Class 6 NCERT bridge course Answers Activity W2.6 Exploring Area – Same Area, Different Shapes Using Strips

Activity W2.6: Exploring Area – Same Area, Different Shapes Using Strips

 Take 16 cutouts of a strip. 

The dimension of the rectangle is 16 x 1 units.

Arrange them in a square shape of dimension 4 x 4 units.

These can also be arranged is a shape of dimension 8 x 2 units.

The regions in all these cases are different but the amount of region occupied by them 

i.e., their areas are the same. 

 Ask the students to make more such cutouts, say, 20, 25, 30, etc., and make different shapes.

Activity W2.6: Exploring Area – Same Area, Different Shapes Using Strips

Objective:

To understand that area remains the same when the total number of unit tiles is the same, even if their shapes and arrangements differ.

Materials Needed:

• Cutouts of rectangular strips of size 1 unit × 1 unit

• Grid or chart paper

• Scissors and glue (optional)

• Pencil or marker

Procedure:

1. Take 16 unit strips (1 × 1) and arrange them in a 1 × 16 rectangle.

2. Rearrange the same 16 unit strips into a 4 × 4 square.

3. Rearrange them again into an 8 × 2 rectangle.

4. Observe the shape, layout, and area of each figure.

5. Try the same process with 20, 25, 30 unit strips.
   Form different rectangles or irregular shapes while using all the strips.

6. Record your observations.

Examples & Shapes:

Total Unit Strips	Possible Arrangements	Area (sq. units)
16	1×16, 2×8, 4×4	16
20	1×20, 2×10, 4×5	20
25	1×25, 5×5	25
30	1×30, 2×15, 3×10, 5×6	30

Discussion Questions:

1. Are all these shapes the same?
   No. They have different shapes and dimensions.

2. Do they cover the same area?
    Yes. All use the same number of unit strips (same total area).

3. What do we learn from this?
    Area is about how much space is covered, not what shape it is.

4. Can we create shapes other than rectangles with the same area?
    Yes! Irregular or L-shaped figures can also be formed using the same unit strips.

Conclusion:

Even though shapes and dimensions differ, the total area remains the same when the same number of unit strips are used. This reinforces the concept that area is independent of shape and is instead determined by the total number of unit squares/tiles used.

This hands-on approach strengthens spatial reasoning and understanding of measurement and geometry.

Class 6 NCERT bridge course Answers Activity W2.5: Area – Same Area, Different Shapes

 

Activity W2.5: Area – Same Area, Different Shapes

● Take 10 pieces of dimension 1 x 1 unit. 

● Look at some of the following arrangements

• Do you find that all these arrangements occupy the same space, that is, they have the same area? 
•  Make some more arrangements of squares in different ways. 
•  What do you conclude?

Activity W2.5: Area – Same Area, Different Shapes

Objective:

To help students understand that area depends on the number of unit squares used, not the shape or arrangement. By arranging the same number of 1×1 unit squares in different ways, students see that the area remains constant.

Materials Needed:

• 10 square tiles or paper cutouts of size 1 unit × 1 unit

• Plain paper or grid paper

• Scissors and glue (optional)

• Pencil/pen for drawing shapes

Procedure:

1. Take 10 square pieces of 1×1 unit.

2. Arrange them in different shapes (straight line, L-shape, rectangle, zig-zag, etc.).

3. Draw or trace the shapes on paper to compare.

4. Observe and answer:

   • Do all the shapes cover the same area?

   • How do they look different?

Suggested Arrangements (Examples):

Shape	Description	Area
🔲🔲🔲🔲🔲🔲🔲🔲🔲🔲	1 row of 10 tiles (10 × 1 rectangle)	10 square units
🔲🔲🔲🔲🔲 🔲🔲🔲🔲🔲	2 rows of 5 tiles each (5 × 2 rectangle)	10 square units
🔲 🔲 🔲 🔲 🔲 🔲 🔲 🔲 🔲 🔲	1 column of 10 tiles (1 × 10 rectangle)	10 square units
🔲🔲🔲 🔲🔲🔲 🔲🔲🔲 🔲	L-shaped with pieces stacked	10 square units
Custom or irregular shape using all 10 tiles	Various	10 square units

Discussion Questions:

1. Do you find that all these arrangements occupy the same space, that is, they have the same area? 

            Yes. All arrangements use 10 unit squares, so they cover 10 square units, regardless of shape.

1. Make some more arrangements of squares in different ways. 

1. Do they look the same?
    No. The shapes look very different, even though the area is the same.

2. What do you conclude? What does this tell you about area?
   Area depends on the number of square units used, not how they are arranged.

3. Can different shapes have the same area?
   Yes! That's the key insight.

Conclusion:

This activity shows that different shapes can have the same area if they are made from the same number of unit squares. Area is a measure of how many square units cover a surface, not the shape or orientation of the figure.

Encourage students to explore:

• Creative patterns

• Symmetry

• New composite shapes
  All with the same total area!

Class 6 NCERT bridge course Answers Activity W2.4 Exploring Volume – Making a Triangular-Shaped Box

Activity W2.4: Exploring Volume – Making a Triangular-Shaped Box

 Discuss and Explore: 

1. Do the above activity by making a triangular shaped box and discuss your observations.

Activity W2.4: Exploring Volume – Making a Triangular-Shaped Box

Objective:

To explore how the shape of the base affects the volume of a box when using the same-sized sheet of paper. In this activity, students will make a triangular prism from the same-sized sheet used in Activity W2.3 and compare its volume with rectangular-based boxes.

 Materials Needed:

• 1 rectangular sheet of paper (same size as previous activity)

• Power tape or glue

• Ruler

• Grains or rice for measuring volume

• Empty container

 Procedure:

1. Take a rectangular sheet (e.g., 20 cm × 16 cm).

2. Fold or cut it to form a triangular prism box.

   • Fold the paper into a strip.

   • Roll or shape the cross-section into a triangle (e.g., equilateral or right-angled).

   • Tape or glue the edges securely.

3. Seal one end of the prism to make a base.

4. Pour grains/rice into the triangular box until full.

5. Pour the contents into a measuring container or another rectangular box made from the same paper.

6. Compare the amount of rice or volume occupied.

 A triangular prism made of paper

                                   

• 
  

Example Calculation:

Let’s assume:

• Base of triangle = 8 cm

• Height of triangle = 5 cm

• Length (height of prism) = 16 cm

Volume of triangular prism =

$$\text{Area of triangle} \times \text{Length} = \frac{1}{2} \times 8 \times 5 \times 16 = 320 \text{ cm³}$$

Compare with:

• Rectangular box from same paper = 640 cm³ (from W2.3)

• Triangular box = 320 cm³

The triangular box holds less than the rectangular box made from the same paper.

Discussion Questions:

1. Why do you think the triangular box holds less?
   Because the base of the triangle has less area than a rectangular base from the same paper.

2. How does the shape of the base affect volume, even with the same surface area?
    Shapes with broader or fuller bases (like rectangles) tend to enclose more volume than narrow ones (like triangles), assuming the same height.

3. What if you made a cylinder instead from the same paper? Would it hold more or less?
    You could explore this in the next activity!

Conclusion:

By folding the same-sized paper into different 3D shapes (rectangular, triangular), we observe that volume is influenced by the shape of the base. Even with identical surface area, design and folding technique can greatly impact how much a box can hold.

Class 6 NCERT bridge course Answers Activity W2.3 Volume – Making Boxes of Different Volumes

 Volume: Making boxes of different volume from same size paper: 

Activity W2.3 

 Take two rectangular papers of the same size and different colours (say blue and yellow). 

First take any paper, say blue colour, crease it along the larger side from the middle such that both parts become equal (Fig. 1).

Crease the same paper from the middle such that both parts become equal and this divides the paper in four equal parts (Fig. 2). 

 Now join the open sides of the paper with power tape and form a box (Fig. 3)

Do the same with another paper, say yellow colour, by creasing it along the shorter side and form another box (Fig. 4 and Fig.5). 

 Now put the blue box on the table vertically so that one open side faces the table and the other side upwards and fill it completely with rice/grains. 

Empty all the rice in a container and fill the yellow box with this rice. 

Does it fill the blue box completely or not?

Activity W2.3: Volume – Making Boxes of Different Volumes

Objective:
To explore how folding the same size paper in different ways creates boxes of different volumes.

 Materials Needed:

• 2 rectangular sheets of the same size (different colors, e.g., blue and yellow)

• Power tape or glue

• Grains or rice

• Container to transfer grains

 Procedure:

1. Blue paper:
   Fold the paper in half along the longer side.
   Then fold it again along the shorter side, dividing it into four equal parts.

2. Tape the open edges to form a tall box.

3. Yellow paper:
   Fold it first along the shorter side, then in half again.
   Tape the open edges to form a shorter, wider box.

4. Fill the blue box with rice.
   Pour the rice into the yellow box.

 Question:

Does the yellow box hold the same amount of rice as the blue one?

 Example Calculation:

Suppose each paper is 20 cm × 16 cm:

• Blue box (base = 8 cm × 10 cm, height = 8 cm)
  Volume = 8 × 10 × 8 = 640 cm³

• Yellow box (base = 16 cm × 5 cm, height = 5 cm)
  Volume = 16 × 5 × 5 = 400 cm³

Result: The blue box holds more!

Conclusion:

Even when using the same sheet size, the way you fold and form a box greatly affects its volume. Taller, narrower shapes can sometimes hold more than shorter, wider ones.