1. A Unit about Change in Geometric Figures and Solids
Dimensions
A Unit about Change in
Geometric Figures and Solids

2. Observe and compare these...

3. What patterns do you see?
Complete the table
What patterns do you see?

4. What patterns do you see?
Complete the table
What patterns do you see?

5. What patterns do you see?
Complete the table
What patterns do you see?

6. What patterns do you see?
Complete the table
What patterns do you see?

7. What patterns do you see?
Complete the table
What patterns do you see?

8. What patterns do you see?
Complete the table
What patterns do you see?

9. Check Your Answers! A E D C B

10. Tell me if... This square is considered a unit.
What is the length of its side?
What is its perimeter?
What is its area?
If the dimensions of this square are halved or doubled, how do the perimeter and the area change?

11. Let’s complete the table...

12. Let’s complete the table...2 8 4

13. Let’s complete the table...1 4 1 2 8 4

14. Let’s complete the table...1 4 1 2 8 4 4 16 16

15. We can say that...
If the length of the side of a square is halved, its perimeter decreases by a factor of ___ and its area decreases by a factor of ___.
If the length of the side of a square is doubled, its perimeter increases by a factor of ___ and its area increases by a factor of ___.

16. About solids... Consider this cube.
What is the length of the side?
What is its surface area?
What is its volume?
If the dimensions of this cube are halved or doubled, how do the surface area and the volume change?

17. Let’s complete the table...

18. Let’s complete the table...

19. Let’s complete the table...1 6 1

20. Let’s complete the table...1 6 1 4 96 64

21. We can say that...
If the length of the side of a cube is halved, its surface area decreases by a factor of ___, and its volume decreases by a factor of ___.
If the length of the side of a cube is doubled, its surface area increases by a factor of ___, and its volume increases by a factor of ___.

22. Let’s explore
What changes in perimeter, area, surface area, and volume would take place if we use other factors to alter the dimensions of a geometric figure or a solid (triplicate, ten-fold, etc.)?
Do other solids and figures respond to changes in dimensions in the same way as the square and the cube?