Rule Here is a pattern of dots on blocks: 3 1. Describe the pattern in words. 2. How many dots must be added to each block to get to the number of dots on the next block? Find a pattern in these added numbers. 3. Draw the fourth block. 4. How many dots must be added to the third block to get the fourth block? 5. Now complete this table for block numbers 3, 4 and 5: Block number 2 0. 4 5 11 15 Number of dots added to the 3 previous block 59 3 6. Let the "block number" be the input number in a flow diagram. The "number of dots added to the previous block" is the output number. Work out a rule to change input numbers to output numbers. Put this rule into the flow diagram and complete it. 7. Use your rule from question 6 to work out which block number will need to have 59 dots added to its previous block in the pattern. Write this number in the table. 8. Now count the number of dots that are in each of the first 4 blocks. Block number 1 2 3 4 5 7 11 Number of dots 1 144 9. Write down the rule for finding the number of dots from the block number. Use the rule to complete the above table for block 5, 7 and 11 10. Which block number will have 144 dots? Fill this in on the table 2. Rule When you look at geometric patterns, it is often quite easy to see what the next diagram in the pattern will be. It can be more difficult to work out a rule that tells you about a diagram much further along the pattern, without you having to draw it. EXERCISE 12.5 Here is a pattern of dots on blocks: 1 2 3 1. Describe the pattern in words. 2. How many dots must be added to each block to get to the number of dots on the next block? Find a pattern in these added numbers. 3. Draw the fourth block. 4. How many dots must be added to the third block to get the fourth block? 5. Now complete this table for block numbers 3, 4 and 5: Block number 2 4 5 11 15 Number of dots added to the previous block 3 59 3 6. Let the "block number" be the input number in a flow diagram. The "number of dots added to the previous block" is the output number. Work out a rule to change input numbers to output numbers. Put this rule into the flow diagram and complete it. 7. Use your rule from question 6 to work out which block number will need to have 59 dots added to its previous block in the pattern. Write this number in the table. 8. Now count the number of dots that are in each of the first 4 blocks. Block number 1 2 3 4 5 7 11 Number of dots 1 144 9. Write down the rule for finding the number of dots from the block number. Use the rule to complete the above table for block 5, 7 and 11 10. Which block number will have 144 dots? Fill this in on the table