Observe the pattern on the right and create a 4th diagram to fit the pattern.
CRITERION B
You will be assessed on the following strands
select and apply mathematical problem-solving techniques to discover complex patterns
describe patterns as relationships and/or general rules consistent with findings
verify and justify relationships and/or general rules
Formula Sheet
Linear Sequences: Un=an+b
1st Term = a+b
d = a
Quadratic Sequence: Un=an2+bn+c
1st Term = a+b+c
d1=3a+b
d2=2a
Observe the pattern on the right and create a 4th diagram to fit the pattern.
How many hollow and coloured tiles will be there in pattern 8?
Write a sequence denoting only the coloured tiles.
What is the general rule for the sequence of coloured tiles? Justify your answer.
Complete the following table by counting the total number of tiles in each pattern:
What kind of sequence is represented above? Justify using a difference diagram.
Find the general rule for the table you created. Verify your rule using a couple of terms from the sequence.
Using your general rule, predict how many tiles the 100th pattern will have.
Command terms:
Apply: Use knowledge or understanding in a given situation.
Explain: Give a detailed account including reasons or causes.
State: Give a specific name, value or brief answer without explanation or calculation
Suggest: Propose a solution, hypothesis or other possible explanation
Verify: Provide evidence that validates the result
Justify: Give valid reasons or evidence to support an answer or conclusion
