Chapter 11 — Grandmother's Quilt

Chapter 11 of the Class 5 Mathematics NCERT textbook (Maths Mela), "Grandmother's Quilt", introduces perimeter and area through the story of a grandmother decorating a quilt — download the PDF to explore hands-on activities on measuring borders, tiling shapes, and computing area using the formula Length x Breadth.

• Perimeter as the Border of a Shape — The chapter opens with Preetha and Adrit's grandmother needing lace to cover the entire border of her quilt. Students learn that the total length of a shape's border is called its perimeter, and practise finding the perimeter of shapes whose sides are all equal.
• Area and Tiling — Area is introduced as the region covered when shapes tile a surface without gaps or overlaps. Students discover that squares, rectangles, and triangles tile cleanly while circles leave gaps, making squares the standard unit for measuring area.
• Using Square Grids to Measure Area — The chapter introduces square grids as the most convenient way to find the area of any region. A square with sides of 1 unit has an area of 1 unit square, and students count grid squares to compare areas of gardens, palms, and leaves.
• Area of a Rectangle and Square by Formula — Instead of counting every square, students learn that a rectangle tiled by rows and columns of unit squares has Area = Length x Breadth (for example, 6 cm x 4 cm = 24 square cm), and a square has Area = Length x Length and Perimeter = 4 x Length.
• Relationship Between Area and Perimeter — Through exploration activities, students find that shapes with the same area can have different perimeters, and shapes with the same perimeter can have different areas, showing that the two measurements are independent of each other.

1. 01Perimeter is the length of the border of a shape; the chapter uses a quilt's lace border as the real-world starting point.
2. 02Shapes that tile (fill a surface with no gaps or overlaps) — squares, rectangles, triangles — can be used to measure area; circles cannot tile and leave gaps.
3. 03A square with sides of 1 unit has an area of 1 unit square, which is the standard unit for measuring area on a grid.
4. 04Area of a rectangle = Length x Breadth (e.g., 6 cm x 4 cm = 24 square cm); this connects area to multiplication.
5. 05Area of a square = Length x Length; Perimeter of a square = 4 x Length.
6. 06Two shapes can have the same area but different perimeters, and the same perimeter but different areas — increasing area does not always increase perimeter.
7. 07Hands-on activities include tracing palms and leaves on square grids, measuring classroom floors, and a tile game where players build shapes until the perimeter reaches 24 units.