Question

name:
date:
functional relationships
diagnostic assessment

1. how many blocks are in figure 4? explain how you know.

a)
figure 1 figure 2 figure 3

b) complete the table to represent the pattern.
figure 1 2 3 4
number of blocks

c) turn the table you found in part b into a set of ordered pairs.
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Explanation:

Step1: Count blocks in Figure 1

Figure 1 has 1 block.

Step2: Count blocks in Figure 2

Figure 2 has 5 blocks. There is 1 central block and 4 surrounding blocks.

Step3: Count blocks in Figure 3

Figure 3 has 9 blocks. There is 1 central block and 8 surrounding blocks (4 on each side).

Step4: Find number of blocks in Figure 4

The pattern is that the number of blocks increases by 4 each time. So for Figure 4, we have $9 + 4=13$ blocks.

Step5: Complete the table

Figure	1	2	3	4

Step6: Form ordered - pairs

The ordered - pairs are of the form (Figure number, Number of blocks). So the set of ordered pairs is $\{(1,1),(2,5),(3,9),(4,13)\}$

Answer:

a) Figure 1 has 1 block, Figure 2 has 5 blocks, Figure 3 has 9 blocks, Figure 4 has 13 blocks.
b)

Figure	1	2	3	4

c) $\{(1,1),(2,5),(3,9),(4,13)\}$