Chapter 7 — Shapes and Patterns

Chapter 7 of the Class 5 Mathematics NCERT textbook (Maths Mela), "Shapes and Patterns", explores weaving patterns, tessellation, and 2D and 3D geometry through hands-on activities — download the PDF and read a summary of how children learn to classify triangles, quadrilaterals, and solid shapes like icosahedra by doing, folding, and building.

• Weaving Patterns — Students make paper mats by weaving strips in alternating over-under sequences. Different row rules (e.g., 1 under 1 over vs. 2 over 1 under) produce distinct repeating patterns, connecting rhythm in craft to mathematical rules.
• Tiling and Tessellation — The chapter investigates which regular shapes — triangles, squares, hexagons — tile a surface without gaps or overlaps, and which do not. Regular pentagons and regular octagons are shown not to tessellate, while equilateral triangles, squares, and hexagons do.
• Triangles and Quadrilaterals — By cutting triangles from a rhombus and fitting them together, students discover isosceles triangles (2 equal sides, 2 equal angles), equilateral triangles (all sides and angles equal), and scalene triangles (no equal sides). Quadrilaterals covered include kites, parallelograms, and rectangles.
• Tangram and Shape Building — Using a tangram set cut from the textbook, students combine pieces to build new shapes, identifying sides and angles. They also use three or four rhombus triangles to form shapes with 3, 4, 5, or 6 sides.
• 3D Shapes and Cube Puzzles — The chapter introduces nets and views of a cube, asks how many small cubes are removed from a larger frame, and explores 3D solids (icosahedron, dodecahedron) built from nets — counting faces, edges, and vertices at each corner.

1. 01Paper mat weaving uses alternating over-under strip rules; Row 1 and Row 2 follow opposite sequences (1 under 1 over vs. 1 over 1 under) to create the pattern.
2. 02Regular pentagons and regular octagons do not tessellate — they leave gaps when placed around a point. Equilateral triangles, squares, and regular hexagons do tessellate.
3. 03Isosceles triangles have 2 equal sides and 2 equal angles; equilateral triangles have all 3 sides and all 3 angles equal; scalene triangles have no equal sides.
4. 04A kite has two pairs of equal adjacent sides (Side 1 = Side 2 and Side 3 = Side 4). A parallelogram has equal opposite sides and equal opposite angles; a rectangle is a parallelogram with all right angles.
5. 05Joining endpoints of two diameters of a circle forms a rectangle (or square), because the four points lie on the circle and the diagonals are equal and bisect each other.
6. 06Nisha's painted-cube problem: a 3x3x3 cube (27 small cubes) painted red has 8 corner cubes with 3 faces painted, 12 edge cubes with 2 faces painted, 6 face-centre cubes with 1 face painted, and 1 inner cube with no faces painted.
7. 07An icosahedron has triangular faces and a dodecahedron has pentagonal faces; students build both from nets provided at the end of the textbook and compare faces, edges, and vertices.