Class 4 | Maths Mela | Ch 1 Shapes Around Us
Sol.
Do it yourself.
Q. 2. Use the nets given at the end of the book to make the models shown below.
Q. What shape of face is common to all the prisms?
Sol. The shape of the face that is common to all the prisms is rectangle.
Q. What other shapes do these prisms have?
Sol. The prisms have other shapes as triangle, square, pentagon, hexagon etc.
Q. How many such faces each?
Sol. A triangular prism has 2 triangular faces, a square prism has 2 square faces, a hexagonal prism has 2 ‘hexagonal faces. These two faces are opposite and identical to each other.
Q. What shape of face common to all the pyramids?
Sol. The shape of the face common to all the pyramids is triangle.
Q. All the triangular faces meet at ........... point.
Sol. All the triangular faces meet at a common point
Q. Identify any other shape in each of the pyramids.
Sol. A triangular pyramid has only triangular faces, a square pyramid has a square face and a pentagonal pyramid has a pentagonal face.
Q. Is a cube also a prism?
Sol. Yes, A cube is a special type of square prism with 6 square faces.
Q. What is the difference between a prism and a pyramid? Discuss.
Sol. There are two main differences between the prism and pyramid
★ A prism has two identical bases while a pyramid has one base.
★ A prism has all rectangular or parallelogram-shaped side faces while a pyramid has all triangular side faces.
Q. 3. Now try to make the above shapes using straws and plasticine/thread and fill in the table.
Calculate F+V–E in each case.
What do you notice?
Can you construct a 3D shape with 3 flat faces?
Sol.
Hence, we observe that number of faces (F) + number of corners (V) – number of edges (E) =2
No! We cannot construct a 3D shape with 3 flat faces.
(Page 5)
Let Us Observe
Q. 1. Take a die. Look at the face that has number 1. The face numbered 6 is opposite to the face numbered 1.
What is the face opposite to the
(a) face numbered 2?
(b) face numbered 3?
(c) face numbered 4?
Sol.
A standard dice is designed so that the numbers on opposite faces always add up to 7.
(a) Since, 7 – 2 = 5, the opposite of face numbered 2 is face numbered 5.
(b) Since, 7 – 3 = 4, the opposite of face numbered 3 is face numbered 4.
(c) Since, 7 – 4 = 3, the opposite of face numbered 4 is face numbered 3.
Note –>
(A) Which Faces Have Common Edges
Each face has common edges with all the other faces except the face opposite of it.
(B) Which Faces Have Non-Common Edges
The face opposite to the face numbered has no common edges
Q. 2. (a) Which faces have common edges with the face numbered 1?
Sol. Each face has common edges with all the other faces except the face opposite of it. So, the faces numbered 2, 3, 4, and 5 have common edges with the face numbered 1.
(b) Which face has no common edge with face numbered 1?
Sol. The face opposite to the face numbered 1 is the face numbered 6. Therefore, face numbered 6 has no common edges with the face numbered 1.
Q. 3. Look at three different views of the same cube.
(a) What colour is the face that is opposite to the red face?
(b) What colour is the face that is opposite to the yellow face?
Sol.
(a) Purple face is opposite to the red face.
(b) Orange face is opposite to the yellow face.
Q. Follow these instructions for the shapes along the border.
1. Colour all shapes with a rectangular face in red.
2. Draw a smiley on shapes with a triangular face.
3. Draw a star on shapes with a curved face.
4. Colour all shapes with no corner in blue.
5. Circle the shapes that have the same opposite faces.
Sol.
Do it yourself.
(Page 6-7)
Sorting 3D Shapes
Q. Write the names of 3D shapes in the correct places.
In which circle did you write triangular prism and rectangular pyramid?
Sol.
In the region common to both circles A and B.
Let us sort shapes in another way.
Using circles like those on the previous page, can you sort shapes into the categories “Shapes with curved faces” and “Shapes with flat faces”?
Solution:
(Page 7)
Cube Towers
Q. How many cubes are in each of these cube towers?
Sol.
- There are 30 cubes in the first tower.
- There are 66 cubes in the second tower.
(Pages 8-9)
Drawing Cubes on a Triangular Dot Paper
Q. Can you complete the following cubes?
Yes, it can be completed as shown above.
(a) I have 5 faces and 5 corners. I have 8 edges, 1 of my faces is a square and 4 of my faces are triangles ______________
(b) I have 1 flat face, 1 curved face and 1 edge ______________
(c) I have 1 curved face. I have no edges or corners ______________
(d) I have 2 flat faces, 1 curved face and 2 edges. I have no corners ______________
(e) I have 5 faces, 6 comers and 9 edges, 2 of my faces are triangles ______________
(f) I have 6 faces, 12 edges and 8 corners ______________
Sol.
(a) Square pyramid
(b) Cone
Q. 2. Each one is different. How? Discuss.
★ The sphere has 1 curved face and no flat face.
★ The cone has 1 flat face and 1 curved face.
★ The triangular pyramid has 4 triangular faces.
★ The cube has all the six square faces.
★ The cuboid has all the 6 rectangular faces.
So, each one of the given solids is different in terms of shape of the faces.
Q. 3. Match the following nets to the appropriate solids given below-
(1)-(b), (2)-(d), (3)-(a), (4)-(c).
Q. 4. Which of the nets can be folded to make a solid of the kind given below.
Q. 5. Nitesh cuts up a net on the folds. Here are its pieces.
Which solid has the above pieces in its net?
Sol. Nitesh cuts up 5 triangles and 1 pentagon. These pieces of the nets can be the piece of a pentagonal pyramid. Therefore, the correct solid is ' d ' a pentagonal pyramid.
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(Pages 10-11)
When Lines Meet
Angels
Depreciation between two lines at a point is known as angle.
There are 3 Main elements of an angle. 2 sides, 1 point, 1 Angle or Depreciation between two lines.
1. Right Angle –> Depreciation between two lines at a point is exact 90° is known as Right Angle.
2. Acute Angle –> Depreciation between two lines at a point is between 0° to 90° is known as Acute Angle.
3. Obtuse Angle –> Depreciation between two lines at a point is between 90° to 180° is known as Acute Angle.
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Q. How many angles are there in this boat drawing?
Sol. There are 10 angles in the boat drawing.
Let Us Do
Q. 1. Mark the angles on the following pictures.
Q. 2. Where do you see angles in the classroom? Give a few examples.
Sol. You can see angles in many places in a classroom. Here are a few examples:
- Corners of the room – Where two walls meet, they form a right angle (90°).
- Door and window frames – The edges and corners make right angles.
- Clock on the wall – The hands of the clock form different angles at different times.
- Desks and tables – The corners of desks and tables form angles.
- Books – When you open a book, the pages form an angle.
- Blackboard/whiteboard edges – The corners form right angles.
These are some common places where we can observe angles in a classroom.
Right Angles
Q. Identify the angles that you think are right angles and circle them in the dot grid given below. Check using your right angles checker.
Q. Check for right angles in a book, window, and any other object. Write the names of objects where you find right angles.
Sol.
★ Door and window frames – The edges and corners make right angles.
★ Books – Where two edge of book meet, they form a right angle (90°).
★ Desks and tables – The corners of desks and tables form angles.
★ Blackboard/whiteboard edges – The corners form right angles.
★ Corners of the room – Where two walls meet, they form a right angle (90°).
(Page 12)
Let Us Do
Q. 1. Draw some right angles on the dot grid.
Sol.
Acute and Obtuse Angles
Q. Name some objects from your classroom which have an acute angle.
Sol. Objects with an acute angle (less than 90°)
★ Objects with an acute angle (less than 90°):
★ Slightly open scissors
★ The angle between the hands of a clock (at times like 1:00 or 2:00)
★ A partially opened book
★ The tip of a set square (triangle ruler)
Q. Name some objects from your classroom which have an obtuse angle.
Sol. Objects with an obtuse angle (more than 90° but less than 180°)
★ A widely opened door
★ The angle between the hands of a clock (at times like 4:00 or 5:00)
★ A more widely opened book
★ The backrest of a chair when slightly tilted
Q. Identify all angles in the following letters.
(Page 13)
Let Us Do
Q. 1. (i) Draw some acute angles on the top grid. Draw a line to make an acute angle using each given line in the bottom grid.
Sol.
Following are drawings of some acute angles.
(ii) Draw some obtuse angles on the top grid. Draw a line to make an obtuse angle using each given line in the bottom grid.
Sol.
Following are drawings of some obtuse angles.
Q. 2. In the figures given below, mark the acute angles in red, right angles in green, obtuse angles in blue.
(Pages 14-16)
Shapes with Straws
Q. What kinds of angles does a triangle have?
Sol. A triangle can have acute, obtuse or right angle.
Q. Make a rectangular shape with straws and clay. What kinds of angles do you see in the rectangle?
Sol.
Q. Does the shape of the rectangle change if we gently push one of its sides?
Yes
Q. What has happened to the angles of the new shape?
Ans. Angels change.
Q. Are they still right angles? What types of angles have been formed?
Ans. No, they are not still right angles. They convert into two acute angles and two obtuse angles.
Q. 1. What has happened to the angles of the new shape?
Ans. When the shape is pushed or tilted, its angles change. They are no longer all equal. Some angles become smaller and some become larger.
Q. 2. Are they still right angles? What types of angles have been formed?
Ans. No, they are not right angles anymore.
★ Some angles become acute angles (less than 90°).
★ Some angles become obtuse angles (more than 90° but less than 180°).
Q. 3. Similarly, push one side of a square.
Ans. When you push one side of a square, it changes its shape (like a slanting figure).
Q. 4. Are they still right angles? What types of angles have been formed?
Ans. No, the angles are no longer right angles.
★ Two angles become acute.
★ Two angles become obtuse.
Q. 5. How are the angles of triangles and rectangles similar or different?
Similarity: Both shapes have angles whose total sum is fixed.
Difference:
★ A triangle has 3 angles, and they can be acute, obtuse, or right (but their sum is always 180°).
★ A rectangle has 4 angles, and all of them are right angles (90°).
Q. Use the dot grid given below to draw several three and four-sided shapes. Circle the shapes that have one or more right angles.
Sol.
Do it yourself
Q. Here are some 4-sided shapes. In what ways are the rectangle and square different from these shapes?
Sol.
Rectangles and squares have all the corners as square corners while the given shapes have not square corners.
Q. Try to make this 5-sided shape with all sides equal (Pentagon). Are these right angles?
Sol.
No.
Q. Does the shape of the pentagon change if we gently push one of its sides?
Are these right angles?
Does the shape of the pentagon change if we gently push one of its sides. Yes/No
How does this change the angles?
Q. 1. Are these right angles?
Ans. No, these are not all right angles. Some angles may be smaller or larger than 90°.
Q. 2. Does the shape of the pentagon change if we gently push one of its sides? (Yes/No)
Ans. Yes, the shape of the pentagon changes.
Q. 3. How does this change the angles?
Ans. When we push one side, the angles change:
★ Some angles become acute (less than 90°).
★ Some angles become obtuse (more than 90°).
So, the angles are no longer the same as before and are not all right angles.
Q. Can you make a circle using straws?
Look at the picture. The lengths of the straws in this picture are ______________
Sol. Equal
Q. What will happen if we take straws of unequal lengths?
Sol. A circle cannot be formed.
Let Us Make
Q. Can you use a scale to draw a circular shape? Let us see. Mark a point A.
Draw many points that are at an equal distance from point A.
Connect the dots freehand. What do you get? …………….
The point A is the centre and the line from the centre to the border of the circle is the radius.
(Page 17)
Amazing Circles
a) Take a piece of circular paper.
b) Fold your paper in half and crease it well.
c) Open the fold and measure the length of the crease using a thread.
d) Fold your paper in half in a different way and crease it well.
e) Open the fold and measure the length of the crease again.
f) Fold it again in half in a different way and crease it well.
g) Open the fold, measure the length of the crease.
Sol. Equal
2. These creases are called ___________ of the circle.
Sol. diameters
3. Discuss where the centre is. Do you notice that all the diameters pass through the centre?
Sol. Centre is the point of intersection of all the crease.
Yes, all the diameters pass through the centre.
4. Measure the length of the creases from the center to the border of the circle. This is called the ___________ of the circle.
Sol. radius
5. Discuss if there is any relationship between the radius and the diameter of a circle.
Sol. Radius is half of the diameter of the circle.
R = D / 2
Look Pages 18-19
Let Us Do
Q. Fold the circular paper in half.
Fold this half again in half.
The length of the diameter is ___________ (half/double) of the length of radius.
Sol. The length of the diameter is double of the length of radius.
Look at the wheels
Sol. All the wheels look like a circle
Q. Name the wheel with the
1. longest radius ………………….
2. shortest radius ………………….
3. longest diameter ………………….
4. shortest diameter ………………….
Sol.
1. longest radius wheel B
2. shortest radius wheel D
3. longest diameter wheel B
4. shortest diameter wheel D
(Pages 19-20)
Puzzling Shapes
Q. 1. Identify the hidden shapes and write their names.
Sol.
The hidden shapes are triangle, square, rectangle, circle, and cylinder.
Q. 2. Draw 2 lines to divide the triangle into 1 square and 2 triangles.
Sol.
Q. 3. Draw 2 lines to divide the square into 3 triangles.
Sol.
(Page 21)
Let Us Try
1. Squiggly spiders
Squiggly, the spider, likes to make webs in different shapes. One day she begins to make triangular webs.
Q. How many triangles are in her web?
Sol. There are 10 triangles in Squiggly’s web.
She likes to take a walk each morning in search of web strength.
Q. Can she begin at point A and reach back to the same point without walking on any wall more than once?
Trace and show Squiggly’s path.
Sol. Yes, Squiggly can begin at point 'A' and reach back to the same point 'A' without walking on any wall more than once by following the order of the walls as shown.
Q. Her brother, Wiggly made a web using rectangles. How many rectangles can you see in his web?
There are 12 rectangles in Wiggly’s web.
He likes to take a walk at the end of each day and check if the walls of his web are strong. Can he begin at point A and leave from point B without walking on any wall more than once?
Trace and show Wigggly’s path.
Solution:
No, Wiggly cannot start from A and leave from B without walking on any walls more than once and also go through all the walls.
Question 2.
Use 5 matchsticks to draw 2 triangles.
Solution:
Question 3.
Move any two of these matchsticks to form 4 triangles.
Solution:
Question 4.
Remove 4 of these matchsticks to leave only _________
Solution:
Question 5.
Model challenge.
Can you make a model of solid shapes which has _________
(а) 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?
Solution:
Question 6.
Classify these shapes based on the number of angles.
Solution:
What relation do you notice between the number of sides and the number of angles?
Solution:
In the figure, the number of sides is equal to the number of angles.
Question 7.
Draw a 2D shape which has less than 5 angles.
Solution:
Following is a 2D shape having only 4 angles.
Draw a 2D shape with more than 5 angles.
Solution:
Following is a 2D shape having 6 angles.
Question 8.
Mark the right angles and write the number of right angles in each figure.
Which of the above shapes have only right angles?
Solution:
The first and the last shapes in the given figure have only right angles.
Question 9.
Identify the shape that has:
Identify the shape that has:
- 2 right angles, 1 acute, and 1 obtuse angle ______________.
- 1 right, 2 obtuse, and 1 acute angle ___________.
- 2 obtuse, and 2 acute angles _____________.
- 4 right angles ____________.
Solution:
- 2 right angles, 1 acute, and 1 obtuse angle 2, 7
- 1 right, 2 obtuse, and 1 acute angle 10
- 2 obtuse, and 2 acute angles 3, 5, 8, 9,11, 13
- 4 right angles 4, 6, 12, 14
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