Activity W 4.5: Building Towers with Blocks
Material Required
Different coloured blocks.
Paper and pencil for recording results.
Explain to the students that each block will represent a number, and stacking blocks will help illustrate exponents.
For example, stacking 2 blocks means 2¹ and stacking 4 blocks means 2² and so on
Procedure & Observation
Ask students to create towers representing different powers of 2:
For 2¹ , they stack 2 blocks.
For 2² , they stack 4 blocks.
For 2³ , they stack 8 blocks.
Students stack blocks to represent powers of 2:
| Exponent | Mathematical Form | Number of Blocks | 3-D Shape Formed |
|---|---|---|---|
| 2¹ | 2 | 2 blocks | Cuboid |
| 2² | 4 | 4 blocks | Cube (if arranged as 2x2x1) |
| 2³ | 8 | 8 blocks | Cuboid or Cube (if arranged as 2x2x2) |
1. After stacking blocks for different exponents, students may be made to explore what 3-D shape they get.
For example, 2¹ gives a cuboid, whereas 2² gives a cube and so on.
Discussion:
What 3-D shape do they get?
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For 2¹ = 2 blocks, students usually get a Cuboid (because two blocks form a rectangular shape).
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For 2² = 4 blocks, if arranged symmetrically (2x2), they can get a Cube.
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For 2³ = 8 blocks, if arranged as 2x2x2, it forms a Perfect Cube.
Conclusion:
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When the blocks can be arranged equally in all three dimensions (length, width, and height), the shape is a cube.
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Otherwise, it remains a cuboid.
They may see for which exponent of 2 they get a cube and for which other a cuboid.
Can they get any other 3-D shape other than a cube or cuboid?
No, using only simple stacking of square or rectangular blocks, the shapes are usually limited to cuboids or cubes.
Other 3-D shapes like pyramids or spheres cannot be formed unless the block shape or stacking style is changed.
2. They may observe as to how the number of blocks increases as the exponent increases.
Is there any pattern?
Is there any pattern in the number of blocks as the exponent increases?
Yes! The number of blocks doubles every time the exponent increases by 1.
| Exponent | Number of Blocks |
|---|---|
| 2¹ | 2 |
| 2² | 4 |
| 2³ | 8 |
| 2⁴ | 16 |
Pattern:
As the exponent increases by 1, the number of blocks is multiplied by 2.
Conclusion:
This activity helps visualize how exponents grow and how they relate to 3-D shapes like cubes and cuboids. The number of blocks follows a clear doubling pattern as the exponent increases.
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