NCERT Class 4 Mathematics Maths Mela Chapter 05 Sharing and Measuring PDF Download

Chapter 5: Sharing and Measuring

Parts and Wholes

Ikra and her little sister, Samina, decide to make a drawing, but they are left with a single drawing sheet. Ikra wants to share the paper by dividing it in half, but Samina insists on having a bigger part of the paper. Ikra thought for a moment and proposed a solution.

Ikra: Would you like half of the paper to draw, or two quarters of the paper?

Samina: One half paper seems smaller, but two quarters sounds like a bigger part. I want two quarters!

[Figure: A sheet of paper divided into one half and two quarters]

Let Us Discuss

1. Which part of the paper you would have chosen - one half or two quarters? Why?
2. Do you think Ikra shared the paper equally? Why? Try with a paper.
3. How do you know that the paper has been divided equally?
4. Why do you think Samina chose two quarters of the paper?

Teacher's Note

One half and two quarters are the same amount, even though they sound different. When you divide something into 2 equal parts, each part is called a half. When you divide something into 4 equal parts, each part is called a quarter, so 2 quarters make exactly the same size as 1 half. Try this with a piece of paper: fold it in half, then unfold it and fold it into quarters - you will see that two of the quarter sections fit exactly on top of one half section.

Let Us Do

1. Samina has divided some figures into two parts. Colour the figures that are divided into halves correctly. How did you get the answer?

   When an object is divided into two equal parts, then each part is called a half. We write half as \( \frac{1}{2} \).

2. Divide the shapes into halves by drawing a line.

   [Figure: Shapes to divide into halves: flower, heart, heart, circle]

When an object is divided into four equal parts, then each part is called a quarter. We write quarter as \( \frac{1}{4} \).

Think: How would we write the fraction for each part if we divided an object into 5 equal parts?

Note for Teachers

Guide students to write fractions using symbols. Begin with examples like \( \frac{1}{2} \) and \( \frac{1}{4} \). Provide numerous opportunities for practice with other fractions by paper folding and drawing images.

Many Ways to Make Halves and Quarters

Let Us Try

1. In how many different ways can you fold/cut a rectangular paper in two equal parts? Try it with a rectangular paper.

   [Figure: Two examples of folding a rectangle into two equal parts]

2. Now try to draw and show five different ways in which we can fold/cut a rectangle into four equal parts (\( \frac{1}{4} \) or quarter).
3. Divide these shapes into 4 equal parts/quarters.

   [Figure: Shapes to divide into quarters: diamond, rectangle, oval, rectangle with extensions]

Teacher's Note

There are many different ways to divide a shape into equal parts - you do not have to divide it in a straight line down the middle. For example, a rectangle can be divided diagonally, or with a curved line, or with a zigzag line. What matters is that all the parts are exactly the same size. Use tracing paper or cut out shapes to check if your parts are truly equal.

4. Match the following parts with their corresponding wholes.

   I am \( \frac{1}{2} \) of	[Figure: A diamond shape, half shaded]
   I am \( \frac{1}{2} \) of	[Figure: A triangle, half shaded]
   I am \( \frac{1}{2} \) of	[Figure: A semi-circle, half shaded]
   I am \( \frac{1}{4} \) of	[Figure: A rectangle, one quarter shaded]
   	[Figure: A rectangle, whole]
   	[Figure: A circle, whole]
   	[Figure: A large rectangle, whole]
   	[Figure: A small square, whole]

Ding Dong Bell!!

Sumedha's mother made yummy dhokla!

Mother: Here is your dhokla. Share it equally amongst yourselves.

[Figure: A whole dhokla and two halves of dhokla]

Sumedha: The dhokla is divided into two equal parts. Half for me and half for Vinayak that's perfect! That means 2 halves of a dhokla makes a whole dhokla.

Ding Dong! The doorbell rang.

Mother: Children, share the dhokla with Kumar also.

[Figure: A whole dhokla and three quarters of dhokla]

Kumar: Hello Kumar.

Sumedha: My share, Vinayak's share and Kumar's share together make a complete dhokla.

Key Points

• When you divide something into 2 equal parts, each part is called a half, written as \( \frac{1}{2} \). Two halves make one whole.
• When you divide something into 4 equal parts, each part is called a quarter, written as \( \frac{1}{4} \). Four quarters make one whole.
• The same whole can be divided in many different ways - what matters is that all the parts are exactly equal in size.
• \( \frac{1}{2} \) and \( \frac{2}{4} \) are the same amount, even though they look different.

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