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
Orb Spiders create webs that are nearly circular, with every new row almost exactly the same distance away from the previous one. No one knows why they use such precision, since they don't seem to catch any more prey than spider that spin webs that don't follow this pattern.
As an Orb Spider spins its web the number of segment increases. After one complete round, there are 13 segments, after the second cycle, there is a total of 26 segments. By the end of the 3rd cycle, there are 39 segments in total.
Simple and Familiar
Applying Problem Solving Techniques
How many segments will there be by the end of the 4th, 5th and 6th cycle?
Coherent Lines of Reasoning
Organize Information
Is this a linear pattern? Explain why you think so with clear examples.
Appropriate Math Language
What is the easy way to calculate the total number of segments after any cycle? If you create a general rule what variables would you be connecting?
Describing Patterns as Relationships
Appropriate forms of Mathematical Representation.
Create a general rule for the pattern with respect to the term position using a term and term position table.
Complex and Familiar
How many segments will there be by the end of the 20th cycle. Use your general rule to find out.
Verify Pattern
Complete the sequence and show that the 20th term in te sequence matches your prediction.
Challenging and Familiar
If you count each cycle, do you think by the end of one of them will have exactly 117 segments?
Challenging and Unfamiliar
If by the end of one cycle you have counted 156 segments in total then how many segments would the next cycle have?
Rewrite this as a sequence by using the number of match sticks in each figure. (7 terms is a good number).
What would the general rule of this sequence be?
Use your general rule to find the 50th term of the sequence.
What is the term position of 31 in the sequence? Use your general form to find the answer.