7. Finding the Unknown

6 topics59 min

Chapter 7 of NCERT Mathematics for Class 7: Finding the Unknown. Three sections — What an equation says, Solving equations systematically and Errors and origins. Six videos, 59 min in all.

Worked answers to the 28 exercise questions in this chapter →

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Part 1

What an equation says

10 minAn equation is a claim of equality, not an instruction to computeFor years the equals sign has been an instruction: work out the left, write the answer on the right. A level bar breaks that habit.10 min · 13 partsहिंदी10 minFinding an unknown by reasoning about what must balanceTwo balanced pictures, both hiding a weight. Only one of them yields to arithmetic you already have.10 min · 13 partsहिंदी

Part 2

Solving equations systematically

10 minDoing the same thing to both sides preserves equalityGuessing until a number fits is a real method and it works. It also stops working the moment the answer is not a whole number.10 min · 13 partsहिंदी10 minIsolating the unknown, step by step“Take it across and change the sign” is not a rule about crossing an equals sign. It is what is left of doing the same thing to both sides.10 min · 13 partsहिंदी10 minGenerating an equation from a situationEvery equation so far has arrived already written down. Out in the world nobody hands you one.10 min · 13 partsहिंदी

Part 3

Errors and origins

10 minA pinch of history: where solving for an unknown came fromThe oldest name for this subject is not algebra. In India more than a thousand years ago it was called bījagaṇita — seed arithmetic.10 min · 13 partsहिंदी

What you will be able to do

  • Read a level hanging bar as an assertion that two collections agree, not as a sum to be carried out
  • Work out an unknown weight from a hanging figure and say which step did the work
  • Carry out a trial-and-error search on a given equation and narrate the closing-in
  • Solve an equation whose unknown appears on both sides, by first collecting it on one side
  • Choose what an unknown letter will denote, and state that choice in words before writing anything
  • Explain what bījagaṇita names and why a seed is the metaphor chosen

What this chapter assumes you already know

  • Adding and subtracting negative numbers, and the meaning of −(−5)
  • Reading a term-by-term count off a picture (the matchstick sequence is revisited from an earlier chapter of Part I)
  • Multiplication tables to the point where 2 × 49 is immediate
  • Adding and subtracting whole numbers, and dividing a total into equal parts
  • Reading a quantity off a picture and holding several at once
  • Working with kilograms as a unit
  • Adding and subtracting negative numbers, including subtracting a negative
  • Multiplication and division as operations that undo each other, from Class 6

It builds directly on Writing a situation as an expression before computing it, Turning a pattern into a formula that predicts, Comparing two expressions by reasoning, not by evaluating, Reciprocals, and Brahmagupta's rule for dividing fractions and A fraction of a fraction, and why the numerators and denominators multiply.

Where people usually slip up

Sentences students actually say, taken from the notes the videos were made from. Each one is answered on the page of the video it belongs to.

  • "The equals sign means now write the answer."
  • "An expression and an equation are the same kind of thing."
  • "The answer always belongs on the right."
  • "A letter is a mystery box you are supposed to guess."
  • "If I cannot solve it, there is no point writing it down."
  • "2n + 1 = 200 just has no answer."
  • "You find the unknown by trying numbers until one fits."
  • "A level bar means each side weighs half the ring number."