NCERT Class 5 Mathematics Maths Mela Chapter 10 Symmetrical Designs PDF Download

Chapter 10: Symmetrical Designs

Alphabet Cutout

Prem and Manu want to paste 'Happy Birthday' cutouts on a wall for Lali's birthday. While preparing cutouts of letters, they observe that some letters can be cut out in an easy way.

They remember that they learnt about reflection symmetry and lines of symmetry in Grade 4. They used their knowledge of lines of symmetry to make the cutouts. The letter A has a vertical line of symmetry. So, to cut out the letter 'A' -

1. Fold a paper in half.
2. Draw half of the letter A along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter A.

[Figure: Steps showing how to fold paper and cut out the letter A, See in your textbook]

The letter H has two lines of symmetry.

1. Fold the paper into one-fourth (once vertically, once horizontally).
2. Draw one-fourth of the letter H along the fold.
3. Cut along the outline.
4. Open the paper to see the full letter H.

[Figure: Steps showing how to fold paper and cut out the letter H, See in your textbook]

Which of the following alphabet cutouts can be made by just drawing half (\(\frac{1}{2}\)) or quarter (\(\frac{1}{4}\)) of the letter? You can do it by drawing lines of symmetry on the letters.

E N X T K V O

Which of the letters have a horizontal line of symmetry? _________________

Which of the letters have a vertical line of symmetry? ____________________

Which letters have both vertical and horizontal lines of symmetry?________

Let Us Do

Use lines of symmetry to make paper cutouts of diya, boat, and other designs. Look along the border of the page to find the pictures.

Teacher's Note

When you fold a paper, you are creating a line of symmetry. If you can fold a shape so that both halves match perfectly, that fold line is a line of symmetry. The letter A folds along one line (vertical), but the letter H folds along two lines (one vertical and one horizontal). Before you answer the questions about E, N, X, T, K, V, and O, try folding each letter or drawing lines through the middle to see which ones have symmetry.

Let Us Make a Windmill Firki

Lali makes firkis for her friends. Follow the steps given below to make your own firki.

1. Take a square paper.
2. Fold the paper in half diagonally to make two triangles.
3. Open and fold it the other way to make two more triangles.
4. Open it again. You will see an 'X' shape on the paper.
5. Use scissors to cut along the four lines of the 'X'. Stop cutting about halfway to the centre.
6. Take one corner of each triangle and fold it gently towards the centre of the paper. Do not press it flat.
7. Fold every other corner towards the centre.
8. Push a pin through the folded corners and the centre of the paper.
9. Push the pin through a stick or straw.

[Figure: Steps showing how to make a windmill firki, See in your textbook]

Make sure the pin is not too tight. Check if your windmill spins when the wind is blowing.

Observe the dot in the firki. Does the firki look the same after \(\frac{1}{4}\), \(\frac{1}{2}\), \(\frac{3}{4}\), and a full turn? ___________________.

[Figure: Initial position, 1/4 turn, 1/2 turn, 3/4 turn, and Full turn of a windmill firki, See in your textbook]

Find symmetry in the digits.

Observe the letters below. Do they look the same when turned? Dots have been marked on the letters to keep track of the orientation of letters. You may also cut out the letters and fix the centre point of the letter by a nail or use a tracing paper to check if the letter looks the same when turned.

[Figure: A table showing Original letter, 1/4 turn, 1/2 turn, 3/4 turn, Full turn, and Rotational symmetry (Yes/No) for letters H, I, X, and Y, See in your textbook]

The letter H has rotational symmetry, as it looks the same when rotated by half a turn.

A firki has rotational symmetry, as it looks the same when rotated by \(\frac{1}{4}\), \(\frac{1}{2}\), and \(\frac{3}{4}\) turn.

Which digit(s) have reflection symmetry? ___________________________

Which digit(s) have rotational symmetry? ___________________________

Which digit(s) have both rotational and reflection symmetries? ________

Now, let us look at the following numbers: || , |00|

Do these have (a) rotational symmetry, (b) reflection symmetry or (c) both symmetries?

Give examples of 2-, 3-, and 4-digit numbers which have rotational symmetry, reflection symmetry, or both.

Teacher's Note

Rotational symmetry means a shape looks the same when you turn it around a centre point. The firki looks the same after a quarter turn (\(\frac{1}{4}\)), half turn (\(\frac{1}{2}\)), and three-quarter turn (\(\frac{3}{4}\)). Reflection symmetry means a shape looks the same when you flip it across a line. These are two different types of symmetry, and a shape can have one, both, or neither. When you check the digits 0 through 9, look at each one carefully: does it look the same when you turn it, and does it look the same when you flip it?

Making Designs

(a) Does the design have rotational symmetry? Yes/No.

(b) Try to change the design by adding some shape(s) so that the new design looks the same after a \(\frac{1}{2}\) turn. Draw the new design in your notebook.

(c) Now try to modify or add more shapes so that the new design looks the same after \(\frac{1}{4}\) turn. Draw the new design in your notebook.

(d) Do the new designs have reflection symmetry? If yes, draw the lines of symmetry.

Let Us Think

Does this design look the same after \(\frac{1}{2}\) turn? __________

Does the design look the same after \(\frac{1}{4}\) turn?__________

Colour the square given in the adjoining figure using two colours so that the design looks the same after every \(\frac{1}{4}\) turn.

How many times does this shape look the same during a full turn?

Do these designs have reflection symmetry also? Draw the line(s) of symmetry.

Let Us Do

Cut out squares and equilateral triangles with the same side length. These are provided at the end of the book.

Make different symmetrical designs by using these two shapes.

[Figure: Examples of squares and triangles that can be used to make designs, See in your textbook]

Now, make your designs. Sort your designs in 3 categories - designs with only rotational symmetry, designs with only reflection symmetry, and designs with both rotational and reflection symmetry.

Let Us Explore

Block printing is a traditional craft of Rajasthan, known for beautiful patterns and bright colours.

Artisans use carved wooden blocks to print designs on fabric.

This art has been practised for centuries and makes Rajasthan's textiles special.

Does this shape have reflection symmetry? If yes, draw its line(s) of symmetry. Does it have rotational symmetry? If yes, at which turn? Does it have both symmetries?

[Figure: A shape with blue squares and gold triangles, See in your textbook]

Below are images of wooden blocks and a part of their prints. Match each block to its correct print by drawing a line. One is done for you.

[Figure: Five wooden blocks with different carved patterns and five prints showing different repetitions of patterns, See in your textbook]

Key Points

• A shape has reflection symmetry if it looks the same when you flip it across a line. This line is called a line of symmetry. You can check reflection symmetry by folding a shape or using a mirror.
• A shape has rotational symmetry if it looks the same when you turn it around a centre point. A firki has rotational symmetry because it looks the same after a quarter turn, half turn, and three-quarter turn.
• Some shapes have only reflection symmetry, some have only rotational symmetry, and some have both types of symmetry. The letter H and the digit 8 are examples of shapes with both reflection and rotational symmetry.
• When you fold paper to cut shapes like the letter A or H, you use lines of symmetry to make the cutting easier. Folding once uses one line of symmetry; folding into quarters uses two lines of symmetry.
• Block printing uses symmetrical designs to create patterns on fabric. The carved wooden blocks can be printed repeatedly to make beautiful textile designs that often have both reflection and rotational symmetry.

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