Chapter Closure
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Look at the figures carefully. Notice what changes from figure to figure to identify the pattern.
Count the number of tiles in each figure.
Use the table from Part B.
| Figure, x | Number of Tiles, y |
|---|---|
| 1 | 4 |
| 2 | 7 |
| 3 | 12 |
| 4 | 19 |
| 5 | 28 |
Looking at the figures, we can notice that there is a clear pattern. Each subsequent figure increases the size of the side of the square by one tile. Therefore, Figure 5 would have a square side of 5 tiles. Figure 1 would have a square with a side length of one tile shorter than in Figure 2, so the square will have 1 tile.
Let's make a table where x represents the figure number and y represents the number of tiles in the figure.
| Figure, x | Number of Tiles, y |
|---|---|
| 1 | 4 |
| 2 | 7 |
| 3 | 12 |
| 4 | 19 |
| 5 | 28 |
We want to make a graph that shows how many tiles each figure has. In Part A we noticed that each figure has a three tiles in a row and a square with a side one tile longer than the previous one. This means that Figure 0 has only 3 tiles.
We can add the number of tiles in Figure 0 to the table we made in Part B.
| Figure, x | Number of Tiles, y |
|---|---|
| 0 | 3 |
| 1 | 4 |
| 2 | 7 |
| 3 | 12 |
| 4 | 19 |
| 5 | 28 |
Let's graph the points (x,y) on the coordinate plane. On the x-axis we will mark the figure number. On the y-axis we will mark the number of tiles in the figure.
