Math - Growing Shapes

Growing Shapes

A

B

How do you see the pattern growing?

A - Three dots are added each time the figure goes up.

Figure 1 - 4 dots

Figure 2 - 7 dots

Figure 3 - 10 dots

B - The figure multiplies itself then adds 1 square.

Figure 1 x Figure 1 = 1 + 1 = 2 squares

F2 x F2 = 4 + 1 = 5 squares

How many squares are in figure 55? Explain how you know

A - In figure 55, there will be 166 squares because we figured out a formula to solve the problem.

3n + 1

B - There will be 3,026 squares because just like the last problem, we figured out a formula to solve the problem. N squared + 1

Can you use 190 squares to make a structure? Mathematically justify your answer?

A -  Yes, because by using the formula we figured out that we can use 190 to make a structure. 

63 x 3 + 1

B -  No, because we tried the formula to figure out whether we can use 190 squares. After trying, we found out that it uses too many squares.

How can you figure out how many total squares are in a figure?

A -  N x 3 + 1

B -  N squared + 1