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CBSE Class 8 · Mathematics

A Story of Numbers

Official NCERT chapter from Ganita Prakash Part I (book code hegp1). ExamMaster notes are original teaching at CBSE Class 8 depth.

This lesson follows the official chapter “A Story of Numbers” in Ganita Prakash Part I. 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

1Reema’s Curiosity

Reema’s curiosity here is a question you can put on a writing: why does 34 mean 3 tens and 4 ones? The curiosity ends in a place-value sentence, not a diary.

A name on a worksheet is not the curiosity-test.

Figure. Reema’s question is why one count can wear three costumes. Twenty-three sticks, the Roman letters XXIII, and the place-value numeral 23 all name the same pile. The curiosity is the writing, not a new number.

How it works

  1. Ask what a digit’s house isThe 3 in 34.
  2. Name the houseTens.
  3. Write the value30, plus 4 ones.

2Some Early Number Systems

Early number systems grouped marks (tallies, bundles) so a new symbol could stand for a bundle. The story is that grouping, not a museum tour of every script.

Copying an old symbol without saying what bundle it stood for is a sticker.

Figure. Early systems write the same 23 by grouping or by letters. Egyptian-style grouping stacks two tens and three ones. Roman adds X + X + I + I + I. Hindu–Arabic place value is the later idea that the same digit can change value by house.

How it works

  1. Name a bundle size you were taughtTen, or twenty, or sixty — as in the lesson.
  2. See a mark that means that bundleThe old writing.
  3. Compare it to our housesSame job, different marks.

3The Idea of a Base

A base is the bundle-size of the houses: base ten means ten ones make a ten. A different base would bundle sooner or later. Our everyday writing is base ten.

Base is not “the bottom of the page”.

Figure. A base is the size of a finished bundle. Twenty-three tokens make 2 bundles of ten plus 3, or 1 bundle of twenty plus 3. The leftover ones are the same; only the bundle size changed. That size is the base.

How it works

  1. Name the bundle sizeTen in our writing.
  2. See each house as a power of that baseOnes, tens, hundreds.
  3. Keep another base only if the lesson named it as a contrastA story, not a new homework system.

4A definition is a test you can run

Place value is a test: a digit times its house. If you cannot name the house, you have a digit-string only.

34 as “three-four” without tens is not the definition.

Figure. A definition is a test you can run. Place value passes only if the same digit means a different amount in a new house. Roman X is ten wherever it sits, so it fails that test. The digit 2 in 23 versus 32 passes it.

How it works

  1. Pick a digitThe 3 in 34.
  2. Name its house and its value3 tens = 30.
  3. Add the housesThe number.

5Name the given before the unknown

The given is the written number (or the old marks). The unknown is the value in houses. Read the given marks before you invent a bundle.

Reading 34 as 3+4 because “old systems added” is a silent swap if this writing is ours.

Figure. Decode a numeral by naming every known mark first. X is 10, X is 10, I is 1 three times. Only then add: 10 + 10 + 1 + 1 + 1 = 23. The unknown is the total, not a new letter.

How it works

  1. Copy the writingThe given.
  2. Name houses or the old bundleThe unknown’s door.
  3. Then evaluateGiven first.

6One worked case is enough at this class

One number read in houses is enough. A page of the same 34 clone does not add a new base-idea.

Ten twins of 30+4 are still one idea.

Figure. One worked expansion is enough to see the rule. 247 means 2 hundreds, 4 tens and 7 ones: 2 × 100 + 4 × 10 + 7 × 1. Do not pile extra contest bases onto this school case.

How it works

  1. Read one number by housesThe case.
  2. A second only as a checkOptional.
  3. StopThis class.

7A miss: swapping the school name for the picture

A museum photo of an old tablet is a setting. The maths is the bundle-size. Admiring the photo and skipping the house-value is the swap-miss.

A pretty script is not 34.

Figure. The miss is swapping the school name for the picture. Writing Hindu–Arabic is not the place-value test. The test is the houses: the same digit changes value when it moves. Draw the houses; do not stop at the label.

How it works

  1. Keep the tablet as a storyA setting.
  2. Name the bundle or the houseThe maths.
  3. EvaluateDo not swap.

8Check by the opposite action or the opposite test

Check a house-read by expanding: 34 = 3×10 + 4. If the expansion fails, the house-names were wrong.

Saying “it looks like thirty-four” without the expand is not the opposite test.

Figure. Check a conversion by the opposite action. Write 23 as two tens and three ones, then count the tokens back. If you do not return to 23, the grouping was wrong. The opposite test is the same pile, read the other way.

How it works

  1. Write the expansionThe check.
  2. Add itMust match the number.
  3. Mend the house if it failsHonest.
In our writing, the 3 in 34 names
  1. 3 tens — base ten
  2. 3 ones
  3. 3 hundreds

A base is the bundle-size of the houses.

Notes

  • The official chapter title is “A Story of Numbers”. 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

  • digit value = digit × house (power of the base)

Recap

Hold these pegs from the official chapter “A Story of Numbers”. The wording is ExamMaster’s teaching, not a textbook recap.

Reema’s Curiosity
Reema’s curiosity here is a question you can put on a writing: why does 34 mean 3 tens and 4 ones? The curiosity ends in a place-value sentence, not a diary.
Some Early Number Systems
Early number systems grouped marks (tallies, bundles) so a new symbol could stand for a bundle.
The Idea of a Base
A base is the bundle-size of the houses: base ten means ten ones make a ten.
A definition is a test you can run
Place value is a test: a digit times its house.
Name the given before the unknown
The given is the written number (or the old marks).
One worked case is enough at this class
One number read in houses is enough. A page of the same 34 clone does not add a new base-idea.

Practise A Story of Numbers

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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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