Class 4 Maths NCERT Book Chapter 11 Fun with Symmetry

 Page 1


Is it a symmetrical pattern?
Where would you draw the line that divides this design 
into two equal halves?
Step 1: Take a sheet of paper and fold it in half.
Step 3: Press it to spread the colour evenly.
Step 2: Open it and sprinkle some drops of water 
colours in the centre of the fold.
Step 4: Look what you made!
Isn’t this line called the line of  
symmetry? I made it while making 
masks and rangolis in Grade  3 too.
Fun with Fun with 
Symmetry Symmetry
In previous grades, we have explored symmetry in rangolis, masks, bead 
strings and in buildings. 
Let us explore more about symmetry.
1. Ink Design
     Let Us Do
11
Chapter
Chapter 11.indd   164 Chapter 11.indd   164 3/26/2025   3:52:42 PM 3/26/2025   3:52:42 PM
Page 2


Is it a symmetrical pattern?
Where would you draw the line that divides this design 
into two equal halves?
Step 1: Take a sheet of paper and fold it in half.
Step 3: Press it to spread the colour evenly.
Step 2: Open it and sprinkle some drops of water 
colours in the centre of the fold.
Step 4: Look what you made!
Isn’t this line called the line of  
symmetry? I made it while making 
masks and rangolis in Grade  3 too.
Fun with Fun with 
Symmetry Symmetry
In previous grades, we have explored symmetry in rangolis, masks, bead 
strings and in buildings. 
Let us explore more about symmetry.
1. Ink Design
     Let Us Do
11
Chapter
Chapter 11.indd   164 Chapter 11.indd   164 3/26/2025   3:52:42 PM 3/26/2025   3:52:42 PM
2. Making a paper airplane
Follow the steps.
a) Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
b) How many lines of symmetry can you see in Fig. 8?
c) 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?
d) Fly the plane. 
e) Will the plane fly if there is no line of symmetry?
f) Try to make an asymmetrical plane.
g) Fly both the planes and see which plane flies for a 
longer time.
h) Share your observations with your friends.
1
4
7
2
5
8
3
6
165
Chapter 11.indd   165 Chapter 11.indd   165 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
Page 3


Is it a symmetrical pattern?
Where would you draw the line that divides this design 
into two equal halves?
Step 1: Take a sheet of paper and fold it in half.
Step 3: Press it to spread the colour evenly.
Step 2: Open it and sprinkle some drops of water 
colours in the centre of the fold.
Step 4: Look what you made!
Isn’t this line called the line of  
symmetry? I made it while making 
masks and rangolis in Grade  3 too.
Fun with Fun with 
Symmetry Symmetry
In previous grades, we have explored symmetry in rangolis, masks, bead 
strings and in buildings. 
Let us explore more about symmetry.
1. Ink Design
     Let Us Do
11
Chapter
Chapter 11.indd   164 Chapter 11.indd   164 3/26/2025   3:52:42 PM 3/26/2025   3:52:42 PM
2. Making a paper airplane
Follow the steps.
a) Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
b) How many lines of symmetry can you see in Fig. 8?
c) 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?
d) Fly the plane. 
e) Will the plane fly if there is no line of symmetry?
f) Try to make an asymmetrical plane.
g) Fly both the planes and see which plane flies for a 
longer time.
h) Share your observations with your friends.
1
4
7
2
5
8
3
6
165
Chapter 11.indd   165 Chapter 11.indd   165 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
3. Holes and Cuts
Mini has made this design by folding and cutting paper.
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.
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?
166
Chapter 11.indd   166 Chapter 11.indd   166 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
Page 4


Is it a symmetrical pattern?
Where would you draw the line that divides this design 
into two equal halves?
Step 1: Take a sheet of paper and fold it in half.
Step 3: Press it to spread the colour evenly.
Step 2: Open it and sprinkle some drops of water 
colours in the centre of the fold.
Step 4: Look what you made!
Isn’t this line called the line of  
symmetry? I made it while making 
masks and rangolis in Grade  3 too.
Fun with Fun with 
Symmetry Symmetry
In previous grades, we have explored symmetry in rangolis, masks, bead 
strings and in buildings. 
Let us explore more about symmetry.
1. Ink Design
     Let Us Do
11
Chapter
Chapter 11.indd   164 Chapter 11.indd   164 3/26/2025   3:52:42 PM 3/26/2025   3:52:42 PM
2. Making a paper airplane
Follow the steps.
a) Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
b) How many lines of symmetry can you see in Fig. 8?
c) 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?
d) Fly the plane. 
e) Will the plane fly if there is no line of symmetry?
f) Try to make an asymmetrical plane.
g) Fly both the planes and see which plane flies for a 
longer time.
h) Share your observations with your friends.
1
4
7
2
5
8
3
6
165
Chapter 11.indd   165 Chapter 11.indd   165 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
3. Holes and Cuts
Mini has made this design by folding and cutting paper.
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.
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?
166
Chapter 11.indd   166 Chapter 11.indd   166 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
4. Complete the designs below
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.
     Let Us Do
167
Chapter 11.indd   167 Chapter 11.indd   167 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
Page 5


Is it a symmetrical pattern?
Where would you draw the line that divides this design 
into two equal halves?
Step 1: Take a sheet of paper and fold it in half.
Step 3: Press it to spread the colour evenly.
Step 2: Open it and sprinkle some drops of water 
colours in the centre of the fold.
Step 4: Look what you made!
Isn’t this line called the line of  
symmetry? I made it while making 
masks and rangolis in Grade  3 too.
Fun with Fun with 
Symmetry Symmetry
In previous grades, we have explored symmetry in rangolis, masks, bead 
strings and in buildings. 
Let us explore more about symmetry.
1. Ink Design
     Let Us Do
11
Chapter
Chapter 11.indd   164 Chapter 11.indd   164 3/26/2025   3:52:42 PM 3/26/2025   3:52:42 PM
2. Making a paper airplane
Follow the steps.
a) Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.
b) How many lines of symmetry can you see in Fig. 8?
c) 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?
d) Fly the plane. 
e) Will the plane fly if there is no line of symmetry?
f) Try to make an asymmetrical plane.
g) Fly both the planes and see which plane flies for a 
longer time.
h) Share your observations with your friends.
1
4
7
2
5
8
3
6
165
Chapter 11.indd   165 Chapter 11.indd   165 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
3. Holes and Cuts
Mini has made this design by folding and cutting paper.
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.
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?
166
Chapter 11.indd   166 Chapter 11.indd   166 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
4. Complete the designs below
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.
     Let Us Do
167
Chapter 11.indd   167 Chapter 11.indd   167 3/26/2025   3:52:43 PM 3/26/2025   3:52:43 PM
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?
______________________________________ ____________________________________
______________________________________ ____________________________________
2. Games with a Mirror
a) Where should we place the mirror in shape A to get 
the shapes given below?
b) Circle the numbers whose mirror image is the same number.
1
A
A
4
2
5 6
3
181 686
181 686
c) 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.
168
Chapter 11.indd   168 Chapter 11.indd   168 3/26/2025   3:52:44 PM 3/26/2025   3:52:44 PM