NCERT Class 4 Mathematics Maths Mela Chapter 11 Fun with Symmetry PDF Download

Chapter 11: Fun with Symmetry

In previous grades, we have explored symmetry in rangolis, masks, bead strings and in buildings.

Let us explore more about symmetry.

Let Us Do

1. Ink Design

Step 1: Take a sheet of paper and fold it in half.

Step 2: Open it and sprinkle some drops of water colours in the centre of the fold.

Step 3: Press it to spread the colour evenly.

Step 4: Look what you made!

Is it a symmetrical pattern?

Where would you draw the line that divides this design into two equal halves?

Isn't this line called the line of symmetry? I made it while making masks and rangolis in Grade 3 too.

2. Making a paper airplane

Follow the steps.

[Figure: Paper airplane folding steps 1 through 8, See in your textbook]

1. Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
2. How many lines of symmetry can you see in Fig. 8?
3. Where will you place a mirror to see the reflection of the right half side of Fig. 8? Will it look the same as the left half side?
4. Fly the plane.
5. Will the plane fly if there is no line of symmetry?
6. Try to make an asymmetrical plane.
7. Fly both the planes and see which plane flies for a longer time.
8. Share your observations with your friends.

Teacher's Note

When you fold paper in half and cut or tear it, the fold line becomes a line of symmetry. The two halves on either side of this line are mirror images of each other. Try folding different shapes and predicting where the holes will appear before you open them - this helps you understand how symmetry works.

3. Holes and Cuts

Mini has made this design by folding and cutting paper.

[Figure: Designs showing different cuts and resulting patterns, See in your textbook]

Now it's your turn! Take a square sheet of paper. Do as instructed below.

Let us see what Rani is making. Rani takes a piece of paper and folds it twice.

[Figure: Rani's folding steps, See in your textbook]

She makes a straight cut at the corner and cuts out two squares on two sides as shown in the picture.

Challenge 1: Where would the hole and cut appear when you open the paper?

Challenge 2: Fold a piece of paper once; put two cuts in the middle as shown. How many sides will this shape have when you open the folded paper?

Challenge 3: Fold a paper twice. Where would you cut to make a square hole in the center of the paper? How many cuts are required?

4. Complete the designs below

[Figure: Six dot grids with partial symmetrical designs to complete, See in your textbook]

Let Us Do

Symmetry in shapes

1. Look at the shapes given along the border. Draw these shapes on the dot grid. Which of the shapes are symmetrical? Draw the lines of symmetry.

   [Figure: Dot grid with border shapes (kite, arrow, envelope, triangle), See in your textbook]

2. Games with a Mirror

1. Where should we place the mirror in shape A to get the shapes given below?

   [Figure: Shape A with 6 different reflection options, See in your textbook]

2. Circle the numbers whose mirror image is the same number.

   [Figure: Four numbers with vertical lines showing mirror positions: 181, 181, 686, 686, See in your textbook]

   Which digits from 0 to 9 have the same mirror image? ___________________

   Make some 4-digit numbers such that the mirror image is the same number. Where would you keep the mirror in each case? How many such numbers can you make?

   ______________________________________ ______________________________________

   ______________________________________ ______________________________________

3. Make similar questions and ask your friends to guess the numbers.

   Guess my number.

   It is a 3-digit number near 120 whose mirror image is the same number. Where is the mirror kept?

   I will call this line a mirror line or line of reflection.

Teacher's Note

Some digits look the same when reflected in a mirror (0, 1, 8) while others look completely different (2, 5, 7). To find a number whose mirror image is the same, use only digits with mirror symmetry and place them symmetrically around the mirror line. For example, 181 reads the same when reflected vertically because 1 and 8 are both symmetric digits arranged symmetrically.

Key Points

• A line of symmetry divides a shape into two halves that are mirror images of each other. When you fold paper along this line, both halves match perfectly.
• Some shapes have one line of symmetry, some have many, and some have none. A circle has unlimited lines of symmetry because any line through its center divides it into two matching halves.
• To predict what will happen when you unfold cut paper, think about how the fold lines create symmetry. Each cut on the folded paper will appear on both sides when unfolded.
• Digits and numbers can also have mirror symmetry. Only certain digits (0, 1, 8) look the same in a mirror, so mirror-symmetric numbers must use only these digits arranged in the correct order.

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