This MCQ module is based on: 6.1 Numbers Tell Us Things
TOPIC 20 OF 31
6.1 Numbers Tell Us Things
🎓 Class 7
Mathematics
CBSE
Theory
Ch 6 — Number Play
⏱ ~15 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: 6.1 Numbers Tell Us Things
Targeting Class 7 level in Number Theory, with Basic difficulty.
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6.1 Numbers Tell Us Things
Do you remember the children from the Grade 6 textbook of mathematics? They are back — and this time they are calling out numbers based on a new rule. Each child looks at the others in the line and decides a number to say.
What do these numbers mean? Notice that the numbers are 0, 1, 2, 3, 4, 5 — exactly the count of children taller than the child holding the number, looking from left to right. Each child is saying "the number of taller children to my left/right."
Could you figure out what these numbers convey? Observe and try to find out.
Rearrange the children so each one says a number based on the new arrangement. The rule might change — it could be the number of shorter children, or the number of children in front, and so on. Exploring such rules is the heart of this chapter.
Rearrange the children so each one says a number based on the new arrangement. The rule might change — it could be the number of shorter children, or the number of children in front, and so on. Exploring such rules is the heart of this chapter.
This chapter is about observing, patterns?, making clever arrangements, and playing games with numbers. Let's dive in!
Clever Statements About Groups
Read each statement and decide whether it is Always True, Only Sometimes True, or Never True. Share your reasoning.
(a) The person says "0", then they are the tallest in the group.
(b) If a person is "0", then their number is the tallest.
(c) The first person's number is "0".
(d) If a person is not first or last (i.e., they are standing somewhere in between), then they cannot say "0".
(e) The person who calls out the largest number is the shortest.
(f) What is the largest possible number in a group of 8 people?
(b) If a person is "0", then their number is the tallest.
(c) The first person's number is "0".
(d) If a person is not first or last (i.e., they are standing somewhere in between), then they cannot say "0".
(e) The person who calls out the largest number is the shortest.
(f) What is the largest possible number in a group of 8 people?
(a) Only sometimes true.
(b) Always true.
(c) Only sometimes true.
(d) Only sometimes true.
(e) Only sometimes true.
(f) 7 — the shortest person could have all 7 others taller, and so calls out "7".
(b) Always true.
(c) Only sometimes true.
(d) Only sometimes true.
(e) Only sometimes true.
(f) 7 — the shortest person could have all 7 others taller, and so calls out "7".
6.2 Picking Parity
Kishor has some number cards and is working on a puzzle. There are 5 boxes, and each box should contain exactly 1 number card. The numbers in the boxes should sum to 30. Can you help him find a way to do it?
Fig. 6.2 — The sum puzzle: 5 boxes, total 30
Let's look at the available cards: suppose Kishor has cards with numbers 5, 7, 9, 11, 13, 15 — all odd numbers. Can he pick 5 of these so they sum to 30?
Can you figure out which 5 cards add to 30? Is it possible?
Try a few combinations. You will discover the answer is no — it is impossible! Sum of any 5 odd numbers is always odd, but 30 is even.
Try a few combinations. You will discover the answer is no — it is impossible! Sum of any 5 odd numbers is always odd, but 30 is even.
Add a few even numbers together. What kind of number do you get? Does it matter how many numbers are added? — Any number of even numbers summed gives an even number.
Definition — Parity
The parity? of a whole number is simply whether it is odd or even. Even numbers can be arranged in pairs with no leftover; odd numbers always have one leftover after pairing.
Rules of Parity (Adding)
Three key rules
- Even + Even = Even. (Sum of any count of even numbers is always even.)
- Odd + Odd = Even. Two odds pair their "leftovers" and cancel.
- Even + Odd = Odd. One leftover remains.
- Sum of 5 odd numbers = Odd (so can never equal 30).
- Sum of an even count of odd numbers = Even.
- Sum of an odd count of odd numbers = Odd.
Odd numbers can be arranged in pairs with one extra. Some odd examples — 11 = 5 pairs + 1, or 13 = 6 pairs + 1.
Figure it Out — Parity of Small Grids
Find the parity of the number of small squares in these grids:
(a) 27 × 13 (b) 42 × 78 (c) 135 × 654
(a) 27 × 13 (b) 42 × 78 (c) 135 × 654
Number of small squares in an \(m \times n\) grid is \(m \times n\). Parity of a product = "odd only if both factors are odd, else even."
(a) \(27 \times 13\) — both odd → odd.
(b) \(42 \times 78\) — both even → even.
(c) \(135 \times 654\) — one odd, one even → even.
(a) \(27 \times 13\) — both odd → odd.
(b) \(42 \times 78\) — both even → even.
(c) \(135 \times 654\) — one odd, one even → even.
Parity of Expressions
Consider the algebraic expression \(3n + 4\). For different values of \(n\), the expression has different parity.
| n | Value of 3n + 4 | Parity |
|---|---|---|
| 3 | 13 | odd |
| 8 | 28 | even |
| 10 | 34 | even |
Come up with an expression that always has even parity. Examples: \(2n, 4n, 2n + 6, 10n\).
Come up with an expression that always has odd parity. Examples: \(2n + 1, 4n - 1, 2n - 5\).
Come up with an expression that can have either odd or even parity. Like \(3n + 4\): depends on \(n\).
The expression \(6k + 2\) evaluates to 8, 14, 20, 26, ... (for \(k = 1, 2, 3, ...\)) — many even numbers with a factor of 2.
Come up with an expression that always has odd parity. Examples: \(2n + 1, 4n - 1, 2n - 5\).
Come up with an expression that can have either odd or even parity. Like \(3n + 4\): depends on \(n\).
The expression \(6k + 2\) evaluates to 8, 14, 20, 26, ... (for \(k = 1, 2, 3, ...\)) — many even numbers with a factor of 2.
Are there expressions using which we can list all even numbers? Hint: All even numbers have a factor of 2.
Yes: \(2n\) lists every even number (0, 2, 4, 6, ...) as \(n\) takes values \(0, 1, 2, 3, \ldots\).
Yes: \(2n\) lists every even number (0, 2, 4, 6, ...) as \(n\) takes values \(0, 1, 2, 3, \ldots\).
Are there expressions using which we can list all odd numbers?
Yes: \(2n - 1\) or \(2n + 1\) lists every odd number.
Yes: \(2n - 1\) or \(2n + 1\) lists every odd number.
What would be the \(n^{th}\) term for multiples of 2? Or the \(n^{th}\) even number?
The \(n^{th}\) even number (if we start counting 2 as the 1st) is \(2n\).
The \(n^{th}\) even number (if we start counting 2 as the 1st) is \(2n\).
What is the 100th odd number? To answer this, consider: we saw \(2n - 1\) lists all odd numbers. The 100th odd number is \(2(100) - 1 = 199\).
Activity: Fill the Grids with Odd/Even Sums
Activity: Parity Grid Puzzles
L3 ApplyMaterials: Paper and pencil.
Predict: When you fill a 3×3 grid so that each row/column has a prescribed sum, how often do parity rules force your answer?
Fill two sample grids below based on stated row-sums and column-sums:
When only the parity of each row/column sum is given, you can deduce the parity of the missing numbers without knowing their values! Parity is a powerful quick-check tool.
Competency-Based Questions
Scenario: In a school fair, teacher gives each of 5 students a card with an odd number written on it. The students must arrange their cards in 5 boxes so that the sum equals 50. One student suspects this is impossible.
Q1. Is it possible? Justify using parity.
L3 ApplySum of 5 odd numbers = odd (odd count of odd numbers). But 50 is even. So it is impossible. The student is correct.
Q2. What is the smallest even target sum that can be reached using 6 odd cards? What about the smallest odd target using 6 odd cards?
L4 AnalyseSmallest even with 6 odds: 6 odds sum to even. Smallest 6 distinct odds: 1+3+5+7+9+11 = 36 (even ✓). Odd target with 6 odds: impossible — sum of 6 odd numbers is always even.
Q3. Evaluate the claim: "The product of two odd numbers is always odd, so the sum of two odd numbers is also odd." Is this correct?
L5 EvaluateIncorrect. The first part is right — odd × odd = odd. But the second part is wrong — odd + odd = even. The student confused multiplication rules with addition rules.
Q4. Create an algebraic expression \(ax + b\) with integers \(a, b\) such that the expression is always even, regardless of whether \(x\) is odd or even. Give two distinct examples and prove they work.
L6 CreateChoose \(a\) even and \(b\) even. Examples: \(2x + 4\) and \(6x + 10\). Proof: \(ax\) is even whenever \(a\) is even (for any integer \(x\)). An even plus an even is even. So \(ax + b\) is always even. Many valid answers possible.
Assertion–Reason Questions
Assertion (A): The sum of five odd numbers can never be 30.
Reason (R): The sum of an odd count of odd numbers is always odd.
Reason (R): The sum of an odd count of odd numbers is always odd.
Answer: (a). 30 is even, but five odds sum to odd (R), so A follows.
Assertion (A): \(2n + 1\) describes every odd number as \(n\) ranges over whole numbers.
Reason (R): Every odd number is one more than some even number.
Reason (R): Every odd number is one more than some even number.
Answer: (a). \(2n\) is always even, adding 1 gives odd. Every odd number equals 2n+1 for some n. R directly explains A.
Assertion (A): In a 42 × 78 grid, the number of unit squares is odd.
Reason (R): A product is odd only when both factors are odd.
Reason (R): A product is odd only when both factors are odd.
Answer: (d). 42 × 78 — both even, so product is even; A is false. R is the correct rule for when a product is odd.
Frequently Asked Questions — Number Play
What is Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool in NCERT Class 7 Mathematics?
Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool is a key concept covered in NCERT Class 7 Mathematics, Chapter 6: 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 Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool step by step?
To solve problems on Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 7 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 6: Number Play?
The essential formulas of Chapter 6 (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 Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool important for the Class 7 board exam?
Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool is part of the NCERT Class 7 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 Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool?
Common mistakes in Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool 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 Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool?
End-of-chapter NCERT exercises for Part 1 — Numbers Tell Us Things & Picking Parity | Class 7 Maths Ch 6 | MyAiSchool 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 6, and solve at least one previous-year board paper to consolidate your understanding.
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