NCERT Textbook: Playing with Constructions | Mathematics (Maths) Class 6 PDF Download

 Page 1


Playing with 
Constru Cti ons
8
8.1 Artwork
Observe the following figures and try drawing them freehand.
Fig. 8.1
Chapter 8_Playing with Constructions.indd   187 10-08-2024   15:58:31
Page 2


Playing with 
Constru Cti ons
8
8.1 Artwork
Observe the following figures and try drawing them freehand.
Fig. 8.1
Chapter 8_Playing with Constructions.indd   187 10-08-2024   15:58:31
Ganita Prakash | Grade 6
188
Now, arm yourself with a ruler and a compass. Let us explore if 
we can draw these figures with these tools and get familiar with a 
compass.
Observe the way a compass is made. What can one draw with the 
compass? Explore!
Do you know what curves are? They are any shapes that can be 
drawn on paper with a pencil, and include straight lines, circles and 
other figures as shown below.
Mark a point ‘P’ in your notebook. Then, mark as many points as 
possible, in different directions, that are 4 cm away from P. 
 Think: Imagine marking all the points of 4 cm distance from the 
point P. How would they look? 
 Try to draw it and verify if it is correct by taking some points on 
the curve and checking if their distances from P are indeed 4 c m.
Explore, if you have not already done so, 
and see if a compass can be used for this 
purpose.
You can start by marking a few points 
of distance 4 cm from P using the compass. 
How can this be done?
R
4 cm
4 cm
P
Q
Chapter 8_Playing with Constructions.indd   188 10-08-2024   15:58:32
Page 3


Playing with 
Constru Cti ons
8
8.1 Artwork
Observe the following figures and try drawing them freehand.
Fig. 8.1
Chapter 8_Playing with Constructions.indd   187 10-08-2024   15:58:31
Ganita Prakash | Grade 6
188
Now, arm yourself with a ruler and a compass. Let us explore if 
we can draw these figures with these tools and get familiar with a 
compass.
Observe the way a compass is made. What can one draw with the 
compass? Explore!
Do you know what curves are? They are any shapes that can be 
drawn on paper with a pencil, and include straight lines, circles and 
other figures as shown below.
Mark a point ‘P’ in your notebook. Then, mark as many points as 
possible, in different directions, that are 4 cm away from P. 
 Think: Imagine marking all the points of 4 cm distance from the 
point P. How would they look? 
 Try to draw it and verify if it is correct by taking some points on 
the curve and checking if their distances from P are indeed 4 c m.
Explore, if you have not already done so, 
and see if a compass can be used for this 
purpose.
You can start by marking a few points 
of distance 4 cm from P using the compass. 
How can this be done?
R
4 cm
4 cm
P
Q
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Playing with Constructions
189
You will have to open up the compass against a ruler (see Fig. 8.2) 
such that the distance between the tip of the compass and the pencil 
is 4 cm. 
  Now, try to get the full curve. 
Hint: Keep the point of the compass fixed moving only the pencil.
What is the shape of the curve? It is a circle!
Take a point on the circle. What will be its distance from P—equal 
to 4 cm, less than 4 cm or greater than 4 cm? Similarly, what will be 
the distance between P and another point on the circle?
As shown in the figure, the point P is called the centre of the circle 
and the distance between the centre and any point on the circle is 
called the radius of the circle.
radius
1 0 2 3 4 5 6 7
centre
Fig. 8.2
P
Having explored the use of a compass, go ahead and recreate the 
images in Fig. 8.1. 
Can you make the figures look as good as the figures shown there? 
Try again if you want to!
Also, has the use of instruments made the construction easier?
Now try constructing the following figures.
Chapter 8_Playing with Constructions.indd   189 10-08-2024   15:58:32
Page 4


Playing with 
Constru Cti ons
8
8.1 Artwork
Observe the following figures and try drawing them freehand.
Fig. 8.1
Chapter 8_Playing with Constructions.indd   187 10-08-2024   15:58:31
Ganita Prakash | Grade 6
188
Now, arm yourself with a ruler and a compass. Let us explore if 
we can draw these figures with these tools and get familiar with a 
compass.
Observe the way a compass is made. What can one draw with the 
compass? Explore!
Do you know what curves are? They are any shapes that can be 
drawn on paper with a pencil, and include straight lines, circles and 
other figures as shown below.
Mark a point ‘P’ in your notebook. Then, mark as many points as 
possible, in different directions, that are 4 cm away from P. 
 Think: Imagine marking all the points of 4 cm distance from the 
point P. How would they look? 
 Try to draw it and verify if it is correct by taking some points on 
the curve and checking if their distances from P are indeed 4 c m.
Explore, if you have not already done so, 
and see if a compass can be used for this 
purpose.
You can start by marking a few points 
of distance 4 cm from P using the compass. 
How can this be done?
R
4 cm
4 cm
P
Q
Chapter 8_Playing with Constructions.indd   188 10-08-2024   15:58:32
Playing with Constructions
189
You will have to open up the compass against a ruler (see Fig. 8.2) 
such that the distance between the tip of the compass and the pencil 
is 4 cm. 
  Now, try to get the full curve. 
Hint: Keep the point of the compass fixed moving only the pencil.
What is the shape of the curve? It is a circle!
Take a point on the circle. What will be its distance from P—equal 
to 4 cm, less than 4 cm or greater than 4 cm? Similarly, what will be 
the distance between P and another point on the circle?
As shown in the figure, the point P is called the centre of the circle 
and the distance between the centre and any point on the circle is 
called the radius of the circle.
radius
1 0 2 3 4 5 6 7
centre
Fig. 8.2
P
Having explored the use of a compass, go ahead and recreate the 
images in Fig. 8.1. 
Can you make the figures look as good as the figures shown there? 
Try again if you want to!
Also, has the use of instruments made the construction easier?
Now try constructing the following figures.
Chapter 8_Playing with Constructions.indd   189 10-08-2024   15:58:32
Ganita Prakash | Grade 6
190
 Construct
1. A Person 
 How will you draw this? 
 This figure has two components.
 You might have figured out a way of drawing the first part. For 
drawing the second part, see this.
 The challenge here is to find out where to place the tip of the 
compass and the radius to be taken for drawing this curve. You 
can fix a radius in the compass and try placing the tip of the 
Chapter 8_Playing with Constructions.indd   190 10-08-2024   15:58:32
Page 5


Playing with 
Constru Cti ons
8
8.1 Artwork
Observe the following figures and try drawing them freehand.
Fig. 8.1
Chapter 8_Playing with Constructions.indd   187 10-08-2024   15:58:31
Ganita Prakash | Grade 6
188
Now, arm yourself with a ruler and a compass. Let us explore if 
we can draw these figures with these tools and get familiar with a 
compass.
Observe the way a compass is made. What can one draw with the 
compass? Explore!
Do you know what curves are? They are any shapes that can be 
drawn on paper with a pencil, and include straight lines, circles and 
other figures as shown below.
Mark a point ‘P’ in your notebook. Then, mark as many points as 
possible, in different directions, that are 4 cm away from P. 
 Think: Imagine marking all the points of 4 cm distance from the 
point P. How would they look? 
 Try to draw it and verify if it is correct by taking some points on 
the curve and checking if their distances from P are indeed 4 c m.
Explore, if you have not already done so, 
and see if a compass can be used for this 
purpose.
You can start by marking a few points 
of distance 4 cm from P using the compass. 
How can this be done?
R
4 cm
4 cm
P
Q
Chapter 8_Playing with Constructions.indd   188 10-08-2024   15:58:32
Playing with Constructions
189
You will have to open up the compass against a ruler (see Fig. 8.2) 
such that the distance between the tip of the compass and the pencil 
is 4 cm. 
  Now, try to get the full curve. 
Hint: Keep the point of the compass fixed moving only the pencil.
What is the shape of the curve? It is a circle!
Take a point on the circle. What will be its distance from P—equal 
to 4 cm, less than 4 cm or greater than 4 cm? Similarly, what will be 
the distance between P and another point on the circle?
As shown in the figure, the point P is called the centre of the circle 
and the distance between the centre and any point on the circle is 
called the radius of the circle.
radius
1 0 2 3 4 5 6 7
centre
Fig. 8.2
P
Having explored the use of a compass, go ahead and recreate the 
images in Fig. 8.1. 
Can you make the figures look as good as the figures shown there? 
Try again if you want to!
Also, has the use of instruments made the construction easier?
Now try constructing the following figures.
Chapter 8_Playing with Constructions.indd   189 10-08-2024   15:58:32
Ganita Prakash | Grade 6
190
 Construct
1. A Person 
 How will you draw this? 
 This figure has two components.
 You might have figured out a way of drawing the first part. For 
drawing the second part, see this.
 The challenge here is to find out where to place the tip of the 
compass and the radius to be taken for drawing this curve. You 
can fix a radius in the compass and try placing the tip of the 
Chapter 8_Playing with Constructions.indd   190 10-08-2024   15:58:32
Playing with Constructions
191
compass in different locations to see which point works for 
getting the curve. Use your Estimate where to keep the tip.
2. Wavy Wave
 Construct this.
 As the length of the central line is not specified, we can take it to 
be of any length.
  Let us take AB to be the central line such that the length of AB  is 
8 cm. We write this as AB = 8 cm.
 Here, the first wave is drawn as a half circle.
A X
?
8 cm
B
?
 Figure it Out
1. What radius should be taken in the compass to get this half circle? 
What should be the length of AX?
2. Take a central line of a different length and try to draw the wave 
on it.
3. Try to recreate the figure where the waves are smaller than a 
half circle (as appearing in the neck of the figure ‘A Person’). 
The challenge here is to get both the waves to be identical. 
This may be tricky! 
Try
This
Chapter 8_Playing with Constructions.indd   191 10-08-2024   15:58:32