← Back 🏠 Home

Mathematics: Class 3 — Chapter 8: Fair Share

8.1 Introduction to Equal Sharing

Shabnam and Mukta are enjoying their lunch break and want to share their food equally. This introduces the concept of a Fair Share.

Let us Discuss

  • How do you share objects equally?
  • Why is Shabnam folding the paratha over itself? (To check if the two pieces are equal by overlapping them perfectly).
8.2 Understanding Halves

When 1 whole is shared equally between 2 people, each share is called a half.

Key Concepts of Halves

  • Two halves make one whole: $\frac{1}{2} + \frac{1}{2} = 1$.
  • To make a half, the division must be perfectly equal.

Let us Do: Halves Activities

  • Identifying Halves: Recognizing shapes where exactly half of the whole is coloured.
  • Symmetry and Folding: Drawing lines to show one-half of various objects (like a kite, pizza, apple, bottle, square, sugarcane, carrom board).
  • Completing the Whole: Drawing the other half of a symmetrical picture to complete it.
8.3 Half and Double

There is a direct relationship between doubling a quantity and halving it.

Practice Exercises

  • $4$ marbles are half of $8$ marbles.
  • $8$ marbles are double of $4$ marbles.
  • $10$ marbles are double of $5$ marbles.
  • $5$ marbles are half of $10$ marbles.
  • $6$ marbles are half of $12$ marbles.
  • $12$ marbles are double of $6$ marbles.

Number Line Challenges

  • On a number line, how far is $13$ from the double of $7$? (Double of $7$ is $14$, so $13$ is $1$ unit away from $14$).
  • How far is $5$ from half of $14$? (Half of $14$ is $7$, so $5$ is $2$ units away from $7$).
8.4 Understanding Quarters

When a whole is shared equally among 4 people, each share is called a quarter.

Quarters and Whole Relationship

  • 1 quarter: One of four equal parts ($\frac{1}{4}$).
  • 2 quarters: Equivalent to one half ($\frac{2}{4} = \frac{1}{2}$).
  • 3 quarters: Three of four equal parts ($\frac{3}{4}$).
  • 4 quarters: Equivalent to a complete whole ($\frac{4}{4} = 1$).

Let us Do: Quarters Activities

  • Ticking objects that show quarters (divided into 4 equal parts).
  • Drawing lines to make a quarter of a whole.
  • Drawing the remaining three quarters to complete a whole.
  • Colouring shapes to show specific fractions (2 quarters, 1 quarter, 3 quarters, 4 quarters).
8.5 Half or Quarter Comparison

Comparing fractional shares helps understand their relative sizes.