CBSE Class 5 · Mathematics
Grandmother's Quilt
Official NCERT chapter from Math-Mela (book code eemm1). ExamMaster notes are original teaching at CBSE Class 5 depth.
This lesson follows the official chapter “Grandmother's Quilt” in Math-Mela. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 5
- Easy level
- 8 concepts
1Perimeter is the lace around the quilt
Perimeter is the border length — the lace. Add the side lengths around the outside once.
Counting patches inside is area, not lace.
Figure. Perimeter is the lace around the quilt — one closed walk of the outer edge. It is not the cloth that fills the inside.
How it works
- Walk the outsideEach outer side once.
- Add those lengthsOne unit.
- Call that the perimeterThe lace.
2Equal-side shapes add the same length each side
A square quilt of side 6 spans has perimeter 4 \times 6 = 24 spans. Four equal sides, one multiplication.
A rectangle needs length and breadth: 2 \times (l + b).
Figure. A square adds the same length on every side. The drawn box is a true square: width on screen equals height (side 3).
How it works
- See if sides are equalSquare, or not.
- If square, 4 × sidePerimeter.
- If rectangle, 2 × (length + breadth)Two pairs.
4Area is the region that tiles without gaps
Area is how much cover. Unit squares that tile with no gap and no overlap measure it.
A lace-count is not the cover.
Figure. Area is the region that tiles without leftover gaps. Six equal patches meet edge to edge and cover the quilt.
How it works
- Choose a tileA unit square.
- Cover with no gapAnd no overlap.
- Count the tilesThat count is the area.
5Squares, rectangles, and triangles can tile; a circle leaves gaps
Squares and rectangles tile a quilt. Some triangles can. Circles leave curved gaps — those gaps are not cover of the circle-tiles.
A pretty circle is not a tile for a rectangular quilt without leftover holes.
Figure. Squares and triangles can meet edge to edge. A round patch (not drawn — no arc) would sit inside and leave the four corner gaps.
How it works
- Try the tile shapeSquare, rectangle, triangle, circle.
- See gaps or overlapsEvidence.
- If gaps remain, that shape did not measure this area aloneHoles are leftover.
6Count patches to find how much cover
If each patch is one unit square, 24 patches are area 24. Mixed patch sizes need a rewrite into one unit.
Counting lace loops is the wrong pile.
Figure. Cover is a count of patches that sit inside. Twelve unit squares, counted without holes, are the area.
How it works
- See if patches are the same unitOne size.
- Count themThe cover.
- If sizes mix, convert firstOne unit.
7Perimeter is the border; area is the cover
Two jobs, two numbers. Do not swap the words because both use “how much”.
A longer lace can enclose a smaller cover.
Figure. The 8-by-5 rectangle is to scale (8:5). The walk is 2(8+5)=26 cm; the cover is 8×5=40 square cm. Fence and tiles are different jobs.
How it works
- Ask border or coverWhich job?
- If border, add outside sidesPerimeter.
- If cover, tile the insideArea.
8The quilt is the story; border and cover are two jobs
Grandmother’s quilt is the picture. Perimeter and area are the two maths jobs.
Do not invent a quilt-only plus.
Figure. The quilt is the story. Lace is the border job; cover is the inside job. Mixing the two is a unit error, not a small slip.
How it works
- Keep the settingA quilt.
- Pick the jobLace or cover.
- Use ordinary P and AThe quilt is not a new rule.
A 2-by-8 and a 4-by-6 rectangle (same unit) can share
- Perimeter 20, not the same area
- Area only, never perimeter
- No numbers
Same lace, different cover.
Notes
- The official chapter title is “Grandmother's Quilt”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Formulas
- Square: P = 4s, A = s\times s.
- Rectangle: P = 2(l+b), A = l\times b.
- Perimeter is border; area is cover.
Recap
Hold these pegs from the official chapter “Grandmother's Quilt”. The wording is ExamMaster’s teaching, not a textbook recap.
- Perimeter is the lace around the quilt
- Perimeter is the border length — the lace.
- Equal-side shapes add the same length each side
- A square quilt of side 6 spans has perimeter 4 \times 6 = 24 spans.
- Two rectangles can share a perimeter
- A 2-by-8 and a 4-by-6 both have perimeter 20 if the unit is the same.
- Area is the region that tiles without gaps
- Area is how much cover. Unit squares that tile with no gap and no overlap measure it.
- Squares, rectangles, and triangles can tile; a circle leaves gaps
- Squares and rectangles tile a quilt. Some triangles can. Circles leave curved gaps — those gaps are not cover of the circle-tiles.
- Count patches to find how much cover
- If each patch is one unit square, 24 patches are area 24.
Practise Grandmother's Quilt
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device