Then we counted the number of 3x3 unit squares, we found 4. We found each of there by starting from each corner of the Figure 1. One 3x3 unit square can be found shaded in Figure 1d.
Figure 1d (3 x 3)
Lastly, we counted Figure 1 as one whole 4x4 unit square, shaded in Figure 1e.
When figuring out how many squares were in Figure 2, we first noticed that the first four rows represent Figure 1; therefore, we did not recount since we previously figured out there were forty squares in Figure 1. We then counted the squares formed by adding two additional rows using the same process as we did for Figure 1. We counted four squares measuring ½ x ½ units, nine squares measuring 1x1 units, six squares measuring 2x2 units, four squares measuring 3x3 units, and four …show more content…
We followed the same steps when figuring out how many squares were in Figure 3 in order to see if we could find a pattern. The first 6 rows represented Figure 2, so we did not recount these squares. We counted the squares formed by adding two additional rows using the same process as previously described, and we noticed adding two rows again formed 25 more additional squares, making the total number of squares 90. Since this pattern of 25 more per two rows continues, we figured out a formula to represent the number of rows. Figure N (rows) = 4 + [2(N-1)]
This equation represents the number of rows there would be in a figure, 4 represents the four rows from Figure 1 (that every figure starts with), 2 represents the two added rows each figure that comes up. From this we could change the number to represent how many squares in Figure N.
Figure N (# of squares) = 40 + [25(N-1)]
This is when 40 represents the number of squares we found in Figure 1, 25 represents the number of squares for each 2 more rows. We know this works because when we plug in Figure 2 it calculates 65 like we counted:
Figure 2 = 40 +