NCERT Solutions for Class 8 Mathematics Chapter Algebra Play
 

This worksheet provides complete and accurate NCERT Solutions for Class 8 Mathematics Chapter Algebra Play. This chapter introduces students to fun and engaging ways of learning algebra through tricks, number patterns, pyramids, grids, and logical reasoning activities. It helps students understand how algebra works in real-life situations using simple and interesting methods. This worksheet is important because it builds strong problem-solving skills and develops logical thinking in a structured NCERT-based approach.

Chapter summary: stories, poems & themes

This chapter is activity-based and focuses on mathematical games, number tricks, and logical puzzles. Students explore “Think of a Number” tricks, number pyramids, grids, and divisibility rules. The main theme of the chapter is to make algebra enjoyable and intuitive through patterns and observations. It also introduces relationships between numbers using visual and activity-based learning methods.

What this NCERT chapter covers?

• Understanding number tricks and logical operations  
• Learning number pyramids and identifying patterns  
• Exploring relationships using algebraic expressions  
• Working with grids and solving based on conditions  
• Understanding divisibility rules and number properties  
• Developing reasoning and observation skills  

How to use these NCERT solutions?

Students should first try solving each question on their own to understand the concept clearly. After attempting, they can use these NCERT Solutions to check their answers and correct mistakes. Parents and teachers can use this worksheet to guide students step-by-step. The solutions follow the exact NCERT order and structure, making it easy for revision and better understanding of concepts.

Student tips & learning tricks

• Carefully observe number patterns before solving  
• Practice number tricks step-by-step to avoid mistakes  
• Pay attention to relationships in pyramids and grids  
• Double-check calculations in divisibility problems  
• Follow the logic used in each solution rather than memorising  

Why NCERT solutions are important?

NCERT Solutions help students build a strong foundation in mathematics by following a structured and reliable approach. They ensure that students understand concepts clearly and solve problems accurately. These solutions improve confidence, enhance logical thinking, and prepare students effectively for school exams and assessments.

Complete answer key – NCERT solutions

Think of a number tricks

1  
To get 3: Add 6 instead of 4  
To get 5: Add 10 instead of 4  

2  
(i) 1269 → 12 September (12/09)  
(ii) 394 → 2 February (02/02)  
(iii) 296 → 1 January (01/01)  

Number pyramids

Basic pyramid filling  

1  
Pyramid 1: Top = 8  
Bottom = 6, 2  

2  
Pyramid 2: Top = 14  
Middle = 7, 7  
Bottom = 3, 4, 3  

3  
Pyramid 3:  
Top = 32  
Bottom = 5, 4, 5, 0  
Second = 9, 9, 5  
Third = 18, 14  

Solved pyramid (algebra)

Final values:  
c = 20, a = 32, b = 28  

Fill the following pyramids

1  
Pyramid 1:  
Bottom = 4, 9, 6, 1  
Second = 13, 15, 7  
Third = 28, 22  
Top = 50  

2  
Pyramid 2:  
Bottom = 5, 14, 7, 2  
Second = 19, 21, 9  
Third = 40, 30  
Top = 70  

Figure it out (number pyramids)

1  
38, 32, 63  

2  
a + 3b + 3c + d  

3  
141, 124, 56  

4  
Grid numbers: 1, 2, 3, 5, 8, 13  
Top number: 8  
Yes, all are Fibonacci numbers  

5  
(i) All numbers are Fibonacci numbers; top is also Fibonacci  
(ii) Same observation holds  

6  
In an n-row pyramid with Fibonacci base:  
All numbers in pyramid are Fibonacci numbers  
Top is Fibonacci number  

Fun with grids

Answers  

1  
Calendar Magic = 5, 6, 12, 13  

2  
Algebra Grids:  
First Grid = Blue square = 9  
Red circle = 5  
Other Grids = All values correctly filled to satisfy row sums  

The largest product

Answer:  
Largest product using 2, 3, 5:  
32 × 5  

Figure it out (the largest product)

1  
Using 1, 3, 7 → 31 × 7  

2  
Using 3, 5, 9 → 53 × 9  

Decoding divisibility tricks

If digits reversed and subtracted:  
Result = 9(a − b) or 9(b − a)  
Always divisible by 9  

Figure it out (decoding divisibility tricks)

1  
Quotient = difference of digits  

2  
Yes, always divisible by 11  

3  
Sum is divisible by 37 and also divisible by 3  

Additional answers

4  
Result after division by 7, 11, 13 → Original number  

5  
Let initial flowers = x, Correct solution:  
Initial flowers = 7  
Flowers in each shrine = 8  

6  
Heads = 55, Legs = 150  
Solution: Hens = 35, Horses = 20  

7  
Daughter’s age = 3 years  

8  
Gauri = 9 cows, Naina = 18 cows  

9  
(i) Selling price = ₹70  
(ii) Required sales = 150 dosas  

10  
All values = 1  

11  
(i) 7 coins  
(ii) Cost per round should be less than 8 coins  
(iii) Cost = 8 coins (to take all money)  

Master algebra concepts easily with these accurate NCERT Solutions for Class 8 Mathematics and strengthen your problem-solving skills step by step.
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