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CBSE Class 3 · Mathematics

Fair Share

Official NCERT chapter from Maths Mela (book code cemm1). ExamMaster notes are original teaching at CBSE Class 3 depth.

This lesson follows the official chapter “Fair Share” in Maths Mela. 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 3
  • Easy level
  • 8 concepts

1Sharing a paratha needs equal parts first

Fair share means parts that match. Fold or cut so each piece covers the same amount of the whole.

A bigger piece “because I am older” is not a fair share of one whole.

Figure. Fair share starts with equal parts of one whole. A bigger piece “because I am older” fails the equal-part test.

How it works

  1. Name the wholeOne paratha, or one bar.
  2. Make equal partsSame size, same shape if you can.
  3. Then give the partsFair is equal first.

2A half is one of two equal parts

Halves are two matching pieces of one whole. Each is \frac{1}{2}.

Two pieces that do not match are not halves, even if you call them “half”.

Figure. A half is one of two matching pieces of the same whole. Each piece is 1/2. Pieces that do not match are not halves.

How it works

  1. Split into twoEqual.
  2. Take one pieceThat is one half.
  3. Check the leftoverThe other half must match.

3A quarter is one of four equal parts

Quarters are four matching pieces. Each is \frac{1}{4}. Two quarters make one half of the same whole.

Four unequal wedges are not quarters.

Figure. A quarter is one of four matching pieces. Two quarters of the same whole cover the same region as one half.

How it works

  1. Split into four equal partsSame amount each.
  2. Take one\frac{1}{4}.
  3. Two such parts\frac{2}{4} = \frac{1}{2} of that whole.

Two quarters of one roti

A roti is cut into 4 equal parts. You take 2. What share is that?

  • Equal parts4
  • Taken2
  • Share2/4 = 1/2

Pro tip. Numerator counts coloured equal parts. Denominator is how many equal parts the whole was cut into.

4Numerator counts the coloured parts

In \frac{3}{4}, 3 is how many equal parts you coloured. 4 is how many equal parts the whole was cut into.

Swapping them names a different share.

Figure. In 3/4 the 3 counts the coloured equal parts and the 4 counts how many equal parts the whole was cut into. Swapping them names a different share.

How it works

  1. Count equal parts of the wholeDenominator.
  2. Count the coloured onesNumerator.
  3. Write coloured over total partsThat is the fraction.

5Same amount, new writing

\frac{2}{4} and \frac{1}{2} can name the same share of one whole. The writing changed; the amount of roti did not.

New writing is not a new extra piece.

Figure. 2/4 and 1/2 can name the same share of one whole. The writing changed; the coloured length did not. Both coloured blocks are 0.42 of the same 0.84 bar.

How it works

  1. Fix the wholeSame roti.
  2. See two writings2 of 4, or 1 of 2.
  3. Check they cover the same regionThen they are the same share.

6Compare shares of one whole

\frac{1}{2} of this roti is more than \frac{1}{4} of this same roti, because two quarters make a half.

Do not compare a half of a large roti to a half of a tiny roti as if they were the same piece.

Figure. On one locked whole, 1/2 covers twice the region of 1/4. Do not compare a half of a large roti with a half of a tiny roti as if they were one piece.

How it works

  1. Lock the wholeSame object.
  2. Compare the coloured regionsWhich covers more?
  3. Name more, less, or the sameOf that whole.

7Adding only when the parts match

You can add \frac{1}{4} + \frac{1}{4} because both parts are quarters of the same whole. That is \frac{2}{4}.

Adding a half of one roti to a quarter of another roti is two wholes mixed.

Figure. Add 1/4 + 1/4 only because both parts are quarters of the same whole. The denominator stays the part-size; the numerators add.

How it works

  1. Same wholeDo not swap the roti.
  2. Same kind of part, or rewrite firstQuarters with quarters.
  3. Add the numeratorsDenominator stays the part-size.

8“Please share” is a fraction story, not a gift of any slice

Please share asks for equal parts. A random broken piece is a gift, not this chapter’s share.

Fair is the equal-part test, not a polite word alone.

Figure. “Please share” asks for equal parts. A random broken piece is a gift, not this chapter’s half.

How it works

  1. Hear “share”Equal parts of one whole.
  2. Make the parts matchFold or measure.
  3. Refuse a random break as “half”If they do not match, they are not halves.
\frac{2}{4} of one roti is the same share as
  1. \frac{1}{2} of that roti
  2. \frac{1}{4} of that roti
  3. Two whole rotis

Same region, new writing.

Notes

  • The official chapter title is “Fair Share”. 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

  • One half = 1 of 2 equal parts = \frac{1}{2}.
  • One quarter = 1 of 4 equal parts = \frac{1}{4}.
  • \frac{2}{4} = \frac{1}{2} of the same whole.

Reference tables

The whole is fixed. Only the writing of the share changes.

Shares of one whole
Equal partsColouredFractionSame as
211/2half
411/4quarter
422/4half
433/4three quarters

Recap

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

Sharing a paratha needs equal parts first
Fair share means parts that match. Fold or cut so each piece covers the same amount of the whole.
A half is one of two equal parts
Halves are two matching pieces of one whole.
A quarter is one of four equal parts
Quarters are four matching pieces. Each is \frac{1}{4}. Two quarters make one half of the same whole.
Numerator counts the coloured parts
In \frac{3}{4}, 3 is how many equal parts you coloured.
Same amount, new writing
\frac{2}{4} and \frac{1}{2} can name the same share of one whole.
Compare shares of one whole
\frac{1}{2} of this roti is more than \frac{1}{4} of this same roti, because two quarters make a half.

Practise Fair Share

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