NCERT Solutions Class 4 Maths Chapter 11 Fun with Symmetry

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 4 · M AT H S

NCERT Solutions

Chapter 11: Fun with Symmetry

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

164 – 174 14 48 English

Solutions, notes, sample papers & more at 63 pages

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

CLASS 4 · MATHS · MATH MELA

NCERT Solutions — Chapter 11: Fun with Symmetry
Chapter 11 of Math Mela is all about symmetry. You fold paper and press ink, fold and cut holes, hold a mirror
to shapes, letters and numbers, count the lines of symmetry in triangles and four-sided shapes, and lay tiles
that fit with no gaps.

TEXTBOOK BOOK PAGES

Math Mela (Class 4) 164 – 174

SECTIONS QUESTIONS

14 48

MEDIUM

English

Let Us Do — Page 164
1. Ink Design

ACTIVITY

Q1 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!

ANSWER

Do the four steps exactly in this order.

1. Take a plain sheet. Fold it in half and press the fold well.
2. Open the sheet. Drop a few drops of water colour close to the fold line.
3. Fold the sheet again on the same fold and press it gently with your palm.
4. Open it. The colour has spread on both sides of the fold.

Page 1 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Sample answer: the ink design a child gets after Step 4.

Why it happens: The colour was still wet, so the top half printed its own picture on
the bottom half.

Tip: Use only 4 or 5 drops. Too much colour makes one big blot.

Page 2 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q2 Is it a symmetrical pattern?

The ink design made in the activity above.

ANSWER

Yes, it is a symmetrical pattern.

The ink design made by folding the paper and pressing.

Look at the design. Whatever is on the left of the fold is there on the right too, in the same
place.

Page 3 of 63

as e
Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: The wet colour was pressed from one half on to the other half, so

m as e
l
the two halves are copies of each other.
.co a g
a s em
gl it yourself: Fold the paper again on the same line. The two coloured halves
aCheck
sit exactly on each other.

com
m . ag
l a se
Q3 g that divides this design into two equal halves?
Where would you draw thealine

co m
em.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
The ink design, with no line drawn on it yet.
se m
com g l a
m . a
ase
ANSWER agl
m
Draw the line along the fold — straight down the middle of the sheet.

. co
e m
m l as
m .co a g
l a se
ag
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 4 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

line of symmetry

The dashed line drawn along the fold of the paper.

The fold line is the middle line of the design.

Left half of the design = right half of the design.

Why it happens: The design was made by pressing one half on the other. So only
the fold can cut it into two matching halves.

Q4 Isn’t this line called the line of symmetry? I made it while making masks and
rangolis in Grade 3 too.

ANSWER

Yes, Diksha is right. This middle line is called the line of symmetry.

Page 5 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

line of symmetry

The line of symmetry of the ink design.

A shape is symmetrical if a fold makes its two halves sit exactly on each other.
The fold you used is its line of symmetry.
Masks, rangolis, bead strings and many buildings are made in the same way.

Why it happens: A line of symmetry is just the fold that makes both halves match.
Diksha folded her mask paper the same way in Grade 3.

Let Us Do — Page 165
2. Making a paper airplane

ACTIVITY

Q1 Mark the line of symmetry in Fig. 3, Fig. 4, and Fig. 5.

ANSWER

In all three figures the line of symmetry is the middle crease that runs from top to bottom.

Page 6 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Fig. 3 Fig. 4 Fig. 5
The paper at three steps of making the plane.

Here are the same three figures with the line marked:

Fig. 3 Fig. 4 Fig. 5
The line of symmetry marked with a dashed red line in each figure.

Why it happens: The very first step was to fold the sheet in half. Every later fold was
made the same on both sides of that crease, so the crease stays the line of
symmetry.

Q2 How many lines of symmetry can you see in Fig. 8?

ANSWER

Fig. 8 has 1 line of symmetry.

Page 7 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Fig. 8
Fig. 8 — the plane opened out, showing all its crease lines.

Number of lines of symmetry in Fig. 8 = 1
It runs from the top middle straight down to the bottom.

Page 8 of 63

as e
Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
em.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m ase
.co a g l
se m
ag l a Fig. 8
se m
com g l a
.
The one line of symmetry of Fig. 8.
m a
gl ase
a
Why it happens: Every crease made on the left has a matching crease on the right,
at the same slant. No other fold of the sheet makes the creases match.
co m
m .
m as e
.co a g l
a s emQ3
gl
Where will you place a mirror to see the reflection of the right half side of Fig. 8?
a c
.
Will it look the same as the left half side?

s e m
m a
m . co agl
ANSWER

ase
l
Stand the mirror upright on the middle crease of Fig. 8, facing the right half.
a g

co m
m .
m as e
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Fig. 8
The mirror is kept standing on the dashed middle line.

Yes — the reflection looks exactly like the left half side.

Why it happens: The middle crease is the line of symmetry. A mirror kept on a line
of symmetry always shows the other half of the shape.

Try This: Now turn the mirror around and face it towards the left half. You will see
the right half in it.

Page 10 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q4 Fly the plane.

ANSWER

Hold the plane by the middle crease, below the wings. Point the nose a little upward and throw
it forward gently.

1. Check that both wings are of the same size.
2. Hold it at the crease so that both wings stay level.
3. Throw it smoothly — do not jerk your hand.

Sample answer: My plane flew straight for about 6 steps and then came down slowly.

Why it happens: Both wings are the same, so the air pushes both of them equally
and the plane goes straight.

Q5 Will the plane fly if there is no line of symmetry?

ANSWER

It will move, but it will not fly straight. It turns to one side and falls quickly.

If one wing is bigger, that side is heavier and catches more air.
The plane leans to that side and starts turning.
It loses height fast and lands near you.

Why it happens: A plane needs the two halves to be alike. When the two halves are
not alike, the air pushes one wing harder and the plane tips over.

Q6 Try to make an asymmetrical plane.

ANSWER

Make a plane in the usual way, then change only one side.

1. Fold a fresh sheet and make the plane up to Fig. 7.
2. Now cut about 2 cm off the tip of one wing only.
3. Or fold one wing down a little more than the other.

Sample answer: I cut one wing shorter. Now the two halves do not match, so the plane has no
line of symmetry.

Page 11 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Check it yourself: Try to fold the plane in half. The two wings will not sit on each
other.

Q7 Fly both the planes and see which plane flies for a longer time.

ANSWER

Throw both planes the same way, one after the other, and count aloud until each one lands.

PLANE HOW IT FLEW COUNT TILL IT LANDED

Symmetrical plane Straight and smooth about 5

Asymmetrical plane Turned to one side about 2

Sample answer: The symmetrical plane flew for a longer time.

Why it happens: Matching wings share the air push equally, so the plane stays level
longer in the air.

Q8 Share your observations with your friends.

ANSWER

Tell your friends what you saw. You can use these three lines.

The plane with a line of symmetry flew straight and stayed up longer.
The plane without a line of symmetry turned to one side and fell soon.
Symmetry is not only pretty to look at — it also helps things work well.

Did you know? Real aeroplanes, birds and kites all have matching left and right
halves for the same reason.

Holes and Cuts — Page 166

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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

3. Holes and Cuts

CHALLENGE

Q1 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.

The square sheet folded over and over, and then snipped along the folded edges.

Page 13 of 63

as e
Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

Mini’s design, opened out.
co m
em.
m l as
m .co a g
ANSWER
l a se
a g
Mini folded a square sheet again and again and then cut small bits off the folded edges.

co m
e m . ag
g l as
a

co m
e m.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co a g l
Mini’s design after the folded paper is opened out.

se m
g l a
a c
.
1. Take a square sheet. Fold it in half — you get a rectangle.
2. Fold it in half again — you get a smaller square.
s e m
com a
. agl
3. Fold it once more along the corner — you get a triangle.
mthe folded triangle.
4. Snip small bits off the edgeseof
s
5. Open it out slowly. agl
a

co m
m .
m as e
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Why it happens: Each fold doubles the layers. One snip cuts through every layer at
once, so the same little hole appears many times, in a neat pattern.

Q2 Challenge 1: Where would the hole and cut appear when you open the paper?

ANSWER

Rani folded twice, so her paper has 4 layers. Every cut she makes is repeated 4 times when the
paper opens.

folded edge

cut

folded
edge

corner cut

Rani’s folded paper after cutting. The top edge and the left edge are folds.

When she opens it out:

The corner cut was at the corner where the two open edges meet, so all four corners of the
square get cut off.

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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The square cut on the folded (left) edge opens into 2 full holes inside the paper, one above
the middle and one below it.
The square cut on the open (right) edge stays on the border. It shows up as 4 notches —
two on the left side and two on the right side.

the two fold lines
The opened sheet: four corners cut, four notches on the sides, two holes inside.

Why it happens: A cut on a folded edge loses its fold when you open it, so the two
halves of the cut join into one whole hole. A cut on an open edge stays a notch on
the border.

Page 16 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q3 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?

fold

two cuts

The paper folded once, with two cuts made in the middle of the folded edge.

ANSWER

The two cuts are made on the folded edge, in the middle.

Page 17 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

fold

two cuts

The paper folded once, with two cuts made in the middle of the fold.

Cuts made on the folded paper = 2
Each cut becomes 2 sides when the fold opens

2 × 2 = 4 sides

So the shape that opens out has 4 sides. It is a four-sided hole, shaped like a diamond.

Page 18 of 63

as e
Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
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m l as
m .co a g
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a g

co m
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a g

co m
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m 3 2 l as
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a opened paper
the
co m
.
The opened paper with the four-sided hole; its sides are numbered 1 to 4.

e m
m l as
.co a g
m it happens: The fold acts like a mirror. Whatever you cut on one side of the fold
s eWhy

agla is copied on the other side when the paper opens.
se m
com g l a
m . a
ase
agl
Q4 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?

co m
ANSWER
m .
m as e
.co l
Cut at the corner where the two folded edges meet. You need only 2 cuts.
a g
se m
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a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 19 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

folded edge

folded
edge

the paper after two folds

The paper after two folds. The circled corner is where both folds meet.

Snip a small square off that corner, using two straight cuts:

when opened

t the small square off the folded corner

Page 20 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Left: the two cuts at the folded corner. Right: the square hole in the middle of the opened sheet.

Sides of the small square = 4

2 sides are already the folded edges

Cuts needed = 4 − 2 = 2

Why it happens: The corner where both folds meet is the centre of the whole sheet.
The two folded edges become two sides of the hole by themselves, so only the other
two sides have to be cut.

In-text Questions — Page 167

Page 21 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

4. Complete the designs below

Q1 Complete the designs below. (the first design — half of the cross)

The first design. Only half of it is drawn on the dot grid.

ANSWER

Only the top half is drawn. Complete it so that both halves match.

Page 22 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The half design given in the book, drawn on the dot grid.

How to do it: Take each corner of the given half, count how many dots it is above the middle
row, and mark a new point the same number of dots below the middle row. Then join the new
points.

Page 23 of 63

as e
Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
.
The completed design. The dashed red line is the fold that was used to complete it.
m a
ase
agl
The finished design is a cross shape. It has 4 lines of symmetry — one across, one down, and
two along the slanting corners.

. c om
m the two halves
Why it happens: Counting dots on both sides of the fold lineekeeps
s
m a
m
o the same size and shape.
.cexactly agl
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ag
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s e m
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a

co m
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m ase
.co


a g l Page 24 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q2 Complete the designs below. (the second design — half of the star)

The second design. Only half of it is drawn on the dot grid.

ANSWER

Here the left half is drawn. The fold line goes straight down the middle this time.

Page 25 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The half design given in the book, drawn on the dot grid.

How to do it: Count how many dots each corner lies to the left of the middle column, and mark
the matching point the same number of dots to the right. Join them in the same order.

Page 26 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The completed design — an eight-pointed star. The dashed red line is the fold that was used.

The finished design is an eight-pointed star. It has 4 lines of symmetry.

Why it happens: Each point on the left is copied at the same distance on the right,
so the star folds on to itself neatly.

Page 27 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q3 Complete the designs below. (the third design — half of the kolam)

The third design. Only half of the kolam is drawn on the dot grid.

ANSWER

This one is a kolam (a dot design) made of loops. Only the loops on the left are drawn.

Page 28 of 63

as e
Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
.
The half kolam given in the book, drawn on the dot grid.
m a
ase
agl
How to do it: Draw the same loops on the right side of the middle column, turned the other
way round, like a picture in a mirror.

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 29 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The completed kolam, with the middle line shown dashed.

Why it happens: A loop and its mirror loop meet the same dots, so the two sides
balance and the kolam looks whole.

Tip: The full kolam printed at the top of the page has one more pair of loops — one
above and one below. Add them if you want four matching sides.

Let Us Do — Page 167

Page 30 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Symmetry in shapes

ACTIVITY

Q1 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.

kite arrow envelope arrowhead

The four shapes printed along the border of the page.

ANSWER

The four shapes along the border are a kite, an arrow, an envelope and an arrowhead.

kite arrow envelope arrowhead

The four shapes printed along the border of the page.

All four shapes are symmetrical. Each one has exactly 1 line of symmetry.

Page 31 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

SHAPE SYMMETRICAL? LINES OF WHERE THE LINE GOES
SYMMETRY

Kite Yes 1 Along the long stick, from the top corner
to the tail

Arrow Yes 1 Straight down the middle, through the tip

Envelope Yes 1 Straight down the middle of the flap

Arrowhead Yes 1 Straight down the middle, through the
point

kite arrow envelope arrowhead

The one line of symmetry of each shape, shown dashed.

Why it happens: Each shape is built the same way on the left and on the right of
one middle line, so only that one fold makes the halves match.

Check it yourself: The kite’s tail in the picture is a wavy string. The tail by itself is not
symmetrical — only the kite paper is. Trace just the kite and fold it to check.

Games with a Mirror — Page 168

Page 32 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

2. Games with a Mirror

MATH TALK

Q1 Where should we place the mirror in shape A to get the shapes given below?

A 1 2
3

4 6
5

Shape A, and the six shapes numbered 1 to 6.

ANSWER

Shape A is made of 2 squares side by side. Stand the mirror upright on shape A and look at the
part in front of the mirror together with its reflection.

A 1 2
3

4 6
5

Shape A and the six shapes to be made from it.

Page 33 of 63

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Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
m.
SHAPE WHERE TO KEEP THE MIRROR ON A WHAT YOU SEE

m as e
1
.co
Upright, across the middle of one square
squarea
g l
half square + half square = 1

se m
g l a
a2 Upright, on the line between the two squares 1 square + 1 square = 2 squares

m
.co ag
3 Upright, along the slanting diagonal of the second the L-shape of 3 squares

sem
square

a
4
agl
Upright, across the middle of the second square 1½ + 1½ = 3 squares in a row

com
5 Lying along the long side (top or bottom edge) of A 2 + 2 = a 2 by 2 square

.
m a s em in a row
co agl
6 Upright, at the short end edge of A 2 + 2 = 4 squares

m .
l a se
ag
Why it happens: A mirror hides everything behind it and shows a copy of everything
in front of it. So you always see the front part twice — once real and once in the

m a s
.co agl
mirror.

a s em
aglone. Keep the mirror along the slanting corner-to-
Try This: Shape 3 is the tricky
corner line of one square and peep — the L-shape appears.

co m
m .
o m l a se
g
.cCircle the numbers whose mirror image is the same number.
a
e m
las
Q2

ag ANSWER
se m
com g l a
. a
Circle the two boxes with 181. The two boxes with 686 should not be circled.
m
ase
agl
181 co m686
m .
181 686 as e
.com a g l
m
ase
agl c
m .
m a s e
co agl
The four boxes printed in the book. The straight line in each box shows where the mirror is kept.

m .
as e
a g l

co m
m .
m ase
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

BOX NUMBER MIRROR KEPT IMAGE CIRCLE IT?

1 181 below the number 181 Yes

2 181 at the side 181 Yes

3 686 at the side not a number No

4 686 below the number not a number No

Why it happens: In 181 every digit — 1, 8, 1 — looks the same in a mirror, and the
number reads the same from either end. In 686 the digit 6 turns into a backward 6,
which is not a digit at all.

Q3 Which digits from 0 to 9 have the same mirror image? ___________________

ANSWER

0, 1 and 8 when the mirror is kept at the side.
0, 1, 3 and 8 when the mirror is kept above or below the digit.

DIGIT MIRROR AT THE SIDE MIRROR ABOVE OR BELOW

0 same same

1 same same

3 changes same

8 same same

2, 4, 5, 6, 7, 9 change change

Why it happens: A digit stays the same in a mirror only when it can be folded on
that line and both halves match. 0, 1 and 8 can be folded down the middle. 3 can be
folded across the middle.

Check it yourself: Write 0 1 3 8 in big block letters and stand a mirror at their side,
then below them.

Page 35 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q4 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?

ANSWER

Keep the mirror at the side of the number. Then use only the digits 0, 1 and 8, and make the
number read the same from both ends.

The 4-digit number looks like a b b a

The first digit a can be 1 or 8 (not 0) → 2 ways

The middle digit b can be 0, 1 or 8 → 3 ways

2 × 3 = 6 numbers

All six numbers are:

1001 1111 1881 8008 8118 8888

So you can make 6 such 4-digit numbers with the mirror kept at the side.

Why it happens: A side mirror turns the number back to front. So the last digit must
look like the first, and the digits themselves must not change in a mirror.

Try This: If you keep the mirror below the number instead, the order of the digits
does not change. Then you may use 0, 1, 3 and 8 in any order, and many more
numbers are possible — 3108, 1380, 8310 and so on.

Q5 Guess my number. It is a 3-digit number near 120 whose mirror image is the same
number. Where is the mirror kept?

ANSWER

The number is 111, and the mirror is kept at its side.

Digits that do not change in a side mirror: 0, 1, 8

3-digit numbers near 120 made only of these: 101, 111, 181

111 is the nearest to 120.

Page 36 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

111 reads the same from both ends, and each 1 looks like a 1 in the mirror. So its mirror image
is 111 again.

Why it happens: A side mirror reverses the order of the digits. The number must
read the same forwards and backwards, and every digit must be a mirror-safe one.

Did you know? 118 also works, but only if the mirror is kept below the number —
then 1, 1 and 8 each stay the same and the order does not change.

Q6 Make similar questions and ask your friends to guess the numbers.

ANSWER

Make your own puzzle in three steps.

1. Pick a number that does not change in a mirror, such as 808, 1881 or 8118.
2. Think of a nearby round number to give as a clue, such as “near 800” or “near 1900”.
3. Ask the question without telling where the mirror is kept.

Sample answer: “Guess my number. It is a 3-digit number near 800 whose mirror image is the
same number. Where is the mirror kept?” — The answer is 808, with the mirror at the side.

Tip: Keep a small mirror ready so your friend can check the answer straight away.

In-text Questions — Page 169
3. Letters on the ambulance

DISCUSSION

Q1 What do you notice about the letters written on the ambulance? Why are they
written this way? Discuss.

ANSWER

The word is written back to front, like a picture in a mirror.

Page 37 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

ECNALUBMA

The front of an ambulance, with the word painted the way it is printed in the book.

It is written this way so that the driver in front can read it.

1. A car driver sees the ambulance in the mirror above the windscreen.
2. The mirror turns the word back to front once more.
3. So the driver reads AMBULANCE the right way round.

Why it happens: A mirror always flips left and right. The painter flips the word first,
so the mirror flips it back and it reads correctly.

Check it yourself: Hold this page up to a mirror. The word on the ambulance will
read normally.

Q2 Can you guess what I have written? Where did I keep the mirror?

ANSWER

The word is CAT. The mirror was kept above (or below) the word, lying across it.

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Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

CAT co m
e m.
m l as
m .co a g
l a se
ag

co m
e m . ag
g l as
a

co m
em.
m l as
.co
The word as it is printed in the book.

a g
se m
g l a
Look carefully at each letter:
a C is the same when turned upside down, so it looks unchanged.

m a s
.co agl
A is printed upside down, like ∀.
T is printed upside down, like ⊥.
se m
g l a
a
The letters are still in the order C, A, T — they have not been swapped.

Why it happens: A mirror kept above the word flips it top to bottom, so each letter
co m
m .
e
turns over but the order stays the same. A mirror kept at the side would have
m l as
.co g
reversed the order to T, A, C.
m a
l a se
a g
Can you identify these words? Where will you place the mirror to read the following
se m
com a
Q3
words correctly?
. a g l
m
ase
ANSWER
agl
The four words are TAP, CAN, WOW and HEN.

co m
m .
as e
.co
m CAN a g l
sem
agl
a PAT WOW NEH c
m .
a s e
. c om agl
s e m words as they are printed in the book.
la
The four

ag

co m
m .
m ase
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

PRINTED THE REAL WHERE TO KEEP THE MIRROR
WORD WORD

first word TAP At the side (left or right) — the letters are in reverse order

second word CAN Above or below — each letter is upside down, order
unchanged

third word WOW At the side — it is printed the same because WOW is its own
mirror image

fourth word HEN At the side — the letters are in reverse order

Why it happens: A mirror at the side reverses the order of the letters. A mirror
above or below turns each letter upside down but keeps the order. Looking at
whether the order has changed tells you where the mirror was kept.

Did you know? W, O, W each look the same in a side mirror, and WOW reads the
same from both ends. That is why WOW looks perfectly normal in the book.

Q4 Now, you try to write some words/names in this way and challenge your friends to
guess them.

ANSWER

Write the word on thin paper, then trace it from the back of the sheet. That gives you the mirror
writing.

1. Write your word in big block letters, for example MILK.
2. Turn the sheet over and hold it against the window.
3. Trace the word from the back — that copy is the mirror writing.

Sample answer: I wrote MILK, RANI and BUS in mirror writing and my friends read them with a
small mirror.

Tip: Words like MOM, TOOT and WOW are fun — they look almost unchanged.

Page 40 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q5 Can you also try doing this with the script of your own language?

ANSWER

Yes. Mirror writing works in every script.

Write a short word in your own script, such as माँ or घर.
Trace it from the back of the sheet to get the mirror form.
Read it with a mirror kept at the side.

Sample answer: In Hindi the letter म changes a lot in a mirror, but the shape ल written plainly is
easier to read back.

Why it happens: A mirror only flips left and right. It does not care which language
the letters belong to.

Q6 Complete the following to make symmetrical shapes.

ANSWER

Each small drawing is only a part of a shape. Add lines so that the finished shape can be folded
into two matching halves.

The six part-drawings printed on the dot grid.

Sample answer: here is one way to finish each one.

Page 41 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The added lines are shown dashed in red.

PART-DRAWING SHAPE MADE LINES OF SYMMETRY

Corner with a long arm and a short arm Rectangle 2

Two slanting lines meeting at a point Triangle with two equal sides 1

Corner with two equal arms Square 4

One standing line Square 4

L-shape of two equal arms Square 4

One sleeping line Rectangle 2

Why it happens: Counting dots keeps every new line the same length as its
matching line, so the finished shape folds neatly on itself.

Tip: There is more than one right answer. Your friend may close the same part-
drawing into a different symmetrical shape.

In-text Questions — Page 170

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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

5. Observe the shapes

Q1 Observe the shapes. How many sides does each shape have?

The two boxes of shapes printed in the book.

ANSWER

The first box holds 6 triangles and the second box holds 8 four-sided shapes.

The two boxes of shapes printed in the book.

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Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
m.
BOX SHAPE NUMBER OF SIDES

m Orange triangle (top left) as e
First box
.co
3
a g l
se m
g l a Blue triangle (top right)
a
First box 3

First box Purple triangle 3

com
First box
e
Orange triangle (middle right)
m . 3 ag
Thin blue triangle gl
as
First box
a 3

First box Green triangle 3
co m
em.
com l as
Second box Purple kite 4

. a g
m
ase
Second box Blue rectangle 4

aglSecond box Light blue square 4

m a s
.co agl
Second box Orange trapezium 4

se m
g l a
a
Second box Light blue parallelogram 4

Second box Orange rhombus (diamond) 4

co m
m .
e
Green four-sided shape

as
Second box 4

. coboxm 4gl
a
m
ase
Second Blue arrowhead

agl
m
Why it happens: Count the straight edges of a shape, going once round its border.

a se
com l
Every shape in the first box is closed by 3 straight edges, and every shape in the
. a g
m
ase
second box by 4.

agl
Tip: The blue arrowhead is a four-sided shape too, even though one of its corners is

co m
.
pushed inwards.

em
m l as
m .co a g
l a se
ag
.c
s e m
m a
e m . co agl
g l as
a

com
m .
m ase
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q2 How many lines of symmetry does each shape have? You may trace these shapes
and check the lines of symmetry by folding the shapes.

The two boxes of shapes printed in the book.

ANSWER

Trace each shape, cut it out and fold it. Count only the folds where the two halves sit exactly on
each other.

Page 45 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

The two boxes of shapes printed in the book.

SHAPE SIDES LINES OF SYMMETRY

Orange triangle, top left (square corner, unequal arms) 3 0

Blue triangle, top right (two equal sides) 3 1

Purple triangle (two equal sides) 3 1

Orange triangle, middle right (two equal sides) 3 1

Thin blue triangle (all sides different) 3 0

Green triangle (square corner, two equal arms) 3 1

Purple kite 4 1

Blue rectangle 4 2

Light blue square 4 4

Orange trapezium (slanting sides equal) 4 1

Light blue parallelogram 4 0

Orange rhombus 4 2

Green four-sided shape 4 1

Blue arrowhead 4 1

Page 46 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Every line of symmetry drawn on the shapes, in dashed red.

Why it happens: A fold is a line of symmetry only when each corner lands on
another corner and each side lands on a side of the same length. A parallelogram
slants, so no fold makes its halves match.

Check it yourself: The green triangle and the green four-sided shape have a slanting
line of symmetry, not an upright one. Turn your traced shape and fold corner to
corner.

Tiling the Tiles — Page 170

Page 47 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Patterns with tiles

Q1 Here are some patterns with tiles. Identify the repeating unit (tile) and continue the
patterns.

The pattern of tiles, and the empty grid where it is to be continued.

ANSWER

Both patterns are made with the same simple tile — a rectangle that is twice as long as it is
wide.

The pattern of tiles, and the empty grid where it is to be continued.

The repeating unit is a square made of two rectangles. These squares are laid by turns:

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Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

co m
em.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
e m.
m l as
m .co a g
l a se 2 sleeping 2 standing
a g
m a s
.co agl
The repeating unit — two sleeping rectangles, then two standing rectangles.

a s em
a gl
1. First square: two rectangles sleeping, one above the other.
2. Next square: two rectangles standing, side by side.

c om
3. Go on like this along the row, and start the next row the other way round.
.
m a s emto the right and then
To continue the pattern in the empty grid, keep sliding this pair of squares

. co a gl
em
downwards.

a s
agl Why it happens: Two rectangles of the same size always make a square, whether
they sleep or stand. So the squares fit together with no gaps and no overlaps.
se m
com g l a
m . a
e
s works. A group of 8 rectangles (four sleeping and
Tip: A bigger repeating unitaalso
g l
four standing) repeats a
exactly as well. The two printed patterns use the same tiles

m
laid the same way — only the blue and green are placed differently.

. co
em
m l as
.co a g
a s em at the Tile Shop — Page 171
Tiles
agl
.c
s e m
m a
e m . co agl
g l as
a

com
m .
m ase
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Bablu Chacha’s tiles

ACTIVITY

Q1 Bablu Chacha makes beautiful tiles of the kinds shown below. Design creative tiles
of your own in the spaces given below. You may use a rangometry kit or shape
cutouts.

Tiles of the kinds Bablu Chacha makes.

ANSWER

Bablu Chacha’s tiles are hexagons and squares filled with smaller shapes.

Tiles of the kinds Bablu Chacha makes: hexagons and squares filled with triangles and rhombuses.

1. Trace the empty hexagon or square from the book.
2. Take triangles and rhombuses from your rangometry kit.
3. Fill the shape completely — no gaps and no overlaps.
4. Colour the pieces, then draw round them in your notebook.

Sample answer: I filled one hexagon with 6 triangles and coloured them orange and yellow by
turns. I filled the square with 8 triangles, blue and yellow by turns.

Tip: A hexagon is filled neatly by 6 triangles, or by 3 rhombuses, or by 2 trapeziums
and 2 triangles.

Page 50 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Q2 Which shapes have you used to make the tiles?

ANSWER

The tiles are built from a few simple shapes.

Bablu Chacha’s tiles, made from triangles and rhombuses.

SMALL SHAPE USED SIDES WHERE YOU SEE IT

Triangle 3 The hexagon cut into 6 pieces; the pinwheel square

Rhombus (diamond) 4 The hexagon made of 3 pieces

Trapezium 4 Half a hexagon

Square 4 The outer shape of the last two tiles

Sample answer: I used triangles and rhombuses to make my tiles.

Why it happens: These shapes have equal sides that match each other, so they sit
together leaving no gaps.

Q3 Which of the tiles are symmetrical? Draw the lines of symmetry (if any).

ANSWER

A tile is symmetrical only if the colours match on both sides of the fold, not just the shapes.

Bablu Chacha’s tiles. Look at the shapes and the colours together.

Page 51 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

TILE SYMMETRICAL? LINES OF SYMMETRY

Hexagon with 6 differently coloured triangles No 0

Hexagon with two orange shades by turns Yes 3

Hexagon with a six-pointed star No 0

Hexagon with 3 rhombuses of 3 colours No 0

Square pinwheel of 8 triangles No 0

Green square with turning bands No 0

Only the second tile is symmetrical. Its three lines run from the middle of one side to the middle
of the opposite side.
Sample answer: My hexagon with orange and yellow triangles by turns has 3 lines of
symmetry, each one running from a corner to the opposite corner.

Why it happens: A fold must match colour to colour. In a pinwheel each triangle
leans the same way round the centre, so folding puts a blue piece on a yellow piece
— there is no line of symmetry.

Check it yourself: Colour the same hexagon in only one colour. Now it has 6 lines of
symmetry, because only the shapes have to match.

Q4 Make more tiles by joining two or more shapes. Trace them in your notebook to
create paths with no gaps or overlaps.

ANSWER

Join two or three cutouts into one bigger tile, then repeat that tile to make a path.

1. Join 2 triangles along one side — you get a rhombus.
2. Join 3 triangles in a row — you get a long trapezium.
3. Trace your new tile again and again along a line in your notebook.
4. Check after every tile: no gap, no overlap.

Sample answer: I joined 2 triangles into a rhombus and traced it 10 times to make a garden
path.

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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Why it happens: When two shapes are joined along equal sides, the new tile still has
straight matching edges, so copies of it fit together.

In-text Questions — Page 172
4. Look at the following shapes

DISCUSSION

Q1 Look at the following shapes. What do you notice? Discuss.

The two designs printed in the book.

ANSWER

Both designs are made from the same small shape — a rhombus (diamond).

The two designs printed in the book, made of rhombus tiles.

Here is what to notice:

Every piece is the same rhombus, only turned in three different ways.
Three rhombuses meeting at a point look like a box (a cube).

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Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

The two designs use the same pieces in the same places — only the colours are different.
co m
There are no gaps and no overlaps anywhere.
e m.
m l as
.co a g
a s em
Why it happens: All the sides of a rhombus are equal, so three of them fit neatly
gl a point. Our eyes then read the flat picture as a solid box.
around

co m
m .
Try This: Colour the whole design in one colour. The boxes disappear and you see
e ag
only flat diamonds.
g l as
a

co m
Let Us Do — Page 172
em.
m l as
.co
1. Make floor patterns
m a g
l a se
g
ACTIVITY

a
m a s
.co agl
Q1 Make floor patterns with your tile. Mini has made a floor pattern as shown below.

se m
Remember there should be no overlaps and no gaps.

g l a
a

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com
Mini’s floor pattern.
g l a
m . a
ase
ANSWER
agl

co m
.
Mini has laid the same box-shaped tile again and again in a long row.

e m
m l as
m .co a g
l a se
ag
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

Mini’s floor pattern — the same tile slid along, with no gaps and no overlaps.

1. Choose one tile, such as three rhombuses joined into a box.
2. Trace it once on the grid.
3. Slide it sideways by exactly one tile and trace it again.
4. Start the next row so that its tiles fit into the dips of the row above.

Sample answer: I traced my box tile 8 times in a row and 3 rows down. The floor was filled with
no gaps.

Why it happens: Sliding a tile does not change its size or shape, so the new copy fits
exactly against the old one.

Tip: If a gap appears, you have slid the tile too far. Move it back until the two edges
touch.

In-text Questions — Page 173

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Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

2. Making a catty wall!

CRAFT

Q1 Step 1: Take a square piece of paper. Mark as shown to make the cat’s head and
ears. Step 2: Now, cut along the outline and slide the top piece down to align with
the larger piece. Step 3: Tape the pieces together. Your wall is ready. Step 4: Now the
real fun begins! Trace the outline of the cat pattern on a large piece of paper and
make its face.

Step 1 Step 2 Step 3 Step 4

The four steps, as they are drawn in the book.

ANSWER

Follow the four steps to make one cat tile.

1. Take a square sheet. On the top edge mark two pointed ears with a dip between them.
2. Cut along that line. You now have a small top piece and a large bottom piece.
3. Slide the top piece down to the bottom edge and tape it there.
4. Trace this new shape on a big sheet and draw eyes, nose and whiskers.

Page 56 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

one tile

the tiles fit with no gaps
Left: one cat tile. Right: the same tile repeated to make a wall.

Why it happens: Whatever you cut off the top is added back at the bottom. The tile
covers just as much space as the square did, so copies of it still fit together.

Q2 Create more of these tiles. Some ideas to make creative wall patterns are given
below.

The ideas printed on page 173: a square with a wavy cut, the tile that cut makes, and a
wall built from arrow tiles.

ANSWER

Trace your cat tile again and again to cover a big sheet.

1. Trace the tile at the top left corner of the sheet.
2. Slide it sideways by one tile and trace it again, right along the row.
3. Start the next row directly below, so the ears fit into the dips above.

Page 57 of 63

Class 4 Maths Chapter 11 Fun with Symmetry AglaSem · NCERT Solutions

4. Colour the cats in two colours, turn by turn.

one tile

the tiles fit with no gaps
Cat tiles repeated to make a wall pattern.

Sample answer: I made 12 cat tiles in two colours and covered a full chart paper. As Mini says,
the tiles still fit perfectly without any gaps or overlaps.

Why it happens: The bump on one edge of the tile is exactly the same size as the
dip on the opposite edge, so one tile slips neatly into the next.

Project Work — Page 174
3. Let us go on a nature walk (Project time)

PROJECT WORK

Q1 Go for a nature walk to a nearby park or around your school with your teacher or
your parents. Observe the patterns, designs, or symmetry around you carefully.
Collect leaves, petals, and flowers that have fallen on the ground.

ANSWER

Go with your teacher or parents, carry a paper bag, and pick up only things that have already
fallen.

1. Walk slowly and look at leaves, flowers, butterflies and spider webs.
2. For each one ask: can it be folded into two matching halves?
3. Collect about 10 fallen leaves, some petals and a few dry flowers.
4. Keep them flat inside an old book so they do not curl.

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Class 4 Maths Chapter 11 Fun with Symmetry
a g l AglaSem · NCERT Solutions

Sample answer: I found that the butterfly, the peepal leaf and the hibiscus flower were
co m
symmetrical. The broken leaf and the pebble were not.
em.
m l as
m .co a g
l a se
Tip: Never pluck leaves or flowers from a plant. Fallen ones work just as well.

a g

co m
Q2
m .
In your project file: Categorise the leaves into symmetrical and non-symmetrical.
e ag
g l as
ANSWER a
Fold each leaf along its middle vein. If the two halves sit on each other, the leaf is symmetrical.
co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
a g

co m
m .
m ase
.co a g l
se m
g l a
a leaf A leaf B
se m
com g l a
. a
Two leaves collected on the walk.
m
ase
agl
Leaf A folds into two matching halves. Leaf B does not — one side is wider than the other.

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 59 of 63