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CBSE Class 7 · Mathematics

Finding the Unknown

Official NCERT chapter from Ganita Prakash Part II (book code gegp2). ExamMaster notes are original teaching at CBSE Class 7 depth.

This lesson follows the official chapter “Finding the Unknown” 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 7
  • Easy level
  • 8 concepts

1Find the Unknowns

An unknown is a letter (or a box) that makes a sentence true: n + 5 = 12 means n is 7. Finding it is making both sides name the same number.

Guessing 10 because it is round is not finding unless it fits.

Figure. An unknown is a seat that must make the sentence true. Here the box plus 7 is 20, so the box is 13. The box is not a decoration — it is the number you still have to name.

How it works

  1. Write the sentencen + 5 = 12.
  2. Ask what n must be so both sides matchThe unknown.
  3. Check by putting it back7 + 5 = 12.

2Solving Equations Systematically

Systematic solving uses opposite operations on both sides: if n + 5 = 12, subtract 5 from both; if 3n = 15, divide both by 3. Do the same to both sides so the balance stays.

Subtracting 5 from one side only breaks the sentence.

Figure. An equation stays true when both sides get the same honest change. Undo +4 on the left and on the right: x = 15 − 4 = 11. Then substitute: 11 + 4 = 15.

How it works

  1. See what was done to n+5, or ×3.
  2. Do the opposite to both sides−5, or ÷3.
  3. Read nThe solution.

Undo +5

Solve n + 5 = 12.

  • Opposite of +5−5 on both sides
  • n = 12 − 57
  • Check7 + 5 = 12

Pro tip. The same undo on both sides keeps the sentence true.

3Mind the Mistake, Mend the Mistake

A mistake is a broken step: a sign slip, an undo on one side, a check that was skipped. Mend means put the number back into the original sentence. If it fails, the step was wrong — fix that step, not the story.

Erasing the check because it failed is not mending.

Figure. The usual miss is undoing the +4 on one side only, which invents x = 19. Mend it: the same change on both sides gives x = 11, and 11 + 4 = 15 checks.

How it works

  1. Substitute the candidate into the originalThe mind.
  2. If both sides disagree, name the broken stepThe miss.
  3. Redo that stepThe mend.

4A Pinch of History

People have solved “what number fits” for a long time; letters for unknowns are a later writing. History here is a pinch: the job is older than the letter n. It is not a proof of a method.

A famous name is not a check of n + 5 = 12.

Figure. A pinch of history for this chapter is three moves that stayed: name the unknown, do the same honest change on both sides, then substitute to check. The names of old books can wait; the test is these three moves.

How it works

  1. Keep the pinch as a noteThe job is old.
  2. Return to the sentence you haveThis n.
  3. Solve and checkHistory is not the undo.

5A definition is a test you can run

An equation is a test: two sides that should match when the unknown is right. If you cannot substitute and get a match, you do not yet have the solution.

A letter with no sentence is not an equation.

Figure. A definition is a test you can run. x is the number that makes x + 2 = 8 true. Six passes: 6 + 2 = 8. Five fails: 5 + 2 = 7. The letter is not a decoration you add “as a letter”.

How it works

  1. Write both sidesThe definition’s object.
  2. Substitute the candidateThe test.
  3. Match or failSolved or not.

6Name the given before the unknown

The given is the sentence. The unknown is the letter’s value. Do not change the given numbers to make a favourite answer fit.

Turning n + 5 = 12 into n + 5 = 15 because 10 is nicer is a silent given.

Figure. Name the given before the unknown. In x + 5 = 17 the givens are the +5 and the 17. x is the seat that is still empty. Finding it is asking which number belongs there, not decorating the page with a letter.

How it works

  1. Copy the sentenceThe given.
  2. Name the letterThe unknown.
  3. Undo on both sidesGiven first.

7One worked case is enough at this class

One solved sentence is enough. A page of n+5=12 clones does not add a new undo.

Ten twins of n=7 are still one idea.

Figure. One worked case is enough at this class: x + 4 = 15. Undo +4 on both sides to get x = 11, then check 11 + 4 = 15. A second case is for checking the same moves, not a new theory.

How it works

  1. Solve one equationThe case.
  2. A second only as a check of a different undoOptional.
  3. StopThis class.

8A miss: swapping the school name for the picture

A balance-scale drawing is a setting. The maths is the sentence. Tipping the drawing and skipping “same to both sides” is the swap-miss.

A pretty scale is not an undo.

Figure. The miss is swapping the school name for the picture. Calling the page “Finding the Unknown” or writing a pretty x does no work. The picture is the test: which number makes the sentence true?

How it works

  1. Keep the scale as a storyA setting.
  2. Write the equationThe maths.
  3. Do the same to both sidesDo not swap.
If n + 5 = 12, then n is
  1. 7 — subtract 5 from both sides
  2. 12
  3. 5

Check: 7 + 5 = 12.

Notes

  • The official chapter title is “Finding the Unknown”. 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.

Formulas

  • if n + a = b then n = b − a
  • if kn = b (k ≠ 0) then n = b/k
  • do the same opposite to both sides

Recap

Hold these pegs from the official chapter “Finding the Unknown”. The wording is ExamMaster’s teaching, not a textbook recap.

Find the Unknowns
An unknown is a letter (or a box) that makes a sentence true: n + 5 = 12 means n is 7.
Solving Equations Systematically
Systematic solving uses opposite operations on both sides: if n + 5 = 12, subtract 5 from both; if 3n = 15, divide both by 3.
Mind the Mistake, Mend the Mistake
A mistake is a broken step: a sign slip, an undo on one side, a check that was skipped.
A Pinch of History
People have solved “what number fits” for a long time; letters for unknowns are a later writing.
A definition is a test you can run
An equation is a test: two sides that should match when the unknown is right.
Name the given before the unknown
The given is the sentence. The unknown is the letter’s value. Do not change the given numbers to make a favourite answer fit.

Practise Finding the Unknown

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  • 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
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