Chapter Overview
Number play uses patterns, parity, sequences and digit puzzles to develop computational thinking. The aim is to notice structure, test conjectures and explain why a pattern works.
This chapter belongs to Ganita Prakash, Grade 7. Focus on explaining each step, checking whether an answer is reasonable, and comparing more than one solution method.
Learning Objectives
After studying this chapter, you should be able to:
- explain and apply parity;
- explain and apply patterns and sequences;
- explain and apply virahanka-fibonacci pattern;
- explain and apply cryptarithms and logic;
- communicate the reasoning behind a solution clearly;
- check answers using estimation, substitution, or a second method.
Key Concepts
| Concept | Meaning | |---|---| | Parity | Even numbers are divisible by 2; odd numbers are not. Even and odd behaviour lets us predict the parity of sums and products. | | Patterns and sequences | A sequence follows a rule. Differences, ratios or recursive relationships can reveal that rule. | | Virahanka-Fibonacci pattern | Starting with suitable initial terms, each later term is formed by adding the previous two. Similar patterns appear in counting arrangements. | | Cryptarithms and logic | Digits are replaced by letters under consistent rules. Place value and carrying constrain the possible digits. |
Detailed Explanation
Parity
Even numbers are divisible by 2; odd numbers are not. Even and odd behaviour lets us predict the parity of sums and products.
Patterns and sequences
A sequence follows a rule. Differences, ratios or recursive relationships can reveal that rule.
Virahanka-Fibonacci pattern
Starting with suitable initial terms, each later term is formed by adding the previous two. Similar patterns appear in counting arrangements.
Cryptarithms and logic
Digits are replaced by letters under consistent rules. Place value and carrying constrain the possible digits.
Do not memorise a rule without testing it on examples. Ask what each number, operation, line, or symbol represents and whether the result fits the original situation.
Important Rules and Formulae
- Even + even and odd + odd are even; even + odd is odd.
- A product is odd only when every factor is odd.
- In a cryptarithm, one letter represents one digit consistently, and leading letters cannot be zero.
Worked Examples
Example 1
Problem: Predict the parity of 137 × 42 + 9.
Solution: 137 × 42 is even because one factor is even; even + odd is odd.
Example 2
Problem: Continue 1, 1, 2, 3, 5, 8 for three terms.
Solution: 13, 21, 34; each term is the sum of the previous two.
Show the mathematical statement, substitution or construction step before writing the final answer. Include units wherever the quantity is measured.
Common Mistakes
- Assuming a visible pattern proves a rule for every term.
- Using different digits for the same letter in a cryptarithm.
- Checking only the units column and ignoring carries.
Quick Revision
- Parity: Even numbers are divisible by 2; odd numbers are not.
- Patterns and sequences: A sequence follows a rule.
- Virahanka-Fibonacci pattern: Starting with suitable initial terms, each later term is formed by adding the previous two.
- Cryptarithms and logic: Digits are replaced by letters under consistent rules.
Practice Questions
- Is the sum of five odd numbers odd or even?
- What parity does the square of an odd number have?
- Continue 2, 5, 8, 11 for two terms.
- Why can an even number never be the product of two odd numbers?
Answers and Explanations
- Odd.
- Odd.
- 14, 17.
- Because odd × odd is always odd.
Self-Check
Explain one rule from this chapter in your own words, create a fresh example, solve it, and verify the answer. If the explanation and verification agree, the concept is understood rather than merely memorised.