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Key Point: Perimeter of a square = 4 × side (P = 4a)
What are shapes? Shapes are the outlines or forms of objects. We study two kinds of shapes: 2‑dimensional (2D) shapes which lie on a flat surface (for example: circle, triangle, square, rectangle) and 3‑dimensional (3D) shapes which have volume (for example: sphere, cube, cylinder, cone).
Key features to observe
How to identify a shape in real life
Simple activity idea: Walk around a classroom or home and list 10 objects, name their shapes and count sides/corners. Make groups: all circles, all rectangles, etc.
Key Point: Perimeter of a square: P = 4 × side
What are 2D shapes?
Two-dimensional (2D) shapes are flat figures that lie on a plane. They have length and width but no thickness. Examples are circle, triangle, square and rectangle.
Basic parts and terms
Kinds of 2D shapes
How to recognise and compare shapes
Why 2D shapes are useful
We use 2D shapes to read maps, design signs, make art, measure rooms on paper and recognise objects around us.
Key Point: Volume of cube: V = a^3 (a = edge length). Units: cubic units (e.g., cm^3).
What are 3D shapes? Three-dimensional (3D) shapes are solids that have length, breadth (width) and height (thickness). Unlike flat 2D shapes, 3D shapes occupy space and you can hold them. They have faces (flat or curved parts), edges (where two faces meet) and vertices (corner points where edges meet).
Two groups of 3D shapes
Common 3D shapes and their simple properties
Nets and models: A net is a flat layout of all faces of a solid that can be folded to form the 3D shape (for example the cross-shaped net of a cube). Making nets with paper and folding them helps understand how faces join along edges.
How to recognise 3D shapes in real life: Look for objects that have depth as well as length and width — e.g., a dice is a cube, a shoebox is a cuboid, a can of juice is a cylinder, an ice-cream cone is a cone, a ball is a sphere.
Key Point: Perimeter of a square: P = 4 × a (a = side length).
What is a shape? A shape is a flat (2D) figure made by joining lines or curves. Shapes can be closed (form a boundary) or open. We study their important properties so we can recognise, compare and use them in real life.
Basic properties to know
Regular vs Irregular — Regular shapes have all sides and angles equal (regular polygons). Irregular shapes have sides or angles of different sizes.
Examples of common 2D shapes and their typical properties:
Key Point: Perimeter of a polygon = sum of the lengths of all its sides.
What is a shape? A shape is the form of an object or its outline. In Class 4 we study two main kinds: 2D (flat) shapes and 3D (solid) shapes.
2D shapes (flat): Examples are triangle, square, rectangle, circle, pentagon. Important properties to notice: number of sides, number of vertices (corners), whether sides are straight or curved, and whether sides or angles are equal.
3D shapes (solid): Examples are cube, cuboid, sphere, cylinder, cone. Important properties: faces (flat surfaces), edges (lines where faces meet), and vertices (corner points). Some solids have curved surfaces (sphere, cylinder, cone).
How to sort and classify shapes
Simple classroom method to sort: Choose one property at a time (e.g., number of sides). Make groups and place shape pictures into each group. Use a table or Venn diagram if a shape belongs to two groups (for example, a square is both a quadrilateral and a regular polygon).
Why this helps: Sorting builds observation skills. Classifying by properties (sides, corners, curves, faces) helps students see patterns and relate shapes to real-life objects.
Activities to try: make a shape-hunt (find objects around you that match shapes), create a classification chart, draw a tree diagram starting from 2D → polygons → triangles/quadrilaterals → special types (square, rectangle).
Key Point: Arithmetic pattern (equal difference): nth term = a + (n - 1) × d, where a = first term, d = common difference. Example: for 2, 4, 6... a=2, d=2, nth = 2 + (n-1)×2 = 2n.
What is a pattern? A pattern is a repeated or regular arrangement of shapes, colours, numbers or objects. Patterns make designs attractive and help us predict what comes next.
Types of patterns
How to read and continue a pattern
Why patterns matter
Patterns appear in clothes, buildings, nature, and number work. Learning patterns helps develop observation, logic and early algebraic thinking.
Key Point: Line reflection rules in a simple coordinate form (introductory): - Reflection across y-axis (vertical mirror): (x, y) → (−x, y) - Reflection across x-axis (horizontal mirror): (x, y) → (x, −y) - Reflection through the origin (turning 180°): (x, y) → (−x, −y)
What is symmetry? Symmetry means that one part of a shape or object matches exactly with another part when folded or reflected. If a line can be drawn so that the two halves of a figure are exactly the same, the line is called the line of symmetry (or axis of symmetry).
What is a mirror image? A mirror image is what you see when an object is reflected in a mirror. The left and right sides swap places. For example, if you raise your right hand, your mirror image appears to raise its left hand.
Types of symmetry:
How to test for symmetry: Fold method: Fold a paper shape along a guessed line of symmetry — if the edges and patterns match exactly, the line is a symmetry line. Mirror method: Place a mirror along the guessed line; if the reflected half completes the original to make a full shape, the line is a symmetry line.
How to draw mirror images (simple methods):
Why it matters: Symmetry helps in art, design, nature study and geometry. Recognising symmetry builds observation and drawing skills and is used to make patterns and shapes neatly.
Key Point: Perimeter of a square = 4 × side (P = 4a)
What are shapes? Shapes are forms made by joining lines. They can be flat (2D) like squares, triangles and circles, or solid (3D) like cubes and spheres. In this topic we learn how to make, identify and draw common 2D shapes and see them around us.
Basic terms:
Tools for making and drawing shapes: Ruler (to measure and draw straight sides), compass (to draw circles and arcs), pencil, eraser, and grid/squared paper (helps to draw accurate shapes). Paper folding (origami) and cutting are simple ways to make shapes physically.
How to draw common shapes (step-by-step):
Tips for neat drawings: Use a sharp pencil, draw lightly first and darken final lines, use a ruler for straight edges, use grid paper to keep sides even, and label vertices (A, B, C ...) and side lengths.
Why this matters (real-world view): Recognising and drawing shapes helps us describe objects, plan designs, measure fencing or framing using perimeters, and make art and maps. Finding shapes around you improves observation and spatial thinking.
Key Point: When the sun’s rays make an angle θ with the ground, height / shadow length = tan(θ). So shadow length = height / tan(θ). (Introduces relation using angle of elevation.)
Views: When we look at an object from different sides we get different views. The three common views are:
Shadows: A shadow is a dark shape made when light is blocked by an object. Shadows depend on the position of the light source:
Perspectives: Perspective is how objects appear to us depending on where we stand. Things that are nearer look bigger; things that are farther look smaller. Artists use perspective lines (they meet at a vanishing point on the horizon) to show depth in drawings.
How these ideas connect: Using views helps us draw objects correctly. Shadows show where the light is and how tall or far the object is compared to its shadow. Perspective helps show depth so objects look real in pictures.
Key Point: Perimeter of a rectangle = 2 × (length + breadth)
Everyday Uses and Creative Work shows how simple mathematics helps us in daily tasks and in making art or useful objects. It links counting, measuring, shapes and patterns to real life. Children use these ideas when they measure cloth, wrap gifts, plan a garden bed, make a Rangoli, draw a card or arrange tiles on a floor.
Key ideas:
How to approach a simple creative task: