CBSE Class 8 · Mathematics
Algebra Play
Official NCERT chapter from Ganita Prakash Part II (book code hegp2). ExamMaster notes are original teaching at CBSE Class 8 depth.
This lesson follows the official chapter “Algebra Play” in Ganita Prakash Part II. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 8
- Easy level
- 8 concepts
1Algebra Play
Algebra play is a letter-game with a rule you can write: think-of-a-number, a pyramid, a grid. The play is the writing, not a magician’s secret. You should be able to say why the trick always lands.
A trick you cannot write as steps is not this play.
Figure. Algebra Play starts with a letter that stands for a number. If n = 7, then 2n+3 = 17. The test is: the same n must work in the whole sentence.
How it works
- Name the gameThink-of-a-number, pyramid, grid…
- Write the steps with a letterThe play.
- See where the letter cancels or what remainsThe why.
2Thinking about ‘Think of a Number’ Tricks
A think-of-a-number trick is a chain of operations on n. If you add 5, double, subtract 10, then halve, you get n back — because each step had an opposite. The “mind-reading” is the cancel, not magic.
A trick that only works on 7 is a coincidence, not a play.
Figure. Think of a number, double it, add 8, halve, subtract the first number. Algebra shows why the answer is always 4: n cancels.
How it works
- Let the number be nThe start.
- Write each told stepn+5, then 2(n+5)…
- Simplify; see n remain or a constant remainThe why.
Why you get n back
Think n, add 4, double, subtract 8, halve. What remains?
- n + 4first
- 2n + 8double
- 2nminus 8
- nhalve
Pro tip. Each step had an opposite. The letter comes back.
3Number Pyramids
A number pyramid adds two bricks to make the brick above. The top is a sum of the bases with counts you can write. Play means finding a missing brick by undoing an add.
A pyramid that multiplies secretly is a different game unless the lesson said so.
Figure. In a number pyramid each brick is the sum of the two it sits on. The test that two pyramids match is the same addition rule, not a tidy look.
How it works
- Write two children → parent as a sumThe rule.
- If the parent and one child are known, subtractThe missing brick.
- Check by adding backThe play.
4Fun with Grids
A grid play is a rule on rows or cells: each row sums to the same, or a letter sits in a cell. Fun is a rule you can check on the cells you have, then fill a missing cell.
Colouring a grid with no sum-rule is decoration.
Figure. Fill a 2-by-2 with a, a+1, a+2, a+3. Both diagonals sum to 2a+3. That equal-sum check is the school test, not a pretty grid.
How it works
- State the row- or cell-ruleThe fun’s law.
- Check the filled cellsEvidence.
- Fill one missing cellThe play.
5The Largest Product
The largest product of a split (as taught) is a compare: 10 as 5+5 gives 25; 10 as 1+9 gives 9. You try a few splits and keep the winner. It is not a proof you tried every split unless the lesson said a method.
Declaring 1×9 the largest because 9 is large is the miss.
Figure. Break 10 into positive integers and compare products: 5\times5=25, 3\times3\times4=36, five 2s give 32, and 10\times1=10. Threes (with a leftover 4) win at this class.
How it works
- Split the given number into taught partsTwo wholes that add to 10.
- Multiply those partsA candidate.
- Compare a few; keep the largest productThe heading.
6Decoding Divisibility Tricks
A divisibility trick you decode is a digit-rule you can write: why 3 cares about the digit-sum. Decoding means the why in letters or houses, not “it works on this example”.
A trick you only memorised with no why is not yet decoded.
Figure. A two-digit number is 10a+b = 9a+(a+b). The 9a piece is always divisible by 3 (and by 9), so the whole number is divisible by 3 exactly when a+b is. For 27, 2+7=9.
How it works
- Write the number in houses10a + b, as taught.
- See why 10a + b shares a factor with the digit-sum or last digitThe decode.
- Check on a new nThe trick earned a why.
7A definition is a test you can run
A trick is a test: write it with n and simplify. If you cannot write n, you have a performance, not algebra play.
A spoken chain with no letter is not this definition.
Figure. A definition is a test you can run. Expand (x+1)^2 and you must get x^2+2x+1. The look-alike x^2+1 fails that test. Marks are earned by the algebra, not by a tidy look.
How it works
- Put n at the startThe object.
- Simplify the chainThe test.
- If n never appears, it was not writtenRun it.
8Name the given before the unknown
The given are the steps or the pyramid bricks. The unknown is what remains, or the missing brick. Copy the steps before you invent a double.
Adding a favourite +7 because last week’s trick had +7 is a silent given.
Figure. Name the given before the unknown. In 3n-5=16 the knowns are 3, 5 and 16. Only then solve: 3n=21, so n=7.
How it works
- Copy the told steps or the known bricksThe given.
- Name what remains or what is missingThe unknown.
- Then write n or undo an addGiven first.
A think-of-a-number trick that always returns n
- Has opposite steps that cancel — write them
- Is magic
- Works only on 7
The letter comes back because of undos.
Notes
- The official chapter title is “Algebra Play”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Recap
Hold these pegs from the official chapter “Algebra Play”. The wording is ExamMaster’s teaching, not a textbook recap.
- Algebra Play
- Algebra play is a letter-game with a rule you can write: think-of-a-number, a pyramid, a grid.
- Thinking about ‘Think of a Number’ Tricks
- A think-of-a-number trick is a chain of operations on n.
- Number Pyramids
- A number pyramid adds two bricks to make the brick above.
- Fun with Grids
- A grid play is a rule on rows or cells: each row sums to the same, or a letter sits in a cell.
- The Largest Product
- The largest product of a split (as taught) is a compare: 10 as 5+5 gives 25; 10 as 1+9 gives 9.
- Decoding Divisibility Tricks
- A divisibility trick you decode is a digit-rule you can write: why 3 cares about the digit-sum.
Practise Algebra Play
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device