A Story of Numbers — Mastery

Q1. Stone-Age humans first felt a real need to count for which everyday purposes?

• A. Writing down their poetry and songs
• B. Measuring angles in geometry
• C. Keeping track of livestock, ritual days and trade items
• D. Calculating compound interest

Q2. A Papua New Guinea community that counts by pointing in a fixed order to body parts — fingers, wrist, elbow, shoulder, etc. The body-part method is best understood is described as

• A. A base-10 place-value system
• B. A subtractive shortcut similar to Roman IV and IX
• C. A way to write zero with no symbol
• D. A standard sequence of reference points used like a one-to-one mapping for counted objects

Q3. Records the Bakairi (South America) names — 'tokale' for 1 and 'ahage' for 2. Following the same 'counting in twos' rule used for Gumulgal, the Bakairi name for 5 would be

• A. ahage-ahage-tokale
• B. tokale-tokale
• C. ahage-ahage-ahage
• D. tokale-ahage-tokale

Q4. I, V, X, L, C, D, M is called 'landmark numbers' of the Roman system. Which property best captures why the chapter uses the word 'landmark'?

• A. They are the only numbers that can be added in the Roman system
• B. They are the numbers used to count people in ancient Rome
• C. They are fixed reference numbers each with its own symbol, and all other numbers are written by combining them
• D. They are the numbers that can also be written in base-60

Q5. The Egyptian landmark numbers as powers of 10. The largest Egyptian landmark number shown in the chapter is

• A. 10^3 (one thousand)
• B. 10^5 (one lakh)
• C. 10^6 (ten lakh / one million)
• D. 10^7 (one crore / ten million)

Q6. Statement I: The Egyptian written system of c. 3000 BCE is a base-10 system. Statement II: A base-10 system is also called a decimal system. Statement III: Therefore the Egyptian written system is a decimal system. Which is correct?

• A. Only I and II are true; III does not follow
• B. Only II is true; I is false
• C. Only III is true; I and II are false
• D. All three are true and III follows logically from I and II

Q7. The Mesopotamian sexagesimal system is a positional (or place-value) number system. What is the defining feature of any positional system?

• A. The value of a digit depends on the position it occupies in the written number
• B. It uses landmark symbols that are repeated, with no fixed place values
• C. It needs exactly ten digits and no zero
• D. It writes numbers using only tally marks

Q8. Places the Chinese rod-numeral system in approximately which period, and gives its base as

• A. 3rd century BCE, base 12
• B. 8th century CE, base 60
• C. 3rd century CE, base 10
• D. 12th century CE, base 20

Q9. The Hindu number system. Which combination of features does the chapter ascribe to it?

• A. Base 60, twelve digits, no zero
• B. Base 10, twenty digits, landmark-additive like the Egyptian system
• C. Base 20, dot-bar-shell symbols, almost positional
• D. Base 10, ten digits 0–9, fully positional with zero as a number

Q10. Names the European scholar who, around 1200 CE, played the leading role in introducing Hindu numerals to Europe

• A. Aryabhata
• B. Al-Khwarizmi
• C. Fibonacci (Leonardo of Pisa)
• D. Brahmagupta

Q11. A Class 8 teacher wants to retrace the historical journey of number for her students. Based on the material, the MOST faithful first concrete step is to have students

• A. Use sticks or pebbles in a one-to-one mapping with objects on the table, mirroring Method 1 of
• B. Solve textbook exercises on the Hindu place-value system
• C. Memorise Roman landmark numerals I, V, X, L, C, D, M
• D. Recite Yajurveda Samhita names of powers of 10 in order

Q12. Two Class 8 teachers debate how to motivate the digit 0. Teacher A spends a period on the Mesopotamian blank-space ambiguity (e.g., 2 vs 120) before introducing 0. Teacher B directly states the place-value rule and asks students to memorise that 0 is a place-holder. Drawing on the chapter, the BEST evaluation is

• A. Teacher B is better because direct telling is faster than historical detours.
• B. Both are equally effective; pedagogy never depends on motivation.
• C. Teacher A is better because the chapter shows that experiencing the blank-space ambiguity first makes the need for 0 self-evident and conceptually permanent.
• D. Neither is correct; 0 should be introduced only in Class 11.

Q13. The 11th-century abacus that uses one line for each power of 10 and counters placed on the lines. The pedagogical value of the abacus, according to the chapter, is that it

• A. Replaces the digit 0 entirely
• B. Counts only in base 60
• C. Converts decimal numbers into Roman numerals
• D. Makes the place-value structure of the decimal system physically visible — units, tens, hundreds, etc., on separate lines

Q14. The digits 0–9 we use today are called by several historical names. Which set of three names does the chapter list for the SAME system of digits?

• A. Hindu numerals, Indian numerals, Arabic numerals
• B. Roman numerals, Greek numerals, Latin numerals
• C. Decimal numerals, sexagesimal numerals, vigesimal numerals
• D. Brahmi numerals, Yajurveda numerals, Mayan numerals

Q15. In a diagnostic test, a Class 6 student writes '3 0 5' (with a clear space between 3 and 5) instead of '305' and reads both the same way. Using the chapter, the teacher should identify the root error as

• A. A spelling mistake unrelated to mathematics
• B. A confusion between Roman and Hindu numerals
• C. A reproduction of the Mesopotamian blank-space confusion — the student treats absent digit and 0 as the same, so place value collapses
• D. A misuse of the abacus that the student has been taught

Q16. Admits that the stick method (one stick per cow) is in principle unending — it can count any size of herd. Yet the chapter still calls it inconvenient for large counts. The MAIN reason is

• A. Sticks cannot be cut to the right length
• B. Sticks have no fixed value, unlike Roman numerals
• C. Sticks are only available in winter
• D. For very large herds the bundle of sticks becomes too bulky to carry, store or compare quickly

Q17. A number system is defined as a standard sequence of reference symbols (or sounds or marks) used for counting. The KEY property of this standard sequence is that

• A. Its symbols come in a fixed order known to everyone in the community, so two people always count the same way
• B. Its symbols change from one community to another every day
• C. It must use exactly ten symbols and no zero
• D. Its symbols are always letters of the English alphabet

Q18. Across human history the most common group sizes for counting have been 2, 5, 10 and 20. Which body-fact best explains why 5, 10 and 20 are so common, while 2 is the oldest?

• A. Humans have two ears, five toes on each foot and ten teeth
• B. Humans have two eyes and four arms
• C. Humans have one pair of hands (2), five fingers on one hand (5), ten fingers on two hands (10), and twenty fingers and toes together (20)
• D. Humans have always preferred prime numbers as groups

Q19. The Bushmen (South Africa) number names — 'xa' for 1, 'toa' for 2, 'quo' for 3 — and says they too count in 2s. Following the same Gumulgal-style rule, the Bushmen name for 6 would most naturally be

• A. xa-xa
• B. toa-toa-toa
• C. quo-quo
• D. xa-toa-quo

Q20. In the Gumulgal counting-in-twos pattern 'urapon' = 1 and 'ukasar' = 2. A herder counts six fish using this system. The Gumulgal name for 6 is

• A. ukasar-ukasar
• B. ukasar-ukasar-ukasar
• C. urapon-urapon-urapon
• D. ukasar-ukasar-urapon

Q21. Builds a constructed base-5 system with landmarks 1, 5, 25, 125, 625, 3125. Using this system, the number 678 is best written as

• A. One 625, two 25s, three 1s
• B. One 625, one 25, two 5s, one 1
• C. Six 100s, seven 10s, eight 1s
• D. One 625, two 25s, no 5s, three 1s

Q22. The Mesopotamian system used only two basic wedge marks — a small wedge for 1 and a larger wedge for 10 — combined to write 1 to 59 in one place. Using this rule, the Mesopotamian writing of 23 (in one place) needs

• A. Two 10-wedges and three 1-wedges
• B. Two 1-wedges and three 10-wedges
• C. One 10-wedge and thirteen 1-wedges
• D. Twenty-three 10-wedges

Q23. Places the Mayan civilisation in which region and time period?

• A. South India, 5th to 12th century CE
• B. Central America, 3rd to 10th century CE
• C. North Africa, 1st to 5th century CE
• D. Western Europe, 11th to 15th century CE

Q24. Statement I: The Chinese rod-numeral system was base-10 and positional. Statement II: The Chinese had a distinct symbol for 0 from the very beginning. Statement III: They used alternating Zong and Heng orientations to keep adjacent places visually separate. Which combination is true per?

• A. Only I and II
• B. Only II and III
• C. Only I and III
• D. I, II and III all

Q25. Names two 9th-century Arab scholars who together helped move Hindu numerals into the Arab world. Around 830 CE, Al-Kindi wrote a treatise titled, in translation

• A. On the Use of the Hindu Numerals
• B. On Calculation with the Hindu Numerals
• C. The Brahma-sphuta-siddhanta
• D. Liber Abaci

Q26. Why the digits 0–9 are called 'Hindu numerals' even though they are used by people of every religion. According to the chapter, the word 'Hindu' here refers to

• A. A specific religion that invented the numerals
• B. The people and geography of India, where the system was developed — not to any religion
• C. An Arab tribe that copied the numerals from Europe
• D. A Sanskrit text on temple architecture

Q27. Pierre-Simon Laplace praising the Indian invention of a method 'which expresses all numbers using only ten symbols'. The deep insight Laplace is praising is

• A. That India invented the abacus
• B. That with just ten digits AND positional place value (including 0), ANY whole number can be written — so the system is simultaneously economical and unbounded
• C. That Indian mathematicians used Sanskrit letters as numerals
• D. That India introduced Roman numerals to Europe

Q28. A Class 4 teacher uses a four-line abacus (one line for 1s, 10s, 100s, 1000s) to teach how to write 'three hundred and seven'. Following the chapter's pedagogy of the abacus , the children should place beads as

• A. Three beads on the 1000-line, zero on the 100-line, seven on the 10-line
• B. Three beads on the 100-line, no beads on the 10-line, seven beads on the 1-line
• C. Three beads on the 100-line, seven beads on the 10-line, zero on the 1-line
• D. Seven beads on the 100-line, zero on the 10-line, three beads on the 1-line

Q29. Teacher P teaches Class 8 only the modern digits 0–9 and their operations, skipping all history of number systems. Teacher Q follows Chapter 3 fully — Stone-Age sticks, Roman numerals, base-n landmarks, Mesopotamian ambiguity, then Hindu place value. Drawing on the chapter's design, the BEST evaluation is

• A. P is better because history wastes time and the digits are already known
• B. Q is better because each historical system surfaces a specific weakness (no zero, fresh symbol per landmark, blank-space ambiguity), so the modern Hindu system arrives as a felt solution rather than an arbitrary rule
• C. Both are equally effective; history of mathematics has no role in pedagogy
• D. Q is better because students must memorise Roman numerals to clear CTET

Q30. A chart of digit shapes evolving from Brahmi (ancient India) through Devanagari to the modern global 0–9. A student concludes: 'Since the shapes changed, the system itself was reinvented at every stage.' Using the chapter, the BEST evaluation of this conclusion is

• A. Correct — each new shape means a new system was created from scratch
• B. Incorrect — what evolved is only the visual shape of each digit; the underlying base-10 + place-value + zero system stayed the same across Brahmi, Devanagari and modern digits
• C. Correct — Brahmi was base 60, Devanagari base 20, modern base 10
• D. Incorrect — Brahmi did not use ten digits at all