NCERT Solutions for Class 4th Maths Chapter 1 Matchstick puzzles, the model challenge and sorting by angles — Let Us Try
Book page 22 Updated on2026-09-19
Q1.
Move two of these matchsticks to form 4 triangles.
The three matchstick triangles printed in the book — 9 matchsticks in all.
Answer
There are 9 matchsticks in the three triangles. Move 2 of them to the
top, so that the triangles start sharing sides.
Take away the bottom matchstick of the third triangle and lay it across
the top, joining the tip of the first triangle to the tip of the second.
Take away the right slanting matchstick of the third triangle and lay it
across the top too, joining the tip of the second triangle to the tip of the third.
Now count the triangles:
the first triangle (pointing up) = 1
the second triangle (pointing up) = 1
a new triangle pointing down between them = 1
one more triangle pointing down on the right = 1
Total = 4 triangles from the same 9 matchsticks
The same 9 matchsticks after 2 of them (shown in green) have been moved to the top.
Why it happens: Three separate triangles need 3 + 3 + 3 = 9
sticks. When triangles share their sides, the same 9 sticks can build a whole strip of
triangles, and each new stick closes one more triangle.
Q2.
Remove 4 of these matchsticks to leave only 3 triangles.
The matchstick figure printed in the book — 13 matchsticks.
Answer
The figure is made of 13 matchsticks, and there are 6 triangles in it.
Take away 4 sticks so that only 3 triangles are left and no loose sticks remain.
Remove these four:
the long middle matchstick lying across the figure;
the slanting matchstick going down-right from the top point;
the slanting matchstick going down-left from the right-hand junction;
the bottom matchstick of the middle triangle.
13 – 4 = 9 matchsticks left
9 sticks make 3 separate triangles — 3 + 3 + 3 = 9
What is left is the triangle at the top left, the triangle at the bottom left and the
triangle on the right.
The same figure with the four matchsticks to be removed crossed out.
Why it happens: The middle matchstick and the slanting ones
are shared by several triangles at once, so taking them out destroys more than one
triangle each. The three triangles that are left do not share any stick with them.
Q3.
Model challenge. Can you make a model of solid shapes which has a) 12 straws and 8 clay balls? b) 9 straws and 6 clay balls? c) 15 straws and 10 clay balls? d) 10 straws and 6 clay balls?
A straw-and-clay model: each straw is an edge and each clay ball is a corner.
Answer
A straw is an edge and a clay ball is a corner. So look for
the solid with that many edges and that many corners.
Straws (edges)
Clay balls (corners)
Model you can make
a)
12
8
cube or cuboid
b)
9
6
triangular prism
c)
15
10
pentagonal prism
d)
10
6
pentagonal pyramid
How each one is checked
Cube: 4 straws on top + 4 below + 4 standing = 12 straws; 4 balls on top
+ 4 below = 8 balls
Triangular prism: 3 + 3 + 3 = 9 straws; 3 + 3 = 6 balls
Pentagonal prism: 5 + 5 + 5 = 15 straws; 5 + 5 = 10 balls
Pentagonal pyramid: 5 straws round the base + 5 going up to the top = 10 straws;
5 balls round the base + 1 at the top = 6 balls
Yes — all four models can be made.
Why it happens: In a prism the two ends are the same, so the
straws come in three equal sets. In a pyramid every corner of the base gets one straw
going up to the single top ball, so the straws come in two equal sets.
Q4.
Classify these shapes based on the number of angles. 3 angles / 4 angles / 5 angles
The seven shapes (a) to (g) printed in the book.
Answer
Count the corners of each shape — each corner is one angle.
3 angles
4 angles
5 angles
(b) triangle
(a) square
(e) pentagon
(d) triangle
(c) parallelogram
(f) four-sided shape
(g) rectangle
The same shapes with the number of angles written under each one.
Why it happens: At every corner two sides meet, and two
sides meeting make one angle. So a shape has exactly as many angles as it has
corners.
Q5.
What relation do you notice between the number of sides and the number of angles?
The seven shapes (a) to (g) printed in the book.
Answer
They are always the same number.
number of angles = number of sides
Shape
Sides
Angles
triangle
3
3
square, rectangle
4
4
pentagon
5
5
hexagon
6
6
Why it happens: Go round the shape with your finger. At the
end of every side you have to turn a corner, and every corner is an angle. So the number
of turns is the same as the number of sides.