Chapter 6: NUMBER PLAY
7th StandardMathematics
Chapter Summary
NUMBER PLAY - Chapter Summary
# Number Play
## Overview
This chapter uses fun puzzles, grids, number arrangements, and creative reasoning to help learners explore the ideas of parity (odd and even), number patterns, expressions, and magic squares. It introduces the famous Fibonacci (Virahāṅka) sequence and cryptarithms (letter puzzles involving arithmetic), building foundational algebraic thinking through playful activities.
## Key Topics Covered
### 1. Numbers Tell Us Things
- Children use a rule: each child says the number of taller children in front of them.
- Students create and interpret sequences like 0, 1, 1, 2, 4, 1, 5 and analyze what they mean.
- Reasoning activities include identifying always/sometimes/never true statements.
### 2. Picking Parity
- Explores parity (odd/even nature) of numbers and their sums:
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
- Practical puzzles show that some number combinations (like five odd numbers adding to 30) are impossible.
- Application problems like checking if the sum of ages (e.g., 51 + 52 = 103) can result in a given number (e.g., 112).
- Real-world application with currency and coin combinations.
### 3. Some Explorations in Grids
- Students complete 3×3 number grids based on row and column sums.
- Learn why certain grids cannot be solved (e.g., sums are outside range 6–24).
- Discover properties of a magic square:
- All rows, columns, and diagonals sum to the same number (magic sum).
- For 3×3 grids using numbers 1 to 9, magic sum is always 15.
- Center of such a grid must be 5.
- Introduced to generalizations and transformations:
- Doubling or adding to all numbers in a grid changes the magic sum accordingly.
### 4. The Virahāṅka–Fibonacci Numbers
- Introduces the sequence: 1, 2, 3, 5, 8, 13, 21, 34, ...
- Originates from ancient Indian studies in poetry: combining short and long syllables into rhythms.
- Mathematically, explores how to write numbers like 5 or 8 as the sum of 1s and 2s.
- Connects the number of ways (combinations) to the Fibonacci pattern.
- Encourages predicting future terms and analyzing the parity of sequence terms.
- Shows how this sequence appears in art, architecture, music, and nature (e.g., number of petals on flowers).
### 5. Digits in Disguise (Cryptarithms)
- Puzzles where letters replace digits in addition problems.
- Learners decode the letters based on logical number patterns.
- Develops algebraic thinking and systematic trial-error strategies.
- Includes problems like:
- T + T + T = UT → find T and U
- K2 + K2 = HMM → find K, H, M
## New Terms and Simple Definitions
| Term | Simple Definition |
|------------------|-----------------------------------------------------------------------------------|
| Parity | Whether a number is even or odd |
| Even Number | A number that can be divided into equal pairs (e.g., 2, 4, 6) |
| Odd Number | A number that cannot be divided into equal pairs (e.g., 1, 3, 5) |
| Magic Square | A grid where the sums of all rows, columns, and diagonals are the same |
| Sequence | A list of numbers in a particular order |
| Fibonacci Number | A number in a sequence where each term is the sum of the two before it |
| Cryptarithm | A math puzzle where digits are replaced by letters |
| Rhythm (in beats)| A pattern of short and long syllables used in poetry (used to explain sequences) |
| Expression | A math phrase made with numbers, variables, and operations (e.g., 2n, 2n–1) |
| Consecutive | Numbers that follow one another in order (e.g., 3, 4, 5) |
## Practice Problems
### Easy (3 Problems)
1. What is the parity of 47 + 26?
**Answer**: 47 (odd) + 26 (even) = 73 → **Odd**
2. What is the 5th term in the Virahāṅka–Fibonacci sequence?
**Answer**: 1, 2, 3, 5, **8**
3. Find the 3rd odd number using the formula 2n – 1.
**Solution**: 2 × 3 – 1 = **5**
### Medium (2 Problems)
4. Complete the 3 × 3 magic square using 1 to 9 so that the sum is 15:
- Top row: 4, 9, 2
- Middle row: 3, __, 7
- Bottom row: 8, 1, 6
**Answer**: Middle value is **5**
5. A person says ‘0’ in the height arrangement rule. Does this always mean they are the tallest?
**Answer**: **Only sometimes true**. If no one taller is in front, then it’s 0. But there could be taller people behind.
### Difficult (3 Problems)
6. Can 5 odd numbers add up to 30?
**Answer**: **No**. Odd + Odd + Odd + Odd + Odd = Odd
7. Find the 10th odd number using the formula.
**Solution**: 2 × 10 – 1 = **19**
8. In a 3 × 3 magic square using 2–10, what should the magic sum be?
**Answer**: Sum of 2 to 10 = 2+3+...+10 = 54; 3 rows → Magic Sum = 54 ÷ 3 = **18**
### Very Difficult (2 Problems)
9. Solve the cryptarithm:
T + T + T = UT
**Solution**: T = 5 → 5 + 5 + 5 = 15 → U = 1, T = 5
10. Angaan climbs 8 steps using 1-step or 2-step moves. How many ways can he reach the top?
**Answer**: Use Fibonacci method: 34 ways (8th Fibonacci number)
---
## Overview
This chapter uses fun puzzles, grids, number arrangements, and creative reasoning to help learners explore the ideas of parity (odd and even), number patterns, expressions, and magic squares. It introduces the famous Fibonacci (Virahāṅka) sequence and cryptarithms (letter puzzles involving arithmetic), building foundational algebraic thinking through playful activities.
## Key Topics Covered
### 1. Numbers Tell Us Things
- Children use a rule: each child says the number of taller children in front of them.
- Students create and interpret sequences like 0, 1, 1, 2, 4, 1, 5 and analyze what they mean.
- Reasoning activities include identifying always/sometimes/never true statements.
### 2. Picking Parity
- Explores parity (odd/even nature) of numbers and their sums:
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
- Practical puzzles show that some number combinations (like five odd numbers adding to 30) are impossible.
- Application problems like checking if the sum of ages (e.g., 51 + 52 = 103) can result in a given number (e.g., 112).
- Real-world application with currency and coin combinations.
### 3. Some Explorations in Grids
- Students complete 3×3 number grids based on row and column sums.
- Learn why certain grids cannot be solved (e.g., sums are outside range 6–24).
- Discover properties of a magic square:
- All rows, columns, and diagonals sum to the same number (magic sum).
- For 3×3 grids using numbers 1 to 9, magic sum is always 15.
- Center of such a grid must be 5.
- Introduced to generalizations and transformations:
- Doubling or adding to all numbers in a grid changes the magic sum accordingly.
### 4. The Virahāṅka–Fibonacci Numbers
- Introduces the sequence: 1, 2, 3, 5, 8, 13, 21, 34, ...
- Originates from ancient Indian studies in poetry: combining short and long syllables into rhythms.
- Mathematically, explores how to write numbers like 5 or 8 as the sum of 1s and 2s.
- Connects the number of ways (combinations) to the Fibonacci pattern.
- Encourages predicting future terms and analyzing the parity of sequence terms.
- Shows how this sequence appears in art, architecture, music, and nature (e.g., number of petals on flowers).
### 5. Digits in Disguise (Cryptarithms)
- Puzzles where letters replace digits in addition problems.
- Learners decode the letters based on logical number patterns.
- Develops algebraic thinking and systematic trial-error strategies.
- Includes problems like:
- T + T + T = UT → find T and U
- K2 + K2 = HMM → find K, H, M
## New Terms and Simple Definitions
| Term | Simple Definition |
|------------------|-----------------------------------------------------------------------------------|
| Parity | Whether a number is even or odd |
| Even Number | A number that can be divided into equal pairs (e.g., 2, 4, 6) |
| Odd Number | A number that cannot be divided into equal pairs (e.g., 1, 3, 5) |
| Magic Square | A grid where the sums of all rows, columns, and diagonals are the same |
| Sequence | A list of numbers in a particular order |
| Fibonacci Number | A number in a sequence where each term is the sum of the two before it |
| Cryptarithm | A math puzzle where digits are replaced by letters |
| Rhythm (in beats)| A pattern of short and long syllables used in poetry (used to explain sequences) |
| Expression | A math phrase made with numbers, variables, and operations (e.g., 2n, 2n–1) |
| Consecutive | Numbers that follow one another in order (e.g., 3, 4, 5) |
## Practice Problems
### Easy (3 Problems)
1. What is the parity of 47 + 26?
**Answer**: 47 (odd) + 26 (even) = 73 → **Odd**
2. What is the 5th term in the Virahāṅka–Fibonacci sequence?
**Answer**: 1, 2, 3, 5, **8**
3. Find the 3rd odd number using the formula 2n – 1.
**Solution**: 2 × 3 – 1 = **5**
### Medium (2 Problems)
4. Complete the 3 × 3 magic square using 1 to 9 so that the sum is 15:
- Top row: 4, 9, 2
- Middle row: 3, __, 7
- Bottom row: 8, 1, 6
**Answer**: Middle value is **5**
5. A person says ‘0’ in the height arrangement rule. Does this always mean they are the tallest?
**Answer**: **Only sometimes true**. If no one taller is in front, then it’s 0. But there could be taller people behind.
### Difficult (3 Problems)
6. Can 5 odd numbers add up to 30?
**Answer**: **No**. Odd + Odd + Odd + Odd + Odd = Odd
7. Find the 10th odd number using the formula.
**Solution**: 2 × 10 – 1 = **19**
8. In a 3 × 3 magic square using 2–10, what should the magic sum be?
**Answer**: Sum of 2 to 10 = 2+3+...+10 = 54; 3 rows → Magic Sum = 54 ÷ 3 = **18**
### Very Difficult (2 Problems)
9. Solve the cryptarithm:
T + T + T = UT
**Solution**: T = 5 → 5 + 5 + 5 = 15 → U = 1, T = 5
10. Angaan climbs 8 steps using 1-step or 2-step moves. How many ways can he reach the top?
**Answer**: Use Fibonacci method: 34 ways (8th Fibonacci number)
---
Number Play
Overview
This chapter uses fun puzzles, grids, number arrangements, and creative reasoning to help learners explore the ideas of parity (odd and even), number patterns, expressions, and magic squares. It introduces the famous Fibonacci (Virahāṅka) sequence and cryptarithms (letter puzzles involving arithmetic), building foundational algebraic thinking through playful activities.
Key Topics Covered
1. Numbers Tell Us Things
- Children use a rule: each child says the number of taller children in front of them.
- Students create and interpret sequences like 0, 1, 1, 2, 4, 1, 5 and analyze what they mean.
- Reasoning activities include identifying always/sometimes/never true statements.
2. Picking Parity
- Explores parity (odd/even nature) of numbers and their sums:
- Even + Even = Even
- Odd + Odd = Even
- Even + Odd = Odd
- Practical puzzles show that some number combinations (like five odd numbers adding to 30) are impossible.
- Application problems like checking if the sum of ages (e.g., 51 + 52 = 103) can result in a given number (e.g., 112).
- Real-world application with currency and coin combinations.
3. Some Explorations in Grids
- Students complete 3×3 number grids based on row and column sums.
- Learn why certain grids cannot be solved (e.g., sums are outside range 6–24).
- Discover properties of a magic square:
- All rows, columns, and diagonals sum to the same number (magic sum).
- For 3×3 grids using numbers 1 to 9, magic sum is always 15.
- Center of such a grid must be 5.
- Introduced to generalizations and transformations:
- Doubling or adding to all numbers in a grid changes the magic sum accordingly.
4. The Virahāṅka–Fibonacci Numbers
- Introduces the sequence: 1, 2, 3, 5, 8, 13, 21, 34, ...
- Originates from ancient Indian studies in poetry: combining short and long syllables into rhythms.
- Mathematically, explores how to write numbers like 5 or 8 as the sum of 1s and 2s.
- Connects the number of ways (combinations) to the Fibonacci pattern.
- Encourages predicting future terms and analyzing the parity of sequence terms.
- Shows how this sequence appears in art, architecture, music, and nature (e.g., number of petals on flowers).
5. Digits in Disguise (Cryptarithms)
- Puzzles where letters replace digits in addition problems.
- Learners decode the letters based on logical number patterns.
- Develops algebraic thinking and systematic trial-error strategies.
- Includes problems like:
- T + T + T = UT → find T and U
- K2 + K2 = HMM → find K, H, M
New Terms and Simple Definitions
| Term | Simple Definition |
|---|---|
| Parity | Whether a number is even or odd |
| Even Number | A number that can be divided into equal pairs (e.g., 2, 4, 6) |
| Odd Number | A number that cannot be divided into equal pairs (e.g., 1, 3, 5) |
| Magic Square | A grid where the sums of all rows, columns, and diagonals are the same |
| Sequence | A list of numbers in a particular order |
| Fibonacci Number | A number in a sequence where each term is the sum of the two before it |
| Cryptarithm | A math puzzle where digits are replaced by letters |
| Rhythm (in beats) | A pattern of short and long syllables used in poetry (used to explain sequences) |
| Expression | A math phrase made with numbers, variables, and operations (e.g., 2n, 2n–1) |
| Consecutive | Numbers that follow one another in order (e.g., 3, 4, 5) |
Practice Problems
Easy (3 Problems)
-
What is the parity of 47 + 26?
Answer: 47 (odd) + 26 (even) = 73 → Odd -
What is the 5th term in the Virahāṅka–Fibonacci sequence?
Answer: 1, 2, 3, 5, 8 -
Find the 3rd odd number using the formula 2n – 1.
Solution: 2 × 3 – 1 = 5
Medium (2 Problems)
-
Complete the 3 × 3 magic square using 1 to 9 so that the sum is 15:
- Top row: 4, 9, 2
- Middle row: 3, __, 7
- Bottom row: 8, 1, 6
Answer: Middle value is 5
-
A person says ‘0’ in the height arrangement rule. Does this always mean they are the tallest?
Answer: Only sometimes true. If no one taller is in front, then it’s 0. But there could be taller people behind.
Difficult (3 Problems)
-
Can 5 odd numbers add up to 30?
Answer: No. Odd + Odd + Odd + Odd + Odd = Odd -
Find the 10th odd number using the formula.
Solution: 2 × 10 – 1 = 19 -
In a 3 × 3 magic square using 2–10, what should the magic sum be?
Answer: Sum of 2 to 10 = 2+3+...+10 = 54; 3 rows → Magic Sum = 54 ÷ 3 = 18
Very Difficult (2 Problems)
-
Solve the cryptarithm:
T + T + T = UT
Solution: T = 5 → 5 + 5 + 5 = 15 → U = 1, T = 5 -
Angaan climbs 8 steps using 1-step or 2-step moves. How many ways can he reach the top?
Answer: Use Fibonacci method: 34 ways (8th Fibonacci number)