NCERT Textbook: Shapes and Patterns

 Page 1


Shapes and  
Patterns
Chapter Chapter
Weaving Mats
You may have seen woven baskets 
of different kinds. If you look closely, 
you will notice different weaving 
patterns on each basket.
We will try weaving some mats with 
paper strips.
1. Let us make paper mats.
You will need — A coloured paper (30 cm long 
and 20 cm wide) and eight paper strips of 
two different colours (3 cm wide and longer  
than 20 cm). 
(a) Take a coloured paper 30 cm long and  
20 cm wide.
(b) Fold the coloured paper in half along the 
longer side.
(c) Draw vertical lines at equal distances from the closed 
end and cut slits leaving a gap of 3 cm at the top.
(d) Carefully unfold the paper. There will be no cuts in the 
paper at the top and the bottom.
(e) Now cut 8 paper strips of 3 cm width in 2 colours and 
of length slightly longer than 20 cm.
(f) Take one colour strip and weave it across the slits going 
1 under and 1 over, and again 1 under and 1 over. 
Repeat it for the first row.
(g) Take one more strip of another colour and weave it  
across the slits going 1 over and 1 under, and again 
1 over and 1 under. Repeat it for the second row.
(h) Weave all the strips in the same alternating pattern. 
Neatly fold any extra strip ends behind the mat. 
Your mat is ready!
We can describe the pattern of the above weave as follows.
Row 1 — 1 under, 1 over, 1 under, 1 over, … (repeat)
Row 2 — 1 over, 1 under, 1 over, 1 under, … (repeat)
7 7
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Page 2


Shapes and  
Patterns
Chapter Chapter
Weaving Mats
You may have seen woven baskets 
of different kinds. If you look closely, 
you will notice different weaving 
patterns on each basket.
We will try weaving some mats with 
paper strips.
1. Let us make paper mats.
You will need — A coloured paper (30 cm long 
and 20 cm wide) and eight paper strips of 
two different colours (3 cm wide and longer  
than 20 cm). 
(a) Take a coloured paper 30 cm long and  
20 cm wide.
(b) Fold the coloured paper in half along the 
longer side.
(c) Draw vertical lines at equal distances from the closed 
end and cut slits leaving a gap of 3 cm at the top.
(d) Carefully unfold the paper. There will be no cuts in the 
paper at the top and the bottom.
(e) Now cut 8 paper strips of 3 cm width in 2 colours and 
of length slightly longer than 20 cm.
(f) Take one colour strip and weave it across the slits going 
1 under and 1 over, and again 1 under and 1 over. 
Repeat it for the first row.
(g) Take one more strip of another colour and weave it  
across the slits going 1 over and 1 under, and again 
1 over and 1 under. Repeat it for the second row.
(h) Weave all the strips in the same alternating pattern. 
Neatly fold any extra strip ends behind the mat. 
Your mat is ready!
We can describe the pattern of the above weave as follows.
Row 1 — 1 under, 1 over, 1 under, 1 over, … (repeat)
Row 2 — 1 over, 1 under, 1 over, 1 under, … (repeat)
7 7
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Row 1 — 2 over, 1 under, 2 over, 1 under, ... (repeat).
Row 2 —  1 under (do not repeat), 3 over, 3 under, 3 over,  
3 under, ... (repeat).
Row 3 — 2 under, 1 over, 2 under, ... (repeat).
Row 4 —  1 over (do not repeat), 3 under, 3 over ... (repeat). 
Continue weaving in this order.
4. Can you work out the steps 
for any of these designs and 
weave the pattern? 
Write the steps of the pattern 
in your notebook for each row 
until it starts repeating.
Draw the following pattern on a grid 
paper. Part of it is done for you. 
Now, complete 
the rest of the 
grid to get the 
full design.
2. Can you figure out how to make this mat?
Let us try to understand how this mat is woven by looking  
at the pattern in the first two rows.
Row 1 — 2 over, 1 under, 2 over, 1 under, ...
Row 2 — 2 under, 1 over, 2 under, 1 over, …
You can use strips of the same colour or 2 different 
colours, one for each row.
3. Try to weave a pattern, using the rules given below.
Let Us Try
Chapter 7.indd   93 Chapter 7.indd   93 2/24/2026   4:35:24 PM 2/24/2026   4:35:24 PM
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Page 3


Shapes and  
Patterns
Chapter Chapter
Weaving Mats
You may have seen woven baskets 
of different kinds. If you look closely, 
you will notice different weaving 
patterns on each basket.
We will try weaving some mats with 
paper strips.
1. Let us make paper mats.
You will need — A coloured paper (30 cm long 
and 20 cm wide) and eight paper strips of 
two different colours (3 cm wide and longer  
than 20 cm). 
(a) Take a coloured paper 30 cm long and  
20 cm wide.
(b) Fold the coloured paper in half along the 
longer side.
(c) Draw vertical lines at equal distances from the closed 
end and cut slits leaving a gap of 3 cm at the top.
(d) Carefully unfold the paper. There will be no cuts in the 
paper at the top and the bottom.
(e) Now cut 8 paper strips of 3 cm width in 2 colours and 
of length slightly longer than 20 cm.
(f) Take one colour strip and weave it across the slits going 
1 under and 1 over, and again 1 under and 1 over. 
Repeat it for the first row.
(g) Take one more strip of another colour and weave it  
across the slits going 1 over and 1 under, and again 
1 over and 1 under. Repeat it for the second row.
(h) Weave all the strips in the same alternating pattern. 
Neatly fold any extra strip ends behind the mat. 
Your mat is ready!
We can describe the pattern of the above weave as follows.
Row 1 — 1 under, 1 over, 1 under, 1 over, … (repeat)
Row 2 — 1 over, 1 under, 1 over, 1 under, … (repeat)
7 7
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93
Row 1 — 2 over, 1 under, 2 over, 1 under, ... (repeat).
Row 2 —  1 under (do not repeat), 3 over, 3 under, 3 over,  
3 under, ... (repeat).
Row 3 — 2 under, 1 over, 2 under, ... (repeat).
Row 4 —  1 over (do not repeat), 3 under, 3 over ... (repeat). 
Continue weaving in this order.
4. Can you work out the steps 
for any of these designs and 
weave the pattern? 
Write the steps of the pattern 
in your notebook for each row 
until it starts repeating.
Draw the following pattern on a grid 
paper. Part of it is done for you. 
Now, complete 
the rest of the 
grid to get the 
full design.
2. Can you figure out how to make this mat?
Let us try to understand how this mat is woven by looking  
at the pattern in the first two rows.
Row 1 — 2 over, 1 under, 2 over, 1 under, ...
Row 2 — 2 under, 1 over, 2 under, 1 over, …
You can use strips of the same colour or 2 different 
colours, one for each row.
3. Try to weave a pattern, using the rules given below.
Let Us Try
Chapter 7.indd   93 Chapter 7.indd   93 2/24/2026   4:35:24 PM 2/24/2026   4:35:24 PM
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94
Tiling and Tessellation
We often use tiles of the same shape or a combination of shapes to cover 
a region.
You can see pentagons (5-sided figures) in this figure. 
As all its sides are equal it is a regular pentagon.
Shapes that have equal sides are called regular shapes.
We have placed 3 pentagons around a point. Can we fit  
one more into the empty space? 
Pentagons cannot fill a region without leaving gaps. So, 
we say that regular pentagons do not tessellate.
Find Out
Can regular triangles fit together at a point without any gap? How many 
of them fit together? (A sample triangle is given at the end of the book).
Do you see that regular triangles fit around a point as  
shown here? 
Regular triangles when fitted around a point leave  
no gaps and there is no overlap.
Triangles with all equal sides are also called equilateral 
triangles. 
Therefore, equilateral triangles tessellate. Can squares 
(a regular 4-sided shape) fit together around a point without 
any gap or overlap? Try it out using cutouts of squares (a sample square is 
given at the end of the book). How many squares did you need?
Can five squares fit together around a point without any gaps or overlaps? 
Why or why not?
Can regular hexagons (6-sided shapes with equal sides) fit 
together around a point without any gaps or overlaps? Try 
and see (a sample hexagon is given at the end of the book). 
How many fit together at a point?
Chapter 7.indd   94 Chapter 7.indd   94 05-07-2025   16:03:08 05-07-2025   16:03:08
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Page 4


Shapes and  
Patterns
Chapter Chapter
Weaving Mats
You may have seen woven baskets 
of different kinds. If you look closely, 
you will notice different weaving 
patterns on each basket.
We will try weaving some mats with 
paper strips.
1. Let us make paper mats.
You will need — A coloured paper (30 cm long 
and 20 cm wide) and eight paper strips of 
two different colours (3 cm wide and longer  
than 20 cm). 
(a) Take a coloured paper 30 cm long and  
20 cm wide.
(b) Fold the coloured paper in half along the 
longer side.
(c) Draw vertical lines at equal distances from the closed 
end and cut slits leaving a gap of 3 cm at the top.
(d) Carefully unfold the paper. There will be no cuts in the 
paper at the top and the bottom.
(e) Now cut 8 paper strips of 3 cm width in 2 colours and 
of length slightly longer than 20 cm.
(f) Take one colour strip and weave it across the slits going 
1 under and 1 over, and again 1 under and 1 over. 
Repeat it for the first row.
(g) Take one more strip of another colour and weave it  
across the slits going 1 over and 1 under, and again 
1 over and 1 under. Repeat it for the second row.
(h) Weave all the strips in the same alternating pattern. 
Neatly fold any extra strip ends behind the mat. 
Your mat is ready!
We can describe the pattern of the above weave as follows.
Row 1 — 1 under, 1 over, 1 under, 1 over, … (repeat)
Row 2 — 1 over, 1 under, 1 over, 1 under, … (repeat)
7 7
Chapter 7.indd   92 Chapter 7.indd   92 2/24/2026   4:35:13 PM 2/24/2026   4:35:13 PM
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93
Row 1 — 2 over, 1 under, 2 over, 1 under, ... (repeat).
Row 2 —  1 under (do not repeat), 3 over, 3 under, 3 over,  
3 under, ... (repeat).
Row 3 — 2 under, 1 over, 2 under, ... (repeat).
Row 4 —  1 over (do not repeat), 3 under, 3 over ... (repeat). 
Continue weaving in this order.
4. Can you work out the steps 
for any of these designs and 
weave the pattern? 
Write the steps of the pattern 
in your notebook for each row 
until it starts repeating.
Draw the following pattern on a grid 
paper. Part of it is done for you. 
Now, complete 
the rest of the 
grid to get the 
full design.
2. Can you figure out how to make this mat?
Let us try to understand how this mat is woven by looking  
at the pattern in the first two rows.
Row 1 — 2 over, 1 under, 2 over, 1 under, ...
Row 2 — 2 under, 1 over, 2 under, 1 over, …
You can use strips of the same colour or 2 different 
colours, one for each row.
3. Try to weave a pattern, using the rules given below.
Let Us Try
Chapter 7.indd   93 Chapter 7.indd   93 2/24/2026   4:35:24 PM 2/24/2026   4:35:24 PM
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94
Tiling and Tessellation
We often use tiles of the same shape or a combination of shapes to cover 
a region.
You can see pentagons (5-sided figures) in this figure. 
As all its sides are equal it is a regular pentagon.
Shapes that have equal sides are called regular shapes.
We have placed 3 pentagons around a point. Can we fit  
one more into the empty space? 
Pentagons cannot fill a region without leaving gaps. So, 
we say that regular pentagons do not tessellate.
Find Out
Can regular triangles fit together at a point without any gap? How many 
of them fit together? (A sample triangle is given at the end of the book).
Do you see that regular triangles fit around a point as  
shown here? 
Regular triangles when fitted around a point leave  
no gaps and there is no overlap.
Triangles with all equal sides are also called equilateral 
triangles. 
Therefore, equilateral triangles tessellate. Can squares 
(a regular 4-sided shape) fit together around a point without 
any gap or overlap? Try it out using cutouts of squares (a sample square is 
given at the end of the book). How many squares did you need?
Can five squares fit together around a point without any gaps or overlaps? 
Why or why not?
Can regular hexagons (6-sided shapes with equal sides) fit 
together around a point without any gaps or overlaps? Try 
and see (a sample hexagon is given at the end of the book). 
How many fit together at a point?
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95
Here is a tessellating pattern with more than one shape.
What shapes have been used in this pattern? _____________, _____________.
Continue the pattern given below and colour it appropriately.
A regular octagon means a shape with eight 
equal sides.
Do regular octagons fit together without any gaps or 
overlaps? Try drawing the same and check.
Regular octagons do not tessellate.
Chapter 7.indd   95 Chapter 7.indd   95 05-07-2025   16:03:12 05-07-2025   16:03:12
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Page 5


Shapes and  
Patterns
Chapter Chapter
Weaving Mats
You may have seen woven baskets 
of different kinds. If you look closely, 
you will notice different weaving 
patterns on each basket.
We will try weaving some mats with 
paper strips.
1. Let us make paper mats.
You will need — A coloured paper (30 cm long 
and 20 cm wide) and eight paper strips of 
two different colours (3 cm wide and longer  
than 20 cm). 
(a) Take a coloured paper 30 cm long and  
20 cm wide.
(b) Fold the coloured paper in half along the 
longer side.
(c) Draw vertical lines at equal distances from the closed 
end and cut slits leaving a gap of 3 cm at the top.
(d) Carefully unfold the paper. There will be no cuts in the 
paper at the top and the bottom.
(e) Now cut 8 paper strips of 3 cm width in 2 colours and 
of length slightly longer than 20 cm.
(f) Take one colour strip and weave it across the slits going 
1 under and 1 over, and again 1 under and 1 over. 
Repeat it for the first row.
(g) Take one more strip of another colour and weave it  
across the slits going 1 over and 1 under, and again 
1 over and 1 under. Repeat it for the second row.
(h) Weave all the strips in the same alternating pattern. 
Neatly fold any extra strip ends behind the mat. 
Your mat is ready!
We can describe the pattern of the above weave as follows.
Row 1 — 1 under, 1 over, 1 under, 1 over, … (repeat)
Row 2 — 1 over, 1 under, 1 over, 1 under, … (repeat)
7 7
Chapter 7.indd   92 Chapter 7.indd   92 2/24/2026   4:35:13 PM 2/24/2026   4:35:13 PM
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93
Row 1 — 2 over, 1 under, 2 over, 1 under, ... (repeat).
Row 2 —  1 under (do not repeat), 3 over, 3 under, 3 over,  
3 under, ... (repeat).
Row 3 — 2 under, 1 over, 2 under, ... (repeat).
Row 4 —  1 over (do not repeat), 3 under, 3 over ... (repeat). 
Continue weaving in this order.
4. Can you work out the steps 
for any of these designs and 
weave the pattern? 
Write the steps of the pattern 
in your notebook for each row 
until it starts repeating.
Draw the following pattern on a grid 
paper. Part of it is done for you. 
Now, complete 
the rest of the 
grid to get the 
full design.
2. Can you figure out how to make this mat?
Let us try to understand how this mat is woven by looking  
at the pattern in the first two rows.
Row 1 — 2 over, 1 under, 2 over, 1 under, ...
Row 2 — 2 under, 1 over, 2 under, 1 over, …
You can use strips of the same colour or 2 different 
colours, one for each row.
3. Try to weave a pattern, using the rules given below.
Let Us Try
Chapter 7.indd   93 Chapter 7.indd   93 2/24/2026   4:35:24 PM 2/24/2026   4:35:24 PM
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94
Tiling and Tessellation
We often use tiles of the same shape or a combination of shapes to cover 
a region.
You can see pentagons (5-sided figures) in this figure. 
As all its sides are equal it is a regular pentagon.
Shapes that have equal sides are called regular shapes.
We have placed 3 pentagons around a point. Can we fit  
one more into the empty space? 
Pentagons cannot fill a region without leaving gaps. So, 
we say that regular pentagons do not tessellate.
Find Out
Can regular triangles fit together at a point without any gap? How many 
of them fit together? (A sample triangle is given at the end of the book).
Do you see that regular triangles fit around a point as  
shown here? 
Regular triangles when fitted around a point leave  
no gaps and there is no overlap.
Triangles with all equal sides are also called equilateral 
triangles. 
Therefore, equilateral triangles tessellate. Can squares 
(a regular 4-sided shape) fit together around a point without 
any gap or overlap? Try it out using cutouts of squares (a sample square is 
given at the end of the book). How many squares did you need?
Can five squares fit together around a point without any gaps or overlaps? 
Why or why not?
Can regular hexagons (6-sided shapes with equal sides) fit 
together around a point without any gaps or overlaps? Try 
and see (a sample hexagon is given at the end of the book). 
How many fit together at a point?
Chapter 7.indd   94 Chapter 7.indd   94 05-07-2025   16:03:08 05-07-2025   16:03:08
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95
Here is a tessellating pattern with more than one shape.
What shapes have been used in this pattern? _____________, _____________.
Continue the pattern given below and colour it appropriately.
A regular octagon means a shape with eight 
equal sides.
Do regular octagons fit together without any gaps or 
overlaps? Try drawing the same and check.
Regular octagons do not tessellate.
Chapter 7.indd   95 Chapter 7.indd   95 05-07-2025   16:03:12 05-07-2025   16:03:12
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96
Look at the pattern given below. What shapes are coming together at the 
marked points? Are the same set of shapes coming together at these points? 
Continue the pattern and colour it appropriately.
What shapes are coming together at the marked points?
Are the same set of shapes coming together at these points? 
Continue the pattern and colour it appropriately.
Create similar patterns using other cutouts of shapes.
A rhombus is a shape with all equal sides. It has been divided 
into four triangles.
Here is a tiling pattern made using two different shapes — squares and 
triangles. Are the triangles equilateral? Why or why not?
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