Question

unit 1 review packet
section 1 - tiling patterns
show all your work.

1. consider the figures below

figure 2 figure 3 figure 4
a. draw the 1st figure and 5th figure on the grid.
b. describe all the patterns you notice.

Explanation:

Step1: Analyze the given figures

By observing Figure 2, 3 and 4, we can see that the pattern seems to be growing in a certain way. Each figure appears to be an 'L - shaped' structure with an increasing number of unit - squares.

Step2: Determine the 1st figure

Assuming the pattern starts simply, the 1st figure could be a single unit - square.

Step3: Determine the 5th figure

Based on the growth pattern (it seems that with each new figure, the 'arms' of the L - shape grow by one unit - square), for the 5th figure, the two 'arms' of the L - shape will be longer than in the 4th figure. The 5th figure will have one arm with 5 unit - squares and the other arm with 5 unit - squares (including the corner square).

Step4: Describe the pattern

The number of unit - squares in each figure is increasing. The figure is in an L - shape, and with each successive figure, both the horizontal and vertical 'arms' of the L - shape grow by one unit - square.

Answer:

a. For the 1st figure, draw a single unit - square. For the 5th figure, draw an L - shape where the horizontal and vertical parts each have 5 unit - squares (sharing a corner square).
b. The pattern is that the figure is in an L - shape, and the number of unit - squares in the horizontal and vertical 'arms' of the L - shape increases by 1 with each successive figure.