This MCQ module is based on: Numbers Can Tell Us Things and Supercells
TOPIC 8 OF 41
Numbers Can Tell Us Things and Supercells
🎓 Class 6
Mathematics
CBSE
Theory
Ch 3 — Number Play
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Numbers Can Tell Us Things and Supercells
Targeting Class 6 level in Number Theory, with Basic difficulty.
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3.1 Numbers Can Tell Us Things
Numbers are not just for counting — they are a rich language we use to describe, compare and organise the world. In this chapter, we will continue our journey by playing with numbers, seeing them around us, spotting patterns?, and learning how to use numbers and operations in fresh ways.
What are these numbers telling us?
Imagine some children standing in a park in a line. Each child announces a number. What could those numbers represent?
Seven children in a line, each saying a number (1, 0, 2, 0, 1, 2, 0)
What the numbers mean
Here each child is announcing the number of children standing next to them who are taller than themselves.
• A child says '1' if exactly one of the two neighbours is taller.
• A child says '2' if both the neighbours are taller.
• A child says '0' if none of the neighbours is taller. The end children have only one neighbour, so their largest possible number is 1.
In-text questions (p. 56):
Q1. Can the children rearrange themselves so that both end-children say '2'? — No. End children have only one neighbour, so they can say 0 or 1 only.
Q2. Can we arrange children in a line so they all say '0'? — Yes, only if everyone has the same height (or the line is in decreasing then increasing or strictly descending/ascending order making each child tallest among neighbours — e.g. tallest in the centre).
Q3. Can two children standing next to each other say the same number? — Yes, it is possible (e.g. two children of same height next to each other).
Q4. For a group of 5 children, is the sequence 1, 1, 1, 1, 1 possible? — Yes, if they stand in ascending (or descending) order of height. Each middle child sees one taller neighbour; the ends also see one taller.
Q5. Is the sequence 0, 1, 2, 1, 0 possible? — Yes, tallest child in the middle.
Q6. A rearrangement for 5 children so that maximum number of children say '2'? — Place the shortest two at ends and tallest at either end of the middle group. At most 3 middle children can say '2' when both their neighbours are taller.
Q1. Can the children rearrange themselves so that both end-children say '2'? — No. End children have only one neighbour, so they can say 0 or 1 only.
Q2. Can we arrange children in a line so they all say '0'? — Yes, only if everyone has the same height (or the line is in decreasing then increasing or strictly descending/ascending order making each child tallest among neighbours — e.g. tallest in the centre).
Q3. Can two children standing next to each other say the same number? — Yes, it is possible (e.g. two children of same height next to each other).
Q4. For a group of 5 children, is the sequence 1, 1, 1, 1, 1 possible? — Yes, if they stand in ascending (or descending) order of height. Each middle child sees one taller neighbour; the ends also see one taller.
Q5. Is the sequence 0, 1, 2, 1, 0 possible? — Yes, tallest child in the middle.
Q6. A rearrangement for 5 children so that maximum number of children say '2'? — Place the shortest two at ends and tallest at either end of the middle group. At most 3 middle children can say '2' when both their neighbours are taller.
3.2 Supercells
Look at a table of numbers. A cell is called a supercell? if the number inside is larger than every neighbour cell touching it (left, right — and up/down when we have more rows).
43
75
63
10
29
28
34
—
200
577
626
345
790
694
109
198
Yellow-shaded cells are supercells — larger than all direct neighbours (Table on p. 57).
Figure it Out (Section 3.2)
Q1. Colour or mark the supercells in the table: 6828, 670, 9435, 3780, 3708, 7308, 8000, 5583, 52.
Compare each with left & right neighbours:
6828 (>670) ✓, 670 (<6828) ✗, 9435 (>670 and >3780) ✓, 3780 (<9435) ✗, 3708 (<3780) ✗, 7308 (>3708 and <8000) ✗, 8000 (>7308 and >5583) ✓, 5583 (<8000) ✗, 52 (only neighbour 5583 > 52) ✗.
Supercells: 6828, 9435, 8000.
6828 (>670) ✓, 670 (<6828) ✗, 9435 (>670 and >3780) ✓, 3780 (<9435) ✗, 3708 (<3780) ✗, 7308 (>3708 and <8000) ✗, 8000 (>7308 and >5583) ✓, 5583 (<8000) ✗, 52 (only neighbour 5583 > 52) ✗.
Supercells: 6828, 9435, 8000.
Q2. Fill the table below with only 4-digit numbers such that the supercells are exactly the coloured cells: 5346, _, 1258, _, 9635, _ (1258 and 9635 must be supercells).
One valid filling: 5346, 1000, 1258, 1200, 9635, 2000. Check: 1258 > 1000 and 1258 > 1200 ✓; 9635 > 1200 and 9635 > 2000 ✓; 5346 is not a supercell (5346 > 1000 but 5346 vs only one neighbour — however it is at the end, so 5346 > 1000 means it would be a supercell! Adjust: swap first two → 1000, 5346, 1258, 1200, 9635, 2000 but now 5346 is a supercell. Trick: pick left end value > 5346 like 6000, 5346, 1258, 1200, 9635, 2000. Now 5346 is not a supercell. Many answers possible.
Q3. Fill the table below such that we get as many supercells as possible. Use numbers between 100 and 1000 without repetitions.
Alternate big and small numbers. E.g. 900, 100, 800, 150, 700, 200, 650, 180, 600. Supercells: 900, 800, 700, 650, 600 — five supercells out of 9 cells (maximum possible, since no two neighbours can both be supercells).
Q4. Out of the 9 numbers, how many supercells are there in the table above?
Based on Q3 arrangement, 5 supercells (every alternate position starting from the first).
Q5. Find out how many supercells are possible for different numbers of cells.
Pattern: For n cells in a row, the maximum number of supercells = \(\lceil n/2 \rceil\). So 5 cells → 3 supercells, 7 cells → 4, 9 cells → 5, 10 cells → 5.
Q6. Can you fill a supercell table without repeating numbers so that there are no supercells? Why or why not?
No. If all numbers are different, the largest number in the table is always greater than its neighbours — hence always a supercell.
Q7. Will the cell having the largest number in a table always be a supercell? Why or why not?
Yes, because it is bigger than every other number in the table, including all its neighbours.
Q8. Fill a table such that the cell having the second largest number is not a supercell.
Put the 2nd largest next to the largest. E.g. 100, 999, 998, 200, 300. Here 998 is the 2nd largest but has 999 as a neighbour, so 998 is NOT a supercell.
Supercells in larger tables (Table 1 & Table 2, p. 58)
In 2-D tables, a supercell must be greater than all four (top, bottom, left, right) neighbours. Using numbers with digits 1, 0, 6, 3 and 7 in some order:
| 2430 | 7500 | 7350 | 9870 |
| 3115 | 4795 | 9124 | 9230 |
| 4580 | 8632 | 8280 | 3446 |
| 5785 | 2944 | 1805 | 6034 |
Table 1 — supercells highlighted (cells greater than all their neighbours).
Table 2 fill-in (p. 58): Biggest number in the table = 60,193 (supercell). Smallest = 10,963. Smallest even number = 10,963? No – 10,963 ends in 3 (odd). The smallest even number in the table is 19,306 (if formed). Smallest number greater than 50,000 = 60,193.
Activity: Predict → Observe → Explain — Supercell Hunt
Predict: In a row of 11 different numbers, how many supercells can there be at most?
- Take any 11 different 3-digit numbers. Write them in a row.
- Mark the supercells (numbers bigger than both neighbours).
- Rearrange them to maximise supercells. Record your best count.
- Repeat with 7 numbers and then 13 numbers.
Observe: Maximum = \(\lceil n/2 \rceil\). For 11 → 6, 7 → 4, 13 → 7. Explain: Supercells cannot be neighbours — if A and B are both supercells and neighbours, each must be bigger than the other, impossible. So supercells alternate at best.
Competency-Based Questions
Scenario: Priya writes the numbers 812, 405, 987, 330, 654, 221, 779 in a row (in this order) and marks supercells.
Q1. How many supercells are there in her row?
L3 ApplyCompare: 812 (left-end, one neighbour 405; 812 > 405) ✓; 405 (<812) ✗; 987 (>405 and >330) ✓; 330 ✗; 654 (>330 and >221) ✓; 221 ✗; 779 (>221) ✓. 4 supercells: 812, 987, 654, 779.
Q2. Analyse: what pattern of big/small numbers maximises supercells?
L4 AnalyseAlternating Big-Small-Big-Small. Every "Big" at an odd position becomes a supercell because both neighbours are small. For n cells, maximum is \(\lceil n/2 \rceil\).
Q3. Evaluate: Aryan claims "No matter how I rearrange 7 different numbers, the largest one is always a supercell." Is he correct? Justify.
L5 EvaluateCorrect. The largest number is greater than every other number in the row, therefore also greater than its (at most two) neighbours. So it will always satisfy the supercell condition.
Q4. Create a 2×4 table using eight different 4-digit numbers so that exactly 3 cells are supercells (each greater than all horizontal and vertical neighbours).
L6 CreateOne solution:
Row 1: 9000, 1200, 8500, 2000
Row 2: 3000, 1100, 4500, 1500
Supercells: 9000 (neighbours 1200, 3000), 8500 (1200, 2000, 4500), 4500 (1100, 8500, 1500)? 4500 < 8500, so not a supercell. Replace: put 8500 further from 4500. Many valid layouts — key is isolating each supercell from higher values.
Row 1: 9000, 1200, 8500, 2000
Row 2: 3000, 1100, 4500, 1500
Supercells: 9000 (neighbours 1200, 3000), 8500 (1200, 2000, 4500), 4500 (1100, 8500, 1500)? 4500 < 8500, so not a supercell. Replace: put 8500 further from 4500. Many valid layouts — key is isolating each supercell from higher values.
Assertion–Reason Questions
A: The end cell of a row can still be a supercell.
R: End cells have only one neighbour; the supercell condition is satisfied if the end value is larger than this single neighbour.
R: End cells have only one neighbour; the supercell condition is satisfied if the end value is larger than this single neighbour.
Answer: (a) — End cell counts as supercell if greater than its sole neighbour.
A: Two adjacent cells can both be supercells.
R: If A > B then B cannot be > A.
R: If A > B then B cannot be > A.
Answer: (d) — A is false (neighbours cannot both be supercells); R is true and explains why A is false.
A: In any table with all distinct numbers, there is at least one supercell.
R: The largest number in such a table is always a supercell.
R: The largest number in such a table is always a supercell.
Answer: (a) — Both true and R explains A.
Frequently Asked Questions
What are supercells in Class 6 Maths?
Supercells are cells in a grid where the number is greater than all its neighbouring numbers. In NCERT Class 6 Ganita Prakash Chapter 3, students identify supercells by comparing each cell with cells immediately around it. This activity builds number sense and comparison skills.
How do numbers 'tell us things' in Chapter 3?
In Chapter 3 of Ganita Prakash, numbers 'tell things' when we observe their properties, compare them, and find patterns. For example, counting objects, spotting the largest number, or noticing which numbers repeat lets numbers communicate information about quantity, order, and relationships.
What is the rule for identifying a supercell?
A cell is a supercell if its number is greater than every adjacent cell's number. In a 1D row, compare the cell with its left and right neighbour. In a 2D grid, compare with all surrounding cells. This rule is applied in NCERT Class 6 Chapter 3 activities.
Why is the Number Play chapter important in Class 6?
Number Play develops intuition about numbers through hands-on games, comparisons, and pattern-spotting. It strengthens Bloom's Apply and Analyse levels by requiring students to reason with quantities instead of just calculating, laying foundations for algebra and logical thinking.
How many neighbours does a cell have in a supercell grid?
In a 1D row, an interior cell has 2 neighbours (left, right); edge cells have 1. In a 2D grid used in NCERT Class 6 Chapter 3, an interior cell has up to 8 neighbours including diagonals, or 4 if only horizontal and vertical are counted.
What skills does the supercells activity develop?
The supercells activity develops number comparison, systematic checking, reasoning, and attention to detail. Students learn to verify every neighbour before declaring a supercell, which strengthens logical verification skills essential for mathematics.
Frequently Asked Questions — Number Play
What is Numbers Can Tell Us Things and Supercells in NCERT Class 6 Mathematics?
Numbers Can Tell Us Things and Supercells is a key concept covered in NCERT Class 6 Mathematics, Chapter 3: Number Play. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Numbers Can Tell Us Things and Supercells step by step?
To solve problems on Numbers Can Tell Us Things and Supercells, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 3: Number Play?
The essential formulas of Chapter 3 (Number Play) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Numbers Can Tell Us Things and Supercells important for the Class 6 board exam?
Numbers Can Tell Us Things and Supercells is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Numbers Can Tell Us Things and Supercells?
Common mistakes in Numbers Can Tell Us Things and Supercells include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Numbers Can Tell Us Things and Supercells?
End-of-chapter NCERT exercises for Numbers Can Tell Us Things and Supercells cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 3, and solve at least one previous-year board paper to consolidate your understanding.
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