NCERT Class 8 Mathematics Chapter 6 Algebra Play Notes cover number tricks, date decoding, number pyramids, calendar grids, largest-product puzzles and divisibility proofs for the 2026-27 Ganita Prakash Part 2 syllabus. The PDF turns each trick into short algebra steps students can revise before class tests.
- Download a 20-page NCERT Notes PDF for Class 8 Mathematics Part 2 Chapter 6.
- Revise algebra tricks, grids, pyramids and divisibility proofs in one place.
- Use the inline images to remember the trick-decoding flow and calendar-grid formula.
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Algebra Play Class 8 Notes PDF Overview
The chapter starts with a simple idea: a puzzle can look like magic until every step is written as algebra. Students learn to name an unknown, translate each instruction, simplify the expression and then explain the result.
The most important habit is to write the changing number as x, M, D, a or another clear letter. Once the letter is in place, the trick becomes a normal expression.
| Topic | What Students Revise | Quick Cue |
|---|---|---|
| Number tricks | Fixed answers after doubling, adding and subtracting. | Cancel the starting number. |
| Pyramids and grids | Missing values using equations. | Use the sum rule. |
| Divisibility | Place-value proofs for 9, 11 and 37. | Factor the expression. |
Algebra Play Number Tricks Video for Class 8
Source: Magnet Brains on YouTube
Think of a Number Tricks in Algebra Play
In the first trick, students think of a number, double it, add 4, divide by 2 and subtract the original number. If the starting number is called x, the final expression becomes 2. That is why every starting number gives the same answer.
Design rule: if students double a number, add 2k, divide by 2 and subtract the original number, the final answer is k. This explains how new tricks can be created.
Date-Decoding Trick for Class 8 Mathematics Chapter 6
The date trick uses the month M and day D. After all instructions, the final answer is 100M plus 165 plus D. So students subtract 165 and read the remaining number as month and day.
For example, 1390 minus 165 is 1225, so the date is 25 December. The last two digits give the day, and the remaining digits give the month.
- Let the month be M and the day be D.
- Translate each arithmetic instruction in order.
- Subtract 165 from the final number.
- Check that the month and day form a real date.
Number Pyramids and Calendar Grids in Algebra Play
In a number pyramid, each block is the sum of the two blocks below it. For a three-row pyramid with bottom row a, b and c, the top value is a plus 2b plus c. The middle value is counted twice.
Calendar grids use a similar idea. If the top-left date in a 2 by 2 grid is a, the other dates are a plus 1, a plus 7 and a plus 8.
Calendar-grid rule: the sum of a 2 by 2 calendar grid is 4a plus 16. If the sum is 36, students solve 4a plus 16 equals 36 and get a equals 5.
Largest Product and Divisibility Tricks in Algebra Play
The largest-product puzzle asks students to place three digits in a two-digit number times a one-digit number. If p is less than q and q is less than r, the largest product is qp times r.
The divisibility tricks use place value. A two-digit number ab is 10a plus b. Its reverse ba is 10b plus a. Their difference is 9 times the difference between the digits, so it is divisible by 9.
| Trick | Algebra Result | Conclusion |
|---|---|---|
| Reverse difference | 9(b minus a) | Always divisible by 9. |
| Reverse sum | 11(a plus b) | Always divisible by 11. |
| Cycled 3-digit sum | 111(a plus b plus c) | Divisible by 37 and 3. |
How to Use These Algebra Play Class 8 Notes
Start with the PDF for one full reading. Then practise one trick from each section without looking at the answer. After that, solve the Figure it Out questions from the textbook.
- Use the number-trick section before writing your own trick.
- Use the pyramid and grid section before missing-value questions.
- Use the divisibility table before reverse-number questions.
Related NCERT Class 8 Mathematics Chapter 6 Resources
Use these links when you want the official book PDF, solved exercises or handwritten-style revision for the same Class 8 Mathematics chapter.
| Resource | Link |
|---|---|
| NCERT Solutions | Class 8 Mathematics Chapter 6 NCERT Solutions (scheduled) |
| NCERT Book PDF | Class 8 Mathematics Chapter 6 Book PDF |
| Handwritten Notes | Class 8 Mathematics Chapter 6 Handwritten Notes |
All Chapters for Class 8 Mathematics Part 2 Notes
| Chapter | Notes |
|---|---|
| Chapter 1 Fractions in Disguise | Class 8 Mathematics Notes |
| Chapter 2 The Baudhayana-Pythagoras Theorem | Class 8 Mathematics Notes |
| Chapter 3 Proportional Reasoning 2 | Class 8 Mathematics Notes |
| Chapter 4 Exploring Some Geometric Themes | Class 8 Mathematics Notes |
| Chapter 5 Tales by Dots and Lines | Class 8 Mathematics Notes |
| Chapter 6 Algebra Play | Current chapter notes |
| Chapter 7 Area | Class 8 Mathematics Notes |
NCERT Class 8 Mathematics Chapter 6 Notes FAQs
Ques. What is covered in NCERT Class 8 Mathematics Chapter 6 Algebra Play?
Ans. The chapter covers number tricks, date decoding, number pyramids, calendar grids, largest-product puzzles, divisibility tricks and algebra-based word problems.
Ques. Why does the think-of-a-number trick always give the same answer?
Ans. The starting number cancels out when the steps are written with a letter-number. The constant left at the end is the fixed answer.
Ques. What is the calendar-grid formula in Algebra Play?
Ans. If the top-left date is a, the 2 by 2 grid sum is a plus a plus 1 plus a plus 7 plus a plus 8, which is 4a plus 16.
Ques. How should students revise divisibility tricks from this chapter?
Ans. Students should write each number in place-value form, simplify the expression and factor out 9, 11, 37 or the required divisor.
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