Grandmother’s Quilt – Class 5 Maths Chapter 11 Notes & NCERT PDF

Class 5MathematicsChapter 11NCERT book: Maths Mela - Mathematics Class 5

Notes and a simple summary of Chapter 11 of the NCERT Class 5 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 11: Grandmother’s Quilt

Introduction

Preetha and Adrit’s grandmother has made a quilt cover from old clothes and now wants to sew lace all around its border. Which lace is long enough? To answer, the children must find the length of the border — the perimeter. Later, Grandmother makes a rug and a patchwork from square patches, and the children find out how many patches cover it — that is the area. This chapter teaches the difference between these two ideas and simple ways to calculate both.

Perimeter = the length of the border (boundary) of a shape.

Area = the amount of surface (region) a shape covers.

Key Ideas

1. Perimeter — going around the border

To find the perimeter, add the lengths of all the sides.

A square with side 5 cm has perimeter 5 + 5 + 5 + 5 = 20 cm.

Different rectangles can have the same perimeter. For a perimeter of 18 cm you can draw 5 cm × 4 cm or 6 cm × 3 cm.

2. Area — covering without gaps and overlaps

Preetha covered tables with triangles and circles; Adrit used squares and rectangles.

Triangles, squares and rectangles tile (cover the table with no gaps and no overlaps). Circles leave gaps, so they cannot be used to measure area.

The number of tiles that cover a region is its area, e.g. “the area of Table 3 is ___ square units”.

You can even measure area with notebooks, lunch boxes or textbooks — but only if they cover the region completely.

3. The unit square and square grids

Comparing rectangles A, B and C by eye is hard. Put them on a square grid and count squares!

A square with sides of 1 unit has an area of 1 unit square (1 cm side → 1 square cm).

Using grids you can find the approximate area of your palm or of leaves: count full squares, and count squares that are about half or more as one.

4. Same area ≠ same perimeter

Shapes made of the same number of squares (same area) can have different perimeters.

Shapes with the same perimeter can have different areas.

Trisha says, “I increased the area of my rectangle, and the perimeter increased.” This is not always true — a longer, thinner shape can have a bigger perimeter but a smaller area.

5. Formulas for rectangles and squares

Grandmother arranges patches in 6 rows of 4 patches — no need to count one by one: 6 × 4 = 24 patches.

Area of rectangle = Length × Breadth

Perimeter of rectangle = 2 × Length + 2 × Breadth (opposite sides are equal)

Area of square = Side × Side, Perimeter of square = 4 × Side

Area is written in square units (square cm, square m); perimeter in units of length (cm, m).

Worked Examples

Example 1 (patchwork): 6 cm × 4 cm rectangle.

Area = 6 × 4 = 24 square cm

Perimeter = 2 × 6 + 2 × 4 = 12 + 8 = 20 cm

Example 2 (square): side 5 cm.

Area = 5 × 5 = 25 square cm; Perimeter = 4 × 5 = 20 cm

Example 3 (field): A rectangular field is 42 m long and 34 m broad.

Area = 42 × 34 = 1428 square m

Example 4 (finding breadth): A garden has area 64 square m and length 16 m.

Length × Breadth = 64 → 16 × ? = 64 → Breadth = 64 ÷ 16 = 4 m

Example 5 (same perimeter, different area): Rectangles with perimeter 20 cm:

9 cm × 1 cm → area 9 square cm

7 cm × 3 cm → area 21 square cm

5 cm × 5 cm → area 25 square cm (the square gives the biggest area!)

Maths Words

Perimeter (परिमाप) – length of the boundary

Area (क्षेत्रफल) – surface covered by a shape

Border / Boundary (किनारा / सीमा)

Tile / Tiling (टाइल लगाना) – covering with no gaps or overlaps

Gap (खाली जगह), Overlap (एक के ऊपर एक आना)

Unit square (इकाई वर्ग) – a square of side 1 unit

Square grid (वर्गांकित जाल)

Length (लंबाई), Breadth (चौड़ाई)

Square cm / Square m (वर्ग सेमी / वर्ग मीटर)

Maths in Daily Life

Lace for a tablecloth, fencing a garden, a frame for a photo → perimeter.

Tiles for a floor, carpet for a room, paint for a wall → area.

Measure your classroom floor with your teacher and find its area in square metres.

Common Mistakes

Mixing up the two: adding sides when area is asked, or multiplying when perimeter is asked.

Writing area in cm instead of square cm.

Adding only two sides of a rectangle (Length + Breadth) and forgetting to double.

Believing that a bigger perimeter always means a bigger area.

Counting circles as tiles — circles always leave gaps.

Practice Tips

Before solving, ask: “Am I going around* (perimeter) or covering (area)?”*

Draw the shape on squared paper and check your formula answer by counting.

Play the tile-and-die game: add tiles to a shape and track its perimeter until it reaches 24.

💡 Key Learning Points

✓Perimeter is the length of the border; it is found by adding all the sides.
✓Area is the region covered by a shape, measured by tiling with no gaps and no overlaps; circles cannot tile.
✓A square of side 1 unit has area 1 unit square; square grids make comparing areas easy.
✓Area of rectangle = Length × Breadth; Perimeter = 2 × Length + 2 × Breadth; for a square, Area = Side × Side and Perimeter = 4 × Side.
✓Shapes with the same area can have different perimeters, and shapes with the same perimeter can have different areas.

👨‍🏫 Teaching Tips

→Bring a real cloth or handkerchief and let children measure lace/string needed for its border before naming it ‘perimeter’.
→Give paper triangles, squares, rectangles and circles to cover a desk top; let children discover that circles leave gaps.
→Let every child trace their palm and a leaf on 1 cm grid paper and estimate the area by counting squares.
→Make 12-square shapes with square tiles in different arrangements and record the perimeter of each to show same area, different perimeter.
→Show Grandmother’s patchwork as rows × columns and link area to the multiplication array children already know.
→Measure the classroom floor together with a measuring tape and calculate its area and perimeter.
→Play the textbook’s die-and-tiles game in pairs until the perimeter becomes 24.

📋 Assessment Questions

Can the child explain the difference between area and perimeter using a real object?
Can the child find the area of a shape on a square grid by counting unit squares?
Can the child use Area = Length × Breadth and Perimeter = 2 × (Length + Breadth) correctly with proper units?
Can the child find a missing side when area and one side are given (e.g. 64 square m, length 16 m)?
Can the child draw two shapes with the same area but different perimeters?

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