Write an algebraic expression for the number of tiles in Step n. Share your methods with the class. Class 8

Write an algebraic expression for the number of tiles in Step n. Share your methods with the class. Class 8

Question 1.

Write an algebraic expression for the number of tiles in Step n. Share your methods with the class. Can you find more than one method to arrive at the answer? Class 8

Solution:

8 + (n - 1) × 4 = 8 + 4n - 4 = 4 + 4n

Note : Do as directed.

Yes. For example, at step 1, tiles = 8; at step 2, tiles = 12 = 4 (2 + 1); at step 3, tiles = 16 = 4(3 + 1), etc. So, at step n, tiles = 4(n + 1) = 4n + 4.

Question 2.

If x = 8 and y = 3, find the area of the shaded region. Class 8

Solution:

Area = x² - xy

= 8² - 8 × 3

= 64 - 24

= 40 sq. units.