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Mathematics: Class 2 — Chapter 4: Shadow Story (Togalu)

4.1 Introduction to Shadows

Nakul and his friends saw a shadow play known as Togalu Gombeyaata in a village fair. They were fascinated by the shadows and started making different animal shadows on the wall using their fingers.

Togalu Gombeyaata: This is a traditional shadow puppetry art form practised in Karnataka, India. The puppets are used to depict scenes from Indian epics.

Let us Talk & Do
  • Role-play: Try making shadows of different animals with your hands and create their sounds.
  • Have you seen your own shadow or the shadow of a tree, a dog, or a cow?
  • When do we see a shadow? (We see a shadow when an object blocks light).
  • When does a shadow vanish? (A shadow vanishes when there is no light source or when the light is completely blocked or diffused).
4.2 Fun with Shadows

By shining a torch light on different 3D objects, we can observe the shapes of their shadows:

  • A cube casts a square shadow.
  • A cone casts a triangular shadow.
  • A cylinder casts a rectangular or circular shadow depending on the direction of light.
  • A sphere casts a circular shadow.

Key Observations
  • Size of Shadows: The size of a shadow changes when we change the position of the light source (torch) relative to the object.
  • Shadow Length during the Day:
    • Your shadow is longest in the early morning and late afternoon when the Sun is low in the sky.
    • Your shadow is shortest at noon when the Sun is directly overhead.
4.3 Tracing Shapes

We can trace the outlines of 3D objects on paper to find their 2D shapes:

  • Tracing a matchbox or eraser gives a Rectangle.
  • Tracing a bottle cap or coin gives a Circle.
  • Tracing a sharpener or pencil box can give various rectangular or polygonal shapes.
4.4 Hide and Seek (Shapes)

Basic 2D shapes like Circle, Rectangle, Triangle, and Square can hide behind objects that share their shape profiles:

  • A Circle can hide in circular objects like a clock, a ball, a wheel, or a plate.
  • A Rectangle can hide in rectangular objects like a shoe box, a photo frame, a book, or a television screen.
  • A Triangle can hide in triangular objects like a slice of pizza, a hanger, a traffic sign, or a sandwich.
  • A Square can hide in square objects like a cushion, a chessboard, a window pane, or a tile.
4.5 Corners and Edges

Catch the Corner Game

In a game played around a rectangular table, children run along the table. When the clapping stops, the child who is not at a corner is out.

  • Corners: The points where two edges meet. A rectangular table has $4$ corners.
  • Edges: The outer boundaries of an object. A rectangular table has $4$ straight edges.
  • Round Tables: This game cannot be played around a round table because a circle has no corners!

Straight vs. Curved Edges
  • Straight Edges: Objects like books, tables, rulers, and boxes have straight edges and corners.
  • Curved Edges: Objects like balls, clocks, and watermelons have curved edges and zero corners.
  • Both Straight and Curved Edges: Objects like a sliced watermelon, a protractor, or a cylinder have both straight and curved edges.

Origami Fun (Paper Folding)
  • A square sheet of paper has $4$ corners and $4$ edges.
  • Folding it in half diagonally by joining two opposite corners creates a triangle, which has $3$ corners and $3$ edges.
  • By folding the corners of the triangle, we can create different shapes, such as a paper dog!
4.6 Patterns and Designs

Patterns can be created by repeating shapes, stamps, or natural objects in a sequence.

  • Stamping: Using objects like bottle caps, erasers, and coins to stamp repeating designs.
  • Leaf Printing: Painting one side of a leaf and printing it repeatedly to form beautiful natural patterns.
  • Visual Patterns: Extending sequences of shapes, arrows, letters, or colors (e.g., alternating up and down arrows: $\uparrow \downarrow \uparrow \downarrow$).
4.7 Number Patterns

Number patterns are sequences of numbers that follow a specific rule of addition or subtraction.

Jumping Patterns
  • Kikku Rabbit's Jumps (Skip counting by $3$): Starting at $1$, Kikku jumps on every $3\text{rd}$ tile:
    $$1, 4, 7, 10, 13, 16, 19, 22, 25, 28, \dots$$
  • Kikku's Mother's Jumps (Skip counting by $5$): Starting at $1$, she jumps on every $5\text{th}$ tile:
    $$1, 6, 11, 16, 21, 26, \dots$$

Extending Number Sequences
  • Pattern A (Adding $5$): $5, 10, 15, 20, 25, 30, 35, 40, \dots$
  • Pattern B (Adding $7$): $7, 14, 21, 28, 35, 42, 49, 56, \dots$
  • Pattern C (Adding $6$): $1, 7, 13, 19, 25, 31, 37, 43, \dots$