NUMBER PLAY
NCERT Class 7 Mathematics Chapter 6: NUMBER PLAY (Pages 127–145)
NUMBER PLAY at a Glance
Board
CBSE
Class
Class 7
Subject
Mathematics
Book
Ganita Prakash
Chapter
6
Pages
127–145
Resources
7 study resources
NUMBER PLAY is a chapter in the CBSE Class 7 Mathematics syllabus from Ganita Prakash. This chapter hub brings together revision notes, practice questions, worksheets, flashcards, formula sheet to help students learn, practice, and revise NUMBER PLAY effectively.
Scroll down to find NUMBER PLAY notes, practice questions, worksheets, and revision resources — all in one place. Use the sidebar to jump to any section, or browse the full page below.
NUMBER PLAY Revision Guide
Download the NUMBER PLAY revision guide with key points, summaries, and quick revision notes for CBSE Class 7 Mathematics.
Key Points
1
Numbers indicate taller children.
Children call out how many in front are taller, building understanding of relative heights.
2
Arrangement rule examples.
Different sequences (0, 1, 1, 2...) help students understand counting and comparison in groups.
3
Understanding Always, Sometimes, Never.
Evaluate statements about height to develop critical thinking on logic and reasoning.
4
Sum of five odd numbers.
Five odd numbers cannot sum to an even number, reinforcing properties of parity.
5
Even numbers sum to even.
Adding even numbers results in an even sum; they can always be paired without leftovers.
6
Odd numbers sum to odd or even.
Adding two odds gives even; thus, odd groups lead to a mix of results. Understand grouping.
7
Consecutive ages problem.
Martin and Maria’s ages as consecutive integers emphasize addition principles yielding odd/even sums.
8
Parity definition.
Parity references whether a number is odd or even; essential in understanding numerical properties.
9
Grid parity insight.
A grid's total squares can deduce even/odd status based on dimensions without calculation.
10
Different sums result in parity.
Determine outcomes of sums involving odd/even numbers to reinforce fundamental concepts.
11
Algebraic expressions and parity.
Expressions like 3n + 4 demonstrate varying parities for different n values; learn variability.
12
Formulas for nth even/odd numbers.
Formulas: 2n gives nth even; 2n-1 gives nth odd. Understand sequences and their implications.
13
Algebraic expressions assessments.
Design expressions to achieve consistent odd/even results, enriching algebra skills and creativity.
14
Exploring sums: even + even.
Two even numbers always sum to even, reaffirming associations through practice problems.
15
Exploring sums: odd - odd.
Two odd numbers subtract to even, highlighting arithmetic properties to memorize.
16
Investigating grid sizes.
Analyze grids of specific sizes for odd or even outcomes, fostering spatial awareness in math.
17
Utilizing statements in proving parity.
Calibrating claims about even and odd sums contributes to rational argument forming in math.
18
Summation of mixed parities.
Practice mixed sums—recognize how parity changes by adding odds to evens or vice versa.
19
Explaining even-count mechanics.
Even counts can be systematically enumerated and paired; essential for mathematical reasoning.
20
Application of parity in real cases.
Deduce real-life problems using parity, connecting theoretical learning to practical scenarios.
21
Formative assessment of logical thinking.
Engage students with logical puzzles to reinforce understanding of parity concepts in fun ways.
NUMBER PLAY Practice Questions & Answers
Practice important questions and exam-style problems from NUMBER PLAY. These questions cover key topics from the CBSE Class 7 Mathematics syllabus.
How to practice: Start with the questions below to test your understanding of NUMBER PLAY. Use the revision guide to review concepts you find difficult, then come back and retry the questions for better retention.
Q1
If a child sees 3 taller children in front of them, what number would they call out?
Single Answer MCQ
Q-00208001
Q2
If a child reports '0', what can you infer about their height compared to those in front?
Single Answer MCQ
Q-00208002
Q3
In a line of 5 children, if the second child can see 1 taller child in front, how many are shorter?
Single Answer MCQ
Q-00208003
Q4
What does the number '2' signify for a child if 4 are in front of them?
Single Answer MCQ
Q-00208004
Q5
If two children report the same number of taller children, what can you conclude?
Single Answer MCQ
Q-00208005
Q6
A child counts 4 taller children in front of them. If they are taller than the one behind, how many tall children must be behind?
Single Answer MCQ
Q-00208006
Q7
Given a scenario where a child sees 2 taller children, how many children in front could be shorter?
Single Answer MCQ
Q-00208007
Q8
If the tallest child is at the end of a line, what might their call number be?
Single Answer MCQ
Q-00208008
View all 60 NUMBER PLAY questionsView all 60 NUMBER PLAY questions
Q9
In a line, if 3 children report '1', what could be true about their heights?
Single Answer MCQ
Q-00208009
Q10
In an arrangement, if a child says '5', what conclusion can you draw?
Single Answer MCQ
Q-00208010
Q11
What is the smallest number a child can call out?
Single Answer MCQ
Q-00208011
Q12
If multiple arrangements report different numbers, what likely causes discrepancies?
Single Answer MCQ
Q-00208012
Q13
A child sees 4 taller children; how many children are in front of them at most?
Single Answer MCQ
Q-00208013
Q14
Why might one child say '3' while another says '2' in a group of 5?
Single Answer MCQ
Q-00208014
Q15
If a taller child is not at the front, what must they see?
Single Answer MCQ
Q-00208015
Q16
What is the parity of the number of small squares in a 5 × 7 grid?
Single Answer MCQ
Q-00208016
Q17
In a 4 × 6 grid, how many small squares are there?
Single Answer MCQ
Q-00208017
Q18
Which grid dimension combination results in an even number of small squares?
Single Answer MCQ
Q-00208018
Q19
What can we infer about the parity of small squares in a grid with both dimensions odd?
Single Answer MCQ
Q-00208019
Q20
A grid of size 8 × 3 has how many small squares?
Single Answer MCQ
Q-00208020
Q21
If a grid is formed using 2 odd numbers, what is the likely parity of small squares?
Single Answer MCQ
Q-00208021
Q22
For the grid dimensions of 12 × 11, what is the parity of the number of small squares?
Single Answer MCQ
Q-00208022
Q23
How many total small squares are in a 6 × 6 grid?
Single Answer MCQ
Q-00208023
Q24
Considering the dimensions 9 × 4, what’s the property regarding their product?
Single Answer MCQ
Q-00208024
Q25
In a grid measuring 15 × 15, what is the total number of small squares?
Single Answer MCQ
Q-00208025
Q26
What can be said about any grid formed with one even and one odd dimension?
Single Answer MCQ
Q-00208026
Q27
If the dimensions of a grid are 20 × 5, what is the total small squares?
Single Answer MCQ
Q-00208027
Q28
What is the parity of small squares in a grid of 3 × 10?
Single Answer MCQ
Q-00208028
Q29
In a grid of dimensions 13 × 9, how many small squares does it contain?
Single Answer MCQ
Q-00208029
Q30
How does the product of two even numbers affect the total small squares?
Single Answer MCQ
Q-00208030
Q31
What is the parity of the expression 5x + 2 when x is an even number?
Single Answer MCQ
Q-00208031
Q32
Which of the following expressions always yields an odd number?
Single Answer MCQ
Q-00208032
Q33
What is the nth term for odd numbers?
Single Answer MCQ
Q-00208033
Q34
If n = 2, what is the value of 7n + 1?
Single Answer MCQ
Q-00208034
Q35
Which of the following expressions will give all even numbers?
Single Answer MCQ
Q-00208035
Q36
What is the parity of the expression 10 + 3x for odd x?
Single Answer MCQ
Q-00208036
Q37
If k is an odd integer, what is the value of 4k + 2?
Single Answer MCQ
Q-00208037
Q38
Which expression can yield both odd and even values depending on n?
Single Answer MCQ
Q-00208038
Q39
For k = 3, what is the output of 6k + 1?
Single Answer MCQ
Q-00208039
Q40
Which of the following expressions will always produce an even integer?
Single Answer MCQ
Q-00208040
Q41
What is the 100th odd number?
Single Answer MCQ
Q-00208041
Q42
How can we express the nth even number?
Single Answer MCQ
Q-00208042
Q43
If m is a variable and m = 4, what is the parity of 3m + 5?
Single Answer MCQ
Q-00208043
Q44
What will be the output of the expression 8a + 4 when a is any integer?
Single Answer MCQ
Q-00208044
Q45
Which expression will evaluate to an even number when n is any integer?
Single Answer MCQ
Q-00208045
Q46
Which expression always produces an odd value regardless of the integer input?
Single Answer MCQ
Q-00208046
Q47
What is the sum of any two even numbers?
Single Answer MCQ
Q-00208047
Q48
If you add three odd numbers, what type of number do you get?
Single Answer MCQ
Q-00208048
Q49
Which of the following sets of numbers will sum to 30?
Single Answer MCQ
Q-00208049
Q50
What is the effect of adding an even number to an odd number?
Single Answer MCQ
Q-00208050
Q51
How many odd numbers must be selected to ensure an even sum?
Single Answer MCQ
Q-00208051
Q52
If you select four odd numbers and one even number, what will the sum's parity be?
Single Answer MCQ
Q-00208052
Q53
Which of these combinations cannot add up to 30?
Single Answer MCQ
Q-00208053
Q54
Which statement is true regarding even numbers?
Single Answer MCQ
Q-00208054
Q55
If the sum of three numbers is 30, which of the following numbers must be included to make it valid?
Single Answer MCQ
Q-00208055
Q56
What happens when an even number is added with an odd number and an even number?
Single Answer MCQ
Q-00208056
Q57
How would adding five even numbers together affect the outcome?
Single Answer MCQ
Q-00208057
Q58
Which of the following sets of numbers contains only odd numbers?
Single Answer MCQ
Q-00208058
Q59
If two even numbers add up to a certain number, which of the following must be true?
Single Answer MCQ
Q-00208059
Q60
Which of these combinations would not add up to an even number?
Single Answer MCQ
Q-00208060
NUMBER PLAY Practice Worksheets
Download and practice NUMBER PLAY worksheets to improve problem-solving accuracy and speed for CBSE Class 7 Mathematics exams.
NUMBER PLAY - Mastery Worksheet
This worksheet challenges you with deeper, multi-concept long-answer questions from NUMBER PLAY to prepare for higher-weightage questions in Class 7.
Mastery
Questions
1
Given a lineup of 7 children, where each calls out the number of children taller than them in front of them, create one possible arrangement that leads to the sequence [0, 1, 1, 2, 4, 1, 5]. Explain the arrangement logic and verify your reasoning.
An arrangement could be: Child1 (tallest), Child2, Child3, Child4, Child5, Child6, Child7 (shortest). Based on relative heights, verify by checking each child's perspective and the total taller children ahead.
2
Analyze the statement: 'If a person says ‘0’, then they are the tallest in the group.' Is this Always True, Sometimes True, or Never True? Provide an example to support your answer.
'Always True.' If a child sees '0', it means no one taller is in front. For example, if Child7 says 0, that implies they are the only one or the tallest.
3
Kishor has five boxes which need to sum to 30 using odd numbered cards only. Demonstrate whether it's possible or not, and explain why.
It's not possible since adding 5 odd numbers results in an odd sum. Therefore, they cannot yield the even total of 30.
4
Two siblings, Maria and Martin, are reportedly 112 years combined in age. Could this be true? Prove your reasoning using the properties of odd and even numbers.
It's false; their ages being consecutive numbers means their combined sum is even, hence can't equal the even number 112.
5
Based on the expressions provided, define your own algebraic expression that would always yield an even result. Justify your choices.
An example is: 2n, where n is a whole number. This produces only even numbers since all multiples of 2 are even.
6
Evaluate the parity of the following scenarios: Sum of 3 odd numbers and 4 even numbers. Is the result even or odd? Explain your reasoning.
The sum is even. 3 odd = odd + odd = even + even = even, combined with 4 even numbers (always even) results in even.
7
For the grids provided, can you deduce the parity of grids 27 × 13, 42 × 78, and 135 × 654 without calculating the products? Explain how.
The parity is odd for 27x13 (odd x odd = odd), even for 42x78 and 135x654 (even x even = even).
8
Address the statement: 'The parity of the sum of any two consecutive numbers is odd.' Give a detailed explanation and include examples to illustrate.
This is true, as one of the consecutive numbers is always even and the other is odd; thus, their sum is odd.
9
Construct a problem around the parity of products. What scenarios result in even and odd products? Provide examples including different combinations of odd and even factors.
The product is even if at least one factor is even. Examples: (2, 3) = 6 (even), (3, 5) = 15 (odd).
10
Analyze and derive a formula that outputs the nth odd number. Explore this against the even number's formula and demonstrate your findings.
The nth odd number is expressed as 2n - 1. Comparably, the nth even number is 2n, showing the consistent relationship in sequences.
NUMBER PLAY - Practice Worksheet
This worksheet covers essential long-answer questions to help you build confidence in NUMBER PLAY from Ganita Prakash for Class 7 (Mathematics).
Practice
Questions
1
Explain the rule of how children call out numbers based on their heights. Why is this arrangement important?
The children call out the number of children taller than them in front. This process allows us to understand relative heights, as each number corresponds to a positional relationship. For example, if a child sees three taller ones, they say '3'. This method provides insight into ordering and comparisons in our environment, helping us grasp concepts of measurement and comparison effectively. Visualizing or drawing heights can further enhance understanding.
2
Discuss the meaning of the statement: 'If a person says ‘0’, then they are the tallest in the group.' What are the conditions for this to be true?
This statement means if someone hears a 0, it indicates no taller persons in front, implying they are indeed the tallest. However, it is true only if the person is at the front of the line. If they are not, the statement may not hold. For example, someone else could have a height similar to theirs who stands between them and the front. Hence, it’s critical to assess positions and the heights of those around.
3
Is it possible for the ages of siblings born one year apart to sum to 112? Justify your answer using concepts from parity.
Since siblings are born one year apart, their ages are consecutive numbers (x and x+1). Given the sum, x + (x + 1) = 112 simplifies to 2x + 1 = 112. Solving yields 2x = 111, giving x = 55.5. Since ages must be whole numbers, they cannot sum to 112. Hence, the question demonstrates how consecutive numbers cannot produce an even sum. Using parity, we see odd+even can’t yield even results.
4
Identify the necessary conditions under which five odd numbers can sum to an even number. Explain why this is the case.
According to parity rules, the sum of odd numbers is always odd unless paired correctly. When summing five odd numbers, this will always yield an odd total. For example, 1+1+1+1+1=5. If 5 boxes must contain 5 odd numbers summing to 30, it is impossible since 30 is even. Hence, understanding parity clarifies why this scenario fails.
5
How can you determine the parity of sums of numbers without calculating their total leads? Provide examples.
To determine parity, analyze the count of odd/even numbers in the sum. For instance, even + even is always even, odd + odd is always even, and even + odd is always odd. For example, the sum of 2 even numbers (4, 6) and 2 odd numbers (1, 3) is even. So, you can categorize and deduce the parity by knowing how many odds and evens exist in the sum without computation.
6
Calculate and explain the parity of small squares in a grid of size 27 × 13.
Considering that rows and columns are odd, a product of an odd number (27) and an odd number (13) will also yield odd. Therefore, 27 × 13 = 351, which is odd. Here's the pattern: odd × odd = odd. Knowing this allows for parity checks of rectangular grids without the need for actual multiplication.
7
Describe a mathematical expression that always returns an odd result. Provide reasoning and examples.
An expression that generates odd results could be structured as 2n + 1, where n is any integer. For instance, if n = 2, then 2(2) + 1 = 5, and for n = 3, it gives 7. This consistent odd output path showcases how odd numbers arise by modifying even integers. Associating numbers this way strengthens numerical understanding.
8
Explore the parity resulting from the expression 3n + 4. Provide examples with varying n values.
The expression 3n + 4 has varying outputs based on the parity of n. If n is odd (i.e., n=1), then output 3(1) + 4 = 7 (odd). If n is even (i.e., n=2), then 3(2) + 4 = 10 (even). This demonstrates how the expression sets up conditions for multiple outputs in terms of parity. Overall, both even and odd parities can emerge from changing n.
9
Find the 100th odd number using a formula you created. Explain the derivation.
To find the 100th odd number, use the formula 2n - 1 where n = 100. Thus, 2(100) - 1 = 200 - 1 = 199. This formula stems from recognizing that odd numbers can be framed as one less than the corresponding even number (2n). This method provides a direct way to pinpoint any odd number in a sequence.
NUMBER PLAY - Challenge Worksheet
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for NUMBER PLAY in Class 7.
Challenge
Questions
1
Analyze the relationship between the heights of children and the numbers they call out based on the new arrangement. How can this scenario illustrate the mathematical concept of inequalities?
Explore the implications of height as a variable. Consider how the arrangement contributes to the inequalities that each child's number represents.
2
Given the scenarios of Kishor's number cards, reason why it is impossible to sum an odd number of odd numbers to an even number. Provide a logical analysis.
Describe the fundamental properties of odd and even numbers. Use examples to illustrate various ways odd numbers interact in addition.
3
Evaluate the claim that two siblings' ages can sum up to 112, given their relationship. What assumptions must be questioned?
Investigate the relationship between consecutive integers and their properties. Provide a mathematical breakdown of age scenarios that uphold or contradict the claim.
4
Propose a method to predict the parity of the total number of squares in a grid based solely on its dimensions without calculating the area.
Utilize properties of multiplication and parity to establish a general rule. Provide varied examples to demonstrate its universal application.
5
Discuss the implications of whether an expression can consistently yield even parity. What factors influence the parity of an expression?
Delve into the role of coefficients and constants within the expression structure that dictate the outcome. Justify your findings with representative examples.
6
Explore the concept of even and odd numbered sums in more complex organizational systems such as tournament brackets or assignment distributions. What conclusions can be drawn?
Analyze how parity impacts such organizational systems and theorize about their operational effectiveness based on numerical structure.
7
Considering the statement 'If a person says 0, then they are the tallest,' provide a comprehensive argument exploring its truthfulness. What scenarios might exemplify this?
Assess the validity of such statements through different examples and counterexamples, exploring the nuances of height and number calling in various arrangements.
8
Investigate the outcomes when different combinations of odd and even integers are added. How can this inform our understanding of general numerical relationships?
Conduct a thorough exploration of addition rules applied to odd and even integers. Provide examples that disprove or support commonly held beliefs.
9
Create a predictive formula for determining the nth odd number in a sequence. How does parity play a role in its derivation?
Outline a step-by-step derivation of the formula while ensuring to discuss the relevance of even position numbers on identifying odds.
NUMBER PLAY Formula Sheet
Use this Class 7 Mathematics NUMBER PLAY Formula Sheet for quick revision before school exams and CBSE exams. It brings together the important formulas, key concepts, and worked examples in one place so students can revise faster and download a printable PDF for offline study.
Important Formulas
1
Sum of 2 even numbers = Even
Adding two even numbers results in an even number. Examples include 2 + 4 = 6, which is even.
2
Sum of 2 odd numbers = Even
The addition of two odd numbers results in an even number. E.g., 3 + 5 = 8.
3
Sum of an even number and an odd number = Odd
Combining an even and an odd number yields an odd number. For instance, 2 + 3 = 5.
4
Number of squares in a grid = Length × Width
The total number of squares in a rectangular grid can be calculated by multiplying the number of rows (length) by columns (width), e.g., in a 3x4 grid: 3 * 4 = 12.
5
nth even number = 2n
This formula gives the nth even number in a sequence. For n = 1, it returns 2, for n = 2, it returns 4, etc.
6
nth odd number = 2n - 1
This formula calculates the nth odd number. For n = 1, it returns 1, for n = 2, it returns 3, etc.
7
Parities of expressions: Even + Even = Even
Similar to the addition of even numbers, it reaffirms that the sum is even.
8
Parities of expressions: Odd + Odd = Even
Confirms that two odd numbers add up to an even number.
9
Parities of expressions: Even - Even = Even
Subtracting two even numbers always results in another even number.
10
Sum of children’s numbers (based on height arrangement)
A child’s number indicates how many of those in front are taller. Understanding height arrangements illustrates real-world applications of numbers.
Worked Examples
1
If X is the number of boxes, and each box has 1 number | X = 5
This emphasizes the necessity of odd numbers in boxes. Understanding sums helps with problem-solving and logic.
2
Sum of ages = (n) + (n+1)
If Maria and Martin's ages differ by one, their combined ages can be expressed as the sum of consecutive numbers.
3
Let S = Sum of cards, S = 30
Kishor’s challenge in arranging numbers in boxes results in an impossible sum when confined to odd numbers.
4
2m + 3n = Total (even + odd considerations)
Mathematical representations signify relations of odd/even in sums; fundamental when dealing with parity.
5
For any positive integers: Even number total = 2 (k), for k = 1, 2, 3,...
This reiterates the patterns in parity results.
6
3x + 4 = Parity evaluation
Varying x provides insights to the alternation of parities depending on x being odd or even.
7
Square of an even number = Even
For example, 4² = 16. Squares maintain parity.
8
Square of an odd number = Odd
For instance, 3² = 9, retaining oddity.
9
x = 2n + 1 (determines odd numbers)
This gives insight into generating odd numbers.
10
Total coins = ₹1 + ₹5 + ₹10 = ₹205
Analyzing coin distributions using even and odd to achieve a specified total demonstrates practical applications of mathematical concepts.
Explore More NUMBER PLAY Resources
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NUMBER PLAY PDF Downloads
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NUMBER PLAY Official Textbook PDF
Download the official NCERT/CBSE textbook PDF for Class 7 Mathematics.
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NUMBER PLAY Revision Guide
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NUMBER PLAY Formula Sheet
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NUMBER PLAY Mastery Worksheet
Work through mixed NUMBER PLAY questions to improve accuracy and speed.
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NUMBER PLAY Practice Worksheet
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NUMBER PLAY Challenge Worksheet
Try harder NUMBER PLAY questions that test deeper understanding.
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NUMBER PLAY Question Bank
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NUMBER PLAY Flashcards
Revise key terms and definitions from NUMBER PLAY with interactive flashcards. Quick recall practice for CBSE Class 7 Mathematics.
These flash cards cover important concepts from NUMBER PLAY in Ganita Prakash for Class 7 (Mathematics).
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