NCERT Class 5 Mathematics Maths Mela Chapter 11 Grandmothers Quilt PDF Download

Chapter 11: Grandmother's Quilt

Preetha and Adrit's grandmother made a quilt cover using old clothes. Now she wants to decorate it with lace. Tick the lace option that would cover the entire border of the quilt.

She decides to use two different coloured laces. How much lace of each kind will be needed to cover the entire border?

Recall that the length of the border of a shape is called its perimeter.

Let Us Do

1. Find the perimeter of the following shapes. All sides of the following shapes are equal.

   [Figure: Pentagon with side 4 cm, and triangle with side 5 cm, See in your textbook]

2. Draw two rectangles each having the following perimeters.

   (a) 26 cm (b) 18 cm

(i) Red lace 40 units

(ii) Green lace 50 units

(iii) Blue lace 25 units

Teacher's Note

Perimeter is the total distance around the outside of a shape. For shapes with equal sides, multiply the length of one side by the number of sides. For a shape with 5 equal sides of 4 cm each, the perimeter is \( 5 \times 4 = 20 \) cm. When finding which lace length is needed, add up all the sides of the quilt's border.

Preetha and Adrit's grandmother is making a rug with square patches. The picture below shows the rug. How many patches have they used to make this?

[Figure: A rug made of square patches in different colours, See in your textbook]

Preetha and Adrit are trying to cover their table with different shapes. Preetha covered it with triangles and circles. Adrit covered with squares and rectangles.

[Figure: Table 1 with triangles, Table 2 with circles, Table 3 with squares, Table 4 with rectangles, See in your textbook]

They found that __________, __________ and __________ shapes cover the top of the table without gaps and overlaps. __________ shape leaves gaps.

__________ triangles cover Table 1.

__________ squares cover Table 3.

__________ rectangles cover Table 4.

The region covered by the triangles, squares or rectangles is called the area of the table.

To find the area of a region, we usually fill it with shapes that tile (no gaps and overlaps), like squares, rectangles and triangles.

Do circles tile? Can we use them to cover a region?

The area of Table 1 is __________ triangle units.

The area of Table 3 is __________ square units.

The area of Table 4 is __________ rectangle units.

Now, try to cover the top of your table without gaps and overlaps with the following objects of same size.

(a) Notebooks (b) Lunch boxes

(c) Pencil boxes (d) Maths textbooks

Which of the above objects covered the region completely?

Comparing Shapes

Preetha is playing with tiles. She covers her desk with different shapes as shown below.

Look at the different tiles on her desk and answer how many of the following shapes will cover the desk.

(a) Green triangles __________

(b) Red triangles __________

(c) Blue squares __________

[Figure: A desk covered with tiles showing coloured shapes (green triangle, red triangles, blue square), See in your textbook]

Which of the above rectangles has the largest area? Trace these shapes on to a paper and cut them to find out the one that has the largest area.

Do you see that the area of rectangle A is larger than that of B? What about B and C?

Which shape has a larger area among A and C? How will you find out?

Let us put these rectangles on a square grid. Now, can you identify the rectangle that has the largest area?

Using square grids is the most convenient way to find the area of regions. We say that the area of a square with sides 1 unit is 1 unit square.

[Figure: A unit square showing 1 unit Area = 1 unit square, See in your textbook]

Let Us Do

1. Compare the areas of the two gardens given below on the square grid. Share your observations.

   [Figure: Garden A and Garden B on a square grid with 1 cm scale, See in your textbook]

   Area of Garden A = _____ cm square

   Area of Garden B = _____ cm square

2. Trace your palm on the square grid given below and find the approximate area of your palm. Compare the area of your palm with your friend's palm. Who has a bigger palm?

   [Figure: A square grid with 1 cm scale for tracing a palm, See in your textbook]

3. Collect leaves of different kinds. Put them on a square grid and find their area.

   (a) Name the leaf with the largest area.

   (b) Name the leaf with the smallest area.

Teacher's Note

Area tells you how much surface a shape covers. When you use a square grid, count the complete squares inside the shape first, then count the partial squares (half squares or more) and add them. This gives you the approximate area in square units. Comparing areas on a grid is easier than trying to guess by looking at the shapes.

Key Points

• The perimeter is the total distance around the edge of a shape. To find it, add up the lengths of all the sides.
• The area is the amount of space inside a shape. Shapes with no gaps and overlaps, like squares and rectangles, are best for measuring area.
• A unit square is a square with sides of 1 unit. The area of a unit square is 1 unit square, and we use it to measure the areas of other shapes.
• Using a square grid is a convenient way to find and compare areas. Count the complete squares and the partial squares inside a shape to find its area.

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