📖 NOTES
Class 5
Chapter 7: Shapes and Patterns
Math Mela · Quick Revision Notes
Class 5Math Mela (NCERT)Chapter 7
📚 What's in this Chapter
🧺 Weaving Patterns
Weaving mats and baskets follow repeating patterns of strips going over and under each other.
🔑 Describing a Weave
Row 1 — 1 under, 1 over, 1 under, 1 over... (repeat)Row 2 — 1 over, 1 under, 1 over, 1 under... (repeat, opposite of Row 1)
💡 Patterns can get more complex too — like "2 over, 1 under, 2 over, 1 under" — the key skill is spotting what repeats!
🔷 Tiling & Tessellation
🔑 Key Terms
Regular shape = all sides (and angles) are equal.Tessellate = shapes fit together perfectly around a point with NO gaps and NO overlaps.
| Regular Shape | Angle at each corner | Fit around a point (360°)? | Tessellates? |
|---|---|---|---|
| Equilateral Triangle | 60° | 360÷60=6 triangles fit exactly | ✅ YES |
| Square | 90° | 360÷90=4 squares fit exactly | ✅ YES |
| Regular Pentagon | 108° | 360÷108=3.33 (doesn't divide evenly) | ❌ NO |
| Regular Hexagon | 120° | 360÷120=3 hexagons fit exactly | ✅ YES |
| Regular Octagon | 135° | 360÷135=2.67 (doesn't divide evenly) | ❌ NO |
🌟 Big idea: A regular shape tessellates ONLY if its corner angle divides evenly into 360°!
🔺 Types of Triangles
| Triangle | Sides | Angles |
|---|---|---|
| Equilateral | All 3 sides equal | All 3 angles equal (60° each) |
| Isosceles | 2 sides equal | 2 angles equal |
| Scalene | No sides equal | No angles equal |
💡 A rhombus can be divided into 4 triangles, each with 2 equal sides — that's why they're isosceles!
🔶 Types of Quadrilaterals
🪁 Kite
Has two pairs of adjacent sides equal (Side1=Side2, and Side3=Side4) — NOT opposite sides.▱ Parallelogram
Has opposite sides equal, and opposite angles equal too.▭ Rectangle
A special parallelogram where all angles are right angles (90°).| Shape | Sides equal? | Angles |
|---|---|---|
| Kite | Adjacent pairs equal | One pair of opposite angles equal |
| Parallelogram | Opposite sides equal | Opposite angles equal |
| Rectangle | Opposite sides equal | All angles = 90° |
| Rhombus | All 4 sides equal | Opposite angles equal |
| Square | All 4 sides equal | All angles = 90° |
⭕ Circles & Circle Designs
🔑 Parts of a Circle
Centre = the middle point. Diameter = a line through the centre touching both sides of the circle.Joining the endpoints of TWO diameters (4 points total) always forms a rectangle! If the two diameters happen to be equal in a special way, you can even get a square.
🧊 3-D Shapes — Cubes & Solids
| Solid | Faces | Face Shape | Faces meeting at a vertex |
|---|---|---|---|
| Icosahedron | 20 | Triangles | 5 |
| Dodecahedron | 12 | Pentagons | 3 |
| Cube | 6 | Squares | 3 |
🔑 Painted Cube Positions
When a big cube (made of smaller cubes) is painted on the outside:- Corner cubes — always have 3 faces painted (there are always 8 corners)
- Edge cubes — have 2 faces painted
- Face-centre cubes — have 1 face painted
- Interior cubes — have 0 faces painted (completely hidden inside)
📝 Chapter Summary
- Weaving patterns follow repeating over/under sequences
- A shape tessellates only if its corner angle divides evenly into 360°
- Triangles: equilateral (3 equal sides), isosceles (2 equal), scalene (0 equal)
- Kite = adjacent sides equal; Parallelogram = opposite sides equal; Rectangle = parallelogram with right angles
- Two diameters of a circle, joined at their endpoints, always form a rectangle
- Painted cube: corners=3 faces, edges=2 faces, face-centres=1 face, interior=0 faces painted