Practicing with Maths Mela Class 4 Solutions Chapter 11 Fun with Symmetry Question Answer NCERT Solutions improves a student’s confidence in the subject.
Class 4 Maths Chapter 11 Fun with Symmetry Question Answer Solutions
Fun with Symmetry Class 4 Maths Solutions
Class 4 Maths Chapter 11 Solutions
Let Us Do (NCERT Pg 164-167)
Question 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!
(i) Is it a symmetrical pattern?
(ii) Where would you draw the line that divides this design into two equal halves?
Answer:
(i) Yes, the design is symmetrical because both sides of the fold are mirror images of each other.
(ii) The line that divides the design into two equal halves is the fold line, also called the line of symmetry.
Question 2.
Making a Paper Airplane
Follow the steps.
(i) Mark the line of symmetry in Fig. 3, Fig. 4 and Fig. 5.
(ii) How many lines of symmetry can you see in Fig. 8?
(iii) 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?
(iv) Fly the plane.
(v) Will the plane fly if there is no line of symmetry?
(vi) Try to make an asymmetrical plane.
(vii) Fly both the planes and see which plane flies for a longer time.
(viii) Share your observations with your friends.
Answer:
(i) The line of symmetry in these figures is the vertical line that divides the figure into two equal mirror halves from top to bottom. Also, Fig. 3 has horizontal line of symmetry.
(ii) We can see only one line of symmetry that is a vertical line right through the centre.
(iii) Place the mirror on the vertical line of symmetry (centre line). Yes, it will look the same as the left half side.
(iv) Do yourself
(v) It may not fly well because one side will be heavier or shaped differently, making the plane unstable or turn to one side.
So, the plane will not fly if there is no line of symmetry.
(vi) Do yourself
(vii) The symmetrical plane usually flies farther and straighter because it is balanced.
(viii) Do yourself
Question 3.
Holes and Cuts
Mini has made this design by folding and cutting paper.
Now, it is 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.
(i) Challenge 1. Where would the hole and cut appear when you open the paper?
(ii) 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?
(iii) Challenge 3. Fold a paper twice. Where would you cut to make a square hold in the centre of the paper? How many cuts are required?
Answer:
(i) When you unfold the paper, the same cut and holes will appear in symmetrical positions on all folded quadrants of the paper. Since, it was folded twice (first horizontally, then vertically), you will see 4 symmetrical shapes.
- Straight cut will create 4 straight slits at the corners.
- Square holes will appear as 4 square holes, arranged symmetrically.
Explanation Folding doubles the effect of cuts. Each fold creates symmetry across that fold.
(ii) The cut will reflect across the fold.
So, each single cut becomes two symmetrical cuts.
When the folded paper is opened, the shape will have 4 sides.
(iii) Fold the paper once vertically and once horizontally (into quarters).
You need to make only 1 cut at the folded corner.
When you unfold it, you will see 1 square hole in the centre.
Explanation: The corner of the folded paper becomes the centre when fully opened.
Question 4.
Complete the designs below.
Answer:
Question 2.
Games with a Mirror
(a) Where should we place the mirror in shape A to get the shapes given below?
Answer:
Question 2.
Games with a Mirror
(a) Where should we place the mirror in shape A to get the shapes given below?
(b) (i) Circle the numbers whose mirror image is the same number.
(ii) Which digits from 0 to 9 have the same mirror image?
(iii) 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?
(iv) Guess my number.
It is a 3-digit number near 120 whose mirror image is the same number. Where is the mirror kept?
(c) Make similar questions and ask your friends to guess the numbers.
Answer:
(a) To get shape 1, place the mirror vertically is the middle of shape A.
- To get shape 2, place the mirror horizontally in the middle of shape A.
- To get shape 3, place the mirror diagonally from the top left corner to the bottom right corner of shape A.
- To get shape 4, place the mirror vertically along the left edge of shape A.
- To get shape 5, place the mirror diagonally from the top right corner to the bottom left corner of shape A.
- To get shape 6, place the mirror horizontally along the top edge of shape A.
(b) (i) 181 with a vertical and horizontal mirror lines – Same
The digits 1,8,1 are vertically and horizontally symmetrical.
686 with a vertical mirror line – Not the same-Digit 6 becomes 9 in a mirror vertically.
686 with a horizontal mirror line – Not the same. 6 and 9 flip across horizontal axis; not symmetrical.
(ii) Digits that have mirror symmetry 0,1,3,8
Note Sometimes 8 has both vertical and horizontal symmetry, depending on the font.
(iii) Examples of such 4-digit numbers (using only digits that are symmetrical)
- 1001
- 1111
- 8008
- 3003
- 1881
We can create several such numbers using combinations of symmetrical digits 0,1,3,8
(iv) The 3 -digit number near 120 whose mirror image is the same is ‘111’.
(c) Do yourself
Question 3.
(i) What do you notice about the letters written on the ambulance? Why are they written this way? Discuss.
(ii) Can you guess what I have written? Where did I keep the mirror?
(iii) Can you identify these words? Where will you place the mirror to read the following words correctly?
(iv) You try to write some words/names in this way and challenge your friends to guess them.
(v) Can you also try doing this with the script of your own language?
Answer:
(i) The word AMBULANCE is written as GOИAJUGMA (reversed).
When viewed through a rearview mirror, it appears correctly as AMBULANCE to drivers in front of the vehicle.
They are written in mirror image so that when drivers see the ambulance in their rearview mirror, they can immediately read the word AMBULANCE clearly and move aside.
(ii) The word written is ‘CAT’.
If you place a mirror below the word (horizontal mirror), you will see the correct word ‘CAT’.
(iii) For first word GAT
This is a mirror image of TAP.
Place the mirror vertically (on the left side) to read it correctly as TAP.
For second word 
This is the mirror image of 
Place the mirror horizontally (on the upper side) to read it correctly.
For third word WOW
This word looks the same in a mirror.
It is symmetrical, so a vertical mirror in the left/right will still show WOW.
For fourth word ИАН
This is the mirror image of 
Place the mirror vertically (on the left/right side) to read it correctly as HEN.
(iv) Do yourself
(v) Do yourself
Question 4.
Complete the following to make symmetrical shapes.
Answer:
Do yourself
Question 5.
Observe the shapes.
(i) How many sides does each shape have?
(ii) How many lines of symmetry does each shape have? You may trace these shapes and check the lines of symmetry by folding the shapes.
Answer:
(i) There are 3 sides in each shape of first box and there are 4 sides in each shape of second box.
(ii) The yellow triangle has 0 line of symmetry. The sky blue triangle has 1 line of symmetry.
The purple triangle has 1 line of symmetry. The orange triangle has 1 line of symmetry. The blue triangle has 0 line of symmetry.
The green triangle has 1 line of symmetry. The purple kite has 1 line of symmetry. The blue rectangle has 2 lines of symmetry. The sky blue square has 4 lines of symmetry.
The yellow trapezium has 1 line of symmetry.
The sky blue parallelogram has 2 lines of symmetry.
The orange rhombus has 2 lines of symmetry.
The green polygon has 0 line of symmetry. The sky blue polygon has 1 line of symmetry.
Tilling the Tiles (NCERT Pg 170)
Question 6.
Here are some patterns with tiles. Identify the repeating unit (tile) and continue the patterns.
Answer:
Do youself
Tiles at the Tile Shop (NCERT Pg 171-172)
Question 7.
Bablu Chacha makes beautiful tiles of the kinds shown below.
(i) Design creative tiles of your own in the spaces given below. You may use a rangometry kit or shape cutouts.
(ii) Which shapes have you used to make the tiles?
(iii) Which of the tiles are symmetrical? Draw the lines of symmetry (if any).
(iv) Make more tiles by joining two or more shapes. Trace them in your notebook to create paths with no gaps or overlaps.
(v) Look at the following shapes. What do you notice? Discuss.
Answer:
(i) Do yourself
(ii) Do yourself
(iii) Do yourself
(iv) Do yourself
(v) Both the shapes are symmetrical and having 3 lines of symmetry.
Let Us Do (NCERT Pg 172)
Question 1.
Make floor patterns with your tile. Mini has made a floor pattern as shown below.
Remember there should be no overlaps and no gaps.
Answer:
Do yourself