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Core Connections: Course 3

CC

Core Connections: Course 3 View details

Chapter Closure

Exercise 94 Page 86

Look at the figures carefully. Notice what changes from figure to figure to identify the pattern. What is the change between the numbers of tiles of consecutive figures?

See solution.

Before we draw Figures 1 and 5, let's consider the differences between the existing figures.

Looking at the figures, we can see that there is a clear pattern. Each figure has one tile at the bottom, as well as a row of two more tiles at the top than the previous one. Therefore, Figure 1 has one tile at the bottom and a row of two tiles less at the top than Figure 2. Figure 5 has one tile at the bottom and a row of two tiles more at the top than Figure 4.

Now we can move on to Part A of the exercise.

Part A

We want to know how many tiles are in each figure. Let's take another look at the given figures and the figures we have drawn.

As we can see, Figure 1 contains 2 tiles, Figure 2 contains 5 tiles, Figure 3 contains 8 tiles, Figure 4 contains 11 tiles, and Figure 5 contains 14 tiles.

Part B

We want to describe how the pattern of the number of tiles in consecutive figures is changing. Note that, as we have already noticed, in each Step 3 tiles are added to the figure: 1 at the bottom and 2 at the top. Therefore, each figure has 3 more tiles than the previous one.

Part C

Finally, we want to know how many tiles Figure 6 would have. As we have found in Part B, each figure has 3 more tiles than the previous one. In Part A, we have found that Figure 5 has 14 tiles. Figure 6 has 3 more tiles than Figure 5, or 14 + 3. Number of tiles in Figure6 : 14 + 3 = 17

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