Mth Sl Type Ii Portfolio - Fishing Rods
Math Summative: Fishing Rods
Fishing Rods
A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently. In this task, you will develop a mathematical model for the placement of line guides on a fishing rod.
The Diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod.
Leo has a fishing rod with overall length 230 cm. The table shown below gives the distances for each of the line guides from the tip of his fishing rod.
Guide Number (from tip)
Distance from Tip (cm)
1
10
2
23
3
38
4
55
5
74
6
96
7
120
8
149
Define suitable variables and discuss parameters/constraints.
Using Technology, pot the data points on a graph.
Using matrix methods or otherwise, find a quadratic function and a cubic function which model this situation. Explain the process you used. On a new set of axes, draw these model functions and the original data points. Comment on any differences.
Find a polynomial function which passes through every data point. Explain you choice of function, and discuss its reasonableness. On a new set of axes, draw this model function and the original data points.
Comment on any differences.
Using technology, find one other function that fits the data. On a new set of axes, draw this model function and the original data points. Comment on any differences.
Which of you functions found above best models this situation? Explain your choice.
Use you quadratic model to decide where you could place a ninth guide. Discuss the implications of adding a ninth guide to the rod.
Mark has a fishing rod with overall length 300cm. The table shown below gives the distances for each of the line guides from the tip of Mark’s fishing rod.
Guide Number (from tip)
Distance from Tip (cm)
1
10
2
22
3
34
4
48
5
64
6
81
7
102
8
124
How well does your quadratic model fit this new data? What changes, if any, would
Fishing Rods
A fishing rod requires guides for the line so that it does not tangle and so that the line casts easily and efficiently. In this task, you will develop a mathematical model for the placement of line guides on a fishing rod.
The Diagram shows a fishing rod with eight guides, plus a guide at the tip of the rod.
Leo has a fishing rod with overall length 230 cm. The table shown below gives the distances for each of the line guides from the tip of his fishing rod.
Guide Number (from tip)
Distance from Tip (cm)
1
10
2
23
3
38
4
55
5
74
6
96
7
120
8
149
Define suitable variables and discuss parameters/constraints.
Using Technology, pot the data points on a graph.
Using matrix methods or otherwise, find a quadratic function and a cubic function which model this situation. Explain the process you used. On a new set of axes, draw these model functions and the original data points. Comment on any differences.
Find a polynomial function which passes through every data point. Explain you choice of function, and discuss its reasonableness. On a new set of axes, draw this model function and the original data points.
Comment on any differences.
Using technology, find one other function that fits the data. On a new set of axes, draw this model function and the original data points. Comment on any differences.
Which of you functions found above best models this situation? Explain your choice.
Use you quadratic model to decide where you could place a ninth guide. Discuss the implications of adding a ninth guide to the rod.
Mark has a fishing rod with overall length 300cm. The table shown below gives the distances for each of the line guides from the tip of Mark’s fishing rod.
Guide Number (from tip)
Distance from Tip (cm)
1
10
2
22
3
34
4
48
5
64
6
81
7
102
8
124
How well does your quadratic model fit this new data? What changes, if any, would