.org/egyptians/ancient-egyptian-numerals/

Citations:

[1] A Story of Numbers NCERT Solutions - Mathematics Class 8

NCERT-Solutions-A-Story-of-Numbers

[2] A Story of Numbers - Chapter Notes For Class 8 https://edurev.in/t/424821/Chapter-Notes-A-Story-of-Numbers

[3] NCERT Solutions for Class 8 Maths Chapter 3 - A Story of ... https://school.careers360.com/ncert/ncert-solutions-class-8-maths-chapter-3

[4] Class 8 Maths Ganita Prakash Chapter 3 A Story of ... https://www.tiwariacademy.com/ncert-solutions/class-8/maths/ganita-prakash-chapter-3/

[5] Identify the features of the Hindu number system that make ... https://askfilo.com/user-question-answers-smart-solutions/identify-the-features-of-the-hindu-number-system-that-make-3338303434363133

[6] Hindu-Arabic Numeral System vs. Roman Numeral System https://www.studocu.com/row/messages/question/5565627/compare-and-contrast-the-hindu-arabic-numeral-system-with-the-roman-numeral-system-highlight-the

[7] Hindu-Arabic vs. Roman Numerals: A Comparison & ... https://www.poojn.in/post/23047/hindu-arabic-vs-roman-numerals-a-comparison-explanation

[9] A STORY OF NUMBERS https://ncert.nic.in/textbook/pdf/hegp103.pdf

[10] Counting in 2s: Find Missing Numbers on Number Line https://www.vedantu.com/maths/counting-in-2s-missing-numbers-number-line

[11] How bases are used to represent numbers around the world https://warwick.ac.uk/fac/sci/maths/general/outreach/diversity/shaw/bases/

[12] Skip Counting by 2 Made Easy: Steps & Examples https://www.vedantu.com/maths/skip-count-by-2

[13] LATEST NCERT CLASS 8 MATHS CHAPTER 3D A ... https://www.youtube.com/watch?v=aCRYekNib9o

[14] The Counting by Twos Song https://www.youtube.com/watch?v=GvTcpfSnOMQ

[15] Australian Aboriginal enumeration https://en.wikipedia.org/wiki/Australian_Aboriginal_enumeration

[16] The Hindu—Arabic Number System and Roman Numerals https://courses.lumenlearning.com/waymakermath4libarts/chapter/the-hindu-arabic-number-system/

[17] Skip Counting By 2s And 5s (introduction) Lessons ... https://wayground.com/library/lessons/elementary/math/number-system/number-concepts/counting-and-cardinality/counting/skip-counting-by-2s-and-5s-introduction

[18] Class 8 Maths Ganita Prakash Chapter 3 A Story of Numbers https://www.netexplanations.com/class-8-maths-ganita-prakash-chapter-3-a-story-of-numbers/

[19] Hindu–Arabic numeral system https://en.wikipedia.org/wiki/Hindu%E2%80%93Arabic_numeral_system

[20] Teaching Children to Count in 2s https://www.youtube.com/watch?v=0b0q7mgzaMo

[21] Australian Aboriginal and Islander mathematics https://aiatsis.gov.au/sites/default/files/e_access/serial/m0005975_v_a.pdf

Search This Blog

CBSE Exam Paper