Notes: Shapes & Spatial Understanding | Mathematics & Pedagogy Paper 1 for CTET & TET Exams - CTET & State TET PDF Download

Shapes and spatial understanding are crucial components of early childhood education, particularly in the context of the Central Teacher Eligibility Test (CTET). These concepts help children develop cognitive skills and understand their environment.

Shapes: Children learn to identify, name, and describe various shapes such as circles, squares, triangles, and rectangles. Recognizing shapes helps in the development of visual perception and categorization skills.

Spatial Understanding: This involves comprehending the position, direction, and movement of objects in space. Key skills include recognizing patterns, understanding symmetry, and grasping concepts like near, far, above, and below. Spatial reasoning is foundational for subjects like mathematics and science, and it also enhances problem-solving abilities.
What are Shapes?

In Mathematics, shapes define the outline or the boundary of an object. The shapes can be classified into different types based on their properties. In general, the shapes are closed by an outline or boundary, which is made up of points, lines and curves, and so on.

Types of Shapes

• Plane shapes are known as 2D shapes (Two dimensional shapes).
• Solid shapes are called 3D shapes (Three dimensional shapes).

➤ 2D Shapes
Shapes like circle, triangle, square, rectangle and oval are called flat or plane shapes.

• Triangle: A triangle has 3 corners and 3 sides. The sides may or may not be equal.
  
• Square: A square has 4 corners and 4 sides. All its sides are equal.
  
• Rectangle: A rectangle has 4 corners and 4 sides. Its opposite sides are equal.
  
• Circle: A circle has no corners and no sides.
  
• Oval: An oval also has no corners and no sides.
  

➤ 3D Shapes
Shapes like cube, cuboid, cone, sphere and cylinder are called solid shapes.

• Cube: A cube has 6 faces, 12 edges and 8 corners. All the faces of a cube are equal.
  
• Cuboid: A cuboid has 6 faces, 12 edges and 8 corners. Opposite faces of a cuboid are equal.
  
• Sphere: A sphere has 1 face, 0 edges and 0 corners.
  
• Cone: A cone has 2 faces, 1 edge and 1 corner.
  
• Cylinder: A cylinder has 3 faces, 2 edges and 0 corners.
  

Point

• It is like a dot. A point has no shape, breadth, length or height.
• It is always named by a capital letter.
• For example: Point P.
• A line is formed by placing many points next to each other
  

Straight and Curved Lines

Hold a thread and stretch it tightly, you get a straight line. Now if you hold it loosely, you get a curved line. Straight line is a line in which both the ends never meet each other. Straight lines may be

This is a scale. We use it to draw straight lines.

Curved line is a line in which both ends may or may not meet each other.

Circle

A circle can be defined as a simple closed curve all of which points are equidistant (at an equal distance) from the fixed point called its centre.
A bangle, a one rupee coin and a cycle tyre are all examples of circular objects.

Terms Related to Circle

(i) Centre: The fixed point in the centre of a circle is called its centre.
(ii) Diameter: Diameter is a line segment that has its endpoints on the circle and passes through the centre.
Diameter = AB
AB = (OA + OB) = 2 × OA or 2 × OB

Radius is half of the diameter.

(iii) Radius: Radius is the distance between the centre of a circle and a point on the circumference.
Radius = OA = OB

Diameter = 2 × Radius
Radius = Diameter ÷ 2

(iv) Chord: Chord is a line segment whose endpoints lie on the circle.
LM, PQ, AB are all chords of the circle. The diameter is the longest chord of the circle.

(v) Arc: Arc is any part of a circle. An arc is usually named by three points out of which two are the endpoints and the third point lies between them. ABC is an arc and is denoted by  .

(vi) Minor Arc: Minor arc is shorter and the major arc is longer.
ABC is a minor arc of the circle. LMN is a major arc of the circle.
Half of a circle is called a semicircle. ABC is a semicircle.

(vii) Circumference: Circumference is the perimeter or boundary of a circle.
Circumference = π × diameter =22/7 × diameter
= 22/7 x 2 x radius
= 2 x 22/7 x radius of the circle

A semicircle is also an arc.

Interior and exterior of a circle

It is clear that

• R lies in the interior of the circle.
  Thus, OR < OA.
• C lies in the exterior of the circle.
  Thus, OC > OA.
• B lies on the circle.
  Thus, OA = OB.

Concentric circles are circles with the same centre but different radii.

Drawing a Circle with Compass

(i) To draw a circle with a compass, fix a pointed pencil in the compass.
(ii) Place a ruler on the table and fix the metal tip of the compass at 0 of the ruler and open the compass to fix the end of the pencil at the given measure (say = 3 cm.)

(iii) Next, take a point ‘O’ on a plane paper and rest the metal tip of the compass at point ‘O’.
(iv) Hold the head of the compass firmly and move the pencil around to form a circle of radius 3 cm.