Shapes and Patterns
Weaving patterns, tiling, types of triangles and quadrilaterals, tangrams, circle designs, and 3-D shapes.
- How weaving patterns repeat (over–under rules)
- Which shapes tessellate (fit together without gaps)
- Triangles: equilateral, isosceles, and scalene
- Quadrilaterals: kite, parallelogram, rectangle, rhombus, and square
- Circle designs, cube puzzles, and solids like the icosahedron
🧺 Let’s Begin: Patterns in a Charpai
Look closely at a charpai (string cot) or a chatai (mat). The rope goes over one, under one, over one, under one… The next row starts the opposite way: under one, over one…
That’s a pattern rule! Change the rule, like “2 over, 1 under”, and you get a new design.
🧵 Part 1: Weaving Patterns
A weaving pattern is written as a rule for each row:
| Row | Rule | Looks like (■ = over, □ = under) |
|---|---|---|
| 1 | 1 over, 1 under | ■ □ ■ □ ■ □ |
| 2 | 1 under, 1 over | □ ■ □ ■ □ ■ |
| 3 | same as row 1 | ■ □ ■ □ ■ □ |
This makes a chessboard pattern. Try a “2 over, 2 under” rule and shift each row by one box. You’ll get slanting stripes!
🧩 Part 2: Tiling and Tessellation
When shapes cover a floor without gaps and without overlapping, we say they tessellate. Think of floor tiles, a honeycomb, or brick walls.
A regular shape has all sides equal and all angles equal.
| Regular shape | Tessellates alone? | How many fit around one point |
|---|---|---|
| Equilateral triangle | ✅ Yes | 6 |
| Square | ✅ Yes | 4 |
| Regular hexagon | ✅ Yes (like a honeycomb) | 3 |
| Regular pentagon | ❌ No, it leaves a gap | 3 fit, with a gap |
| Regular octagon | ❌ No | 2 fit, with a gap |
Why? Around a point, the shapes must make exactly one full turn. Six triangle corners, four square corners, and three hexagon corners each make exactly a full turn. Pentagon corners don’t add up to a full turn.
Some patterns mix shapes, like octagons with small squares filling the gaps (you’ve seen this on old floors!), or hexagons with triangles.
🔺 Part 3: Types of Triangles
| Triangle | Sides | Angles | Example |
|---|---|---|---|
| Equilateral | All 3 equal | All 3 equal | A samosa cut perfectly |
| Isosceles | 2 equal | 2 equal | A roof top, a kite’s corner |
| Scalene | None equal | None equal | A torn piece of paper |
Fold an equilateral triangle in half. Each half is a scalene triangle with a right angle.
🔷 Part 4: Four-Sided Shapes (Quadrilaterals)
| Shape | Sides | Angles |
|---|---|---|
| Kite | Two pairs of adjacent (neighbouring) sides are equal | One pair of opposite angles is equal |
| Parallelogram | Opposite sides are equal | Opposite angles are equal |
| Rectangle | Opposite sides are equal | All 4 are right angles |
| Rhombus | All 4 sides are equal | Opposite angles are equal |
| Square | All 4 sides are equal | All 4 are right angles |
Shape family: A square is a special rectangle (all sides equal). It is also a special rhombus (all right angles). A rectangle and a rhombus are special parallelograms.
✅ A square has 4 right angles and equal opposite sides, so it is a rectangle too, just a special one!
⭕ Part 5: Circles and Designs
Draw a circle and two diameters (lines through the centre). Join their four end points and you always get a rectangle. If the diameters cross at a right angle, the rectangle becomes a square!
String art: Mark 24 equal points on a circle. Join each point to the one some steps ahead, like 1 → 11, 11 → 2, 2 → 12 … Curved flower-like designs appear, made only of straight lines.
🧊 Part 6: Cubes and Solids
A cube made of 3 × 3 × 3 = 27 small cubes, painted on the outside:
| Painted faces | Where are they? | How many |
|---|---|---|
| 3 faces | Corners | 8 |
| 2 faces | Middle of each edge | 12 |
| 1 face | Centre of each face | 6 |
| 0 faces | Hidden in the very middle | 1 |
Check: 8 + 12 + 6 + 1 = 27 ✅
Special solids: An icosahedron has 20 faces (“icosa” = 20), all equilateral triangles. A dodecahedron has 12 faces (“dodeca” = 12), all regular pentagons.
❌ Common Mistakes to Avoid
✅ Regular pentagons and octagons leave gaps.
✅ Kite: neighbouring sides equal. Parallelogram: opposite sides equal.
✅ Count layer by layer.
✅ Check both the sides and the angles.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Pages 92–93 · Weaving MatsPaper mats and patterns
Which regular shapes fit around a point?
Shapes in the pattern
Same shapes at each point?
Triangles and quadrilaterals from 2 pieces
Q2: An equilateral triangle is possible only if the rhombus has a 60° angle, so with this rhombus it is usually not possible.
Q3: A single rhombus piece is itself a triangle with all sides unequal (scalene), so yes.
Try This: all angles of an equilateral triangle are equal. After cutting it in half, each new triangle has no equal sides (scalene), and no two angles are equal.
Q4: You can make a kite, a parallelogram, and a rectangle.
Q5: In A and B, opposite sides are equal. A has 2 acute and 2 obtuse angles, and its opposite angles are equal. B has 4 right angles (a rectangle).
More shapes from the pieces
Q7: With 3 pieces you can make a triangle, a 4-sided shape (like a trapezium or parallelogram), and a 5-sided shape.
Q8: With all 4 pieces you can make a rectangle, a triangle, a pentagon, and a hexagon. A square is possible only if the rhombus was a square. An octagon is not possible.
Tangram: 5 triangles (2 big, 1 medium, 2 small), 1 square, and 1 parallelogram. All the triangles are right-angled isosceles triangles. The square has 4 right angles, and the parallelogram has 2 acute and 2 obtuse angles.
Match the statements
Yes, some statements describe more than one shape, because these shapes are “family members”.
Kite from paper: You can see a kite, and triangles inside it.
Diameters and circle designs
Circle design: join each point to the point 10 steps ahead (1 → 11 → 2 → 12 …). To copy the given design, find the jump size by checking which point the first line goes to.
Views, frames, and painted cubes
Q2: (a) 3 × 3 × 3 cube: 27 − 20 = 7 removed (b) 4 × 4 × 4 cube: 64 − 32 = 32 removed (c) 5 × 5 × 5 cube: 125 − 44 = 81 removed. (A frame keeps only the 12 edges: 8 corners + the cubes along each edge.)
Q3: (a) 8 (b) 12 (c) 6 (d) 1
Puzzle: Circle, Square, Rectangle, Triangle, Square, Triangle, Hexagon
Count faces, vertices, and edges
| Icosahedron | Dodecahedron | |
|---|---|---|
| Face shape | Equilateral triangles | Regular pentagons |
| Number of faces | 20 | 12 |
| All faces the same? | Yes | Yes |
| Faces at each vertex | 5 (same everywhere) | 3 (same everywhere) |
| Edges | 30 | 30 |
👨👩👧 Tips for Parents
- Look for tiling patterns on floors, walls, and footpaths, and name the shapes together.
- Fold paper to make kites, triangles, and squares.
- Weave paper strips or look at a charpai and describe the over–under rule.