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High School Mathematics Problems from Alaska

A database of lessons and units searchable by content and cultural standards, cultural region and grade level. More units will be available soon. You can use Acrobat Reader to look at the PDF version of the Cover Sheet for the Units and Self-Assessment for Cultural Standards in Practice.

Investigation of Herring Statistics

 

Bobbi Jordan
bew2@ptialaska.net

MS Word Download

 

Standards: Estimation and Computation, Statistics and Probability.

Performance Standards: A3.3.4, A6.2.3, A.6.3.1, A6.3.2

Concepts: Reading a fairly complex chart, finding measures of central tendency, making calculation with large numbers, creating histograms and box plots.

Carnegie Chapter: Analyzing Data and Making Predictions

Overview: Students answer a variety of questions using the "Fisherman’s Copy" of statistics from the Alaska Department of Fish & Game that gives the history of the Sitka Sac Roe Herring Fishery. This fishery is a limited entry fishery that occurs every spring in Sitka. The fishermen are given this data, updated each year, to help them work with Fish & Game to decide when to open the fishery. For more information or an updated "Fisherman’s Copy," please contact the Alaska Department of Fish and Game.


 

 Sitka Sound Sac Roe Fishery Effort and Value, 1975-1996

Year
Quota (tons)
Harvest (tons)
Percent of Quota Harvested
Roe Percent
Price/Ton
Fishery Value (millions)
Number of Vessels
Number of Tenders
2 hr Notice In Effect
Fishing Dates
Total Hours Fished (hr:min)
Dominant Age
Percent at Age
Foot-note
1975
550
1,532
279
 

 

 

 

 

 

40
16
 

 

 

 

1:30
 

 

 

 

1
1976
780
800
103
9-11.5
 

 

0.23
38
26
 

 

4/16
4:00
 

 

 

 

 

 

1977
0
0
0
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1978
 

 

175
70
 

 

 

 

 

 

23
9
 

 

4/5
5:30
 

 

 

 

 

 

1979
2,000
2,250
113
9.34
$2,000
4.5
48
50
 

 

4/12
NA
3
65
2
1980
4,000
4,385
110
10.8
 

 

 

 

50
76
9AM, 4/4
4/4, 4/5
17:00
3
11
 

 

1981
3,000
3,506
103
11.04
 

 

 

 

51
63
10PM, 3/23
3/24, 3/26
4:30
5
62
 

 

1982
3,000
4,363
146
11.7
 

 

 

 

51
88
2AM, 3/26
3/30
6:10
6
57
 

 

1983
5,500
5,450
99
11.1
$760 + $76/1%
4.5
51
139
4AM, 3/23
3/26, 3/29
10:05
3
59
 

 

1984
5,000
5,830
117
11.05
$450 + $45/1%
2.8
50
76
10PM, 3/22
3/26-3/28
11:10
4
67
 

 

1985
7,700
7,475
97
11.33
$800 + $80/1%
6.77
52
152
6AM, 3/24
3/29, 4/1, 4/5
6:55
5
44
 

 

1986
5,029
5,543
108
11.89
$1000 + $100/1%
6.5
52
99
7AM, 3/28
4/2, 4/8
3:10
3
36
 

 

1987
3,600
4,216
117
9.88
$1000 + $100/1%
4.17
52
74
7AM, 3/23
3/31
4:10
3
53
 

 

1988
9,200
9,575
104
9.45
$500 + $50/1%
4.5
52
81
7AM, 3/25
4/4-4/14
114:00:00
4
78
2
1989
11,700
12,135
104
9.36
$100 + $10/1%
1.21
51
99
6AM, 3/22
3/31-4/8
88:00:00
5
77
2
1990
4,150
3,804
92
10.6
$520
1.97
52
76
6AM, 4/4
4/5-4/6
3:30
6
71
 

 

1991
3,200
1,908
60
8.88
$106
0.2
22
70
7AM, 3/29
4/10-4/13
78:30:00
3
75
2
1992
3,356
5,368
160
9.38
$275
1.5
52
67
8AM, 3/30
4/6
1:23
4
89
 

 

1993
9,700
10,186
105
10.67
$325
3.07
50
76
8AM, 3/26
3/27-4/3
52:20:00
5
82
2
1994
4,432
4,758
107
11.03
$650 + $65/1%
3.4
51
68
8AM, 3/28
3/29, 3/31
6:45
6
80
 

 

1995
2,609
2,908
111
11.8
$1100 + $100/1%
3.67
51
50
8AM, 3/23
3/25, 3/27
3:30
7
62
 

 

1996
8,144
8,144
100
9.6
 

 

13.86
52
97
8AM, 3/23
3/31-4/8
159:00:00
3
47
3

 

28 purse seine and 12 gillnet vessels participated

Coop fishery

[4168 Competitive (10.1%) with 2000 + 200/1%] & [3976 Cooperative (9.2%0 with 1500 + 150/1%)

 

Sitka Sound Herring Fishery Information

 

Year

 

Quota (tons)

 

Harvest (tons)

 

Roe Percent

 

2 hr Notice In Effect

 

Fishing Dates

 

Total Hours Fished (hr:min)

 

Date of First Spawn

 

Nautical Miles Spawn

 

Estimated Escapement (tons)

 

Total Return (tons)

 

Pre-season Forecast (tons)

 

ASA Model Return

 

Foot-note

 

1956

 

100

 

45,500

 

45,500

 

 

 

1957

 

80

 

36,300

 

36,300

 

 

 

1958

 

93

 

42,200

 

42,200

 

 

 

1959

 

46

 

20,950

 

20,950

 

 

 

1960

 

45

 

20,250

 

20,250

 

 

 

1961

 

NA

 

NA

 

NA

 

 

 

1962

 

NA

 

NA

 

NA

 

 

 

1963

 

NA

 

NA

 

NA

 

 

 

1964

 

234

 

1-Apr

 

19

 

8,750

 

8,984

 

 

 

1965

 

315

 

8-Apr

 

21

 

9,450

 

9,765

 

 

 

1966

 

340

 

8-Apr

 

23

 

10,450

 

10,790

 

 

 

1967

 

268

 

5-Apr

 

15

 

6,850

 

7,118

 

 

 

1968

 

260

 

31-Mar

 

17

 

7,500

 

7,760

 

 

 

1969

 

573

 

8-Apr

 

15

 

6,850

 

7,423

 

 

 

1970

 

743

 

5-10

 

12-Apr

 

11

 

5,150

 

5,893

 

 

 

1971

 

750

 

676

 

8.3

 

6-Apr

 

9

 

5,950

 

6,636

 

6,284

 

1

 

1972

 

850

 

558

 

28-Apr

 

14

 

6,600

 

7,158

 

11,940

 

 

 

1973

 

600

 

597

 

8-9

 

11-Apr

 

10

 

9,400

 

9,997

 

10,823

 

 

 

1974

 

600

 

681

 

10-13

 

3:30

 

13-Apr

 

10

 

3,850

 

4,531

 

11,999

 

 

 

1975

 

550

 

1,532

 

10-12

 

1:30

 

18-Apr

 

8

 

4,900

 

6,432

 

6,400

 

10,743

 

 

 

1976

 

780

 

800

 

9-11.5

 

4/16

 

4:00

 

15-Apr

 

13

 

2,350

 

3,150

 

7,300

 

10,243

 

 

 

1977

 

0

 

0

 

8-Apr

 

11

 

2,950

 

2,950

 

5,650

 

11,329

 

 

 

Year

 

Quota (tons)

 

Harvest (tons)

 

Roe Percent

 

2 hr Notice In Effect

 

Fishing Dates

 

Total Hours Fished (hr:min)

 

Date of First Spawn

 

Nautical Miles Spawn

 

Estimated Escapement (tons)

 

Total Return (tons)

 

Pre-season Forecast (tons)

 

ASA Model Return

 

Foot-note

 

1978

 

175

 

10-12

 

4/5

 

5:30

 

8-Apr

 

13

 

2,700

 

2,875

 

4,500

 

6,740

 

 

 

1979

 

2,000

 

2,250

 

9.34

 

4/12

 

NA

 

13-Apr

 

41

 

17,750

 

20,000

 

20,300

 

20,270

 

2

 

1980

 

4,000

 

4,385

 

10.8

 

9AM, 4/4

 

4/4, 4/5

 

17:00

 

3-Apr

 

63

 

35,100

 

39,485

 

39,500

 

37,700

 

 

 

1981

 

3,000

 

3,506

 

11.04

 

10PM, 3/23

 

3/24, 3/26

 

4:30

 

22-Mar

 

60

 

30,000

 

33,506

 

27,000

 

38,962

 

 

 

1982

 

3,000

 

4,363

 

11.7

 

2AM, 3/26

 

3/30

 

6:10

 

24-Mar

 

41

 

29,700

 

34,063

 

30,000

 

25,379

 

 

 

1983

 

5,500

 

5,450

 

11.1

 

4AM, 3/23

 

3/26, 3/29

 

10:05

 

21-Mar

 

68

 

23,250

 

28,700

 

32,750

 

35,559

 

 

 

1984

 

5,000

 

5,830

 

11.05

 

10PM, 3/22

 

3/26 - 3/28

 

11:10

 

21-Mar

 

65

 

38,500

 

44,330

 

30,550

 

49,916

 

 

 

1985

 

7,700

 

7,475

 

11.33

 

6AM, 3/24

 

3/29, 4/1, 4/5

 

6:55

 

29-Mar

 

61

 

30,950

 

38,425

 

38,500

 

38,677

 

 

 

1986

 

5,029

 

5,443

 

11.89

 

7AM, 3/28

 

4/2, 4/8

 

3:10

 

27-Mar

 

52

 

24,750

 

30,193

 

30,950

 

29,045

 

 

 

1987

 

3,600

 

4,216

 

9.88

 

7AM, 3/23

 

3/31

 

4:10

 

21-Mar

 

86

 

46,050

 

50,266

 

24,750

 

44,699

 

 

 

1988

 

9,200

 

9,575

 

9.45

 

7AM, 3/25

 

4/4 - 4/14

 

114:00

 

23-Mar

 

104

 

58,650

 

68,225

 

46,050

 

61,070

 

2

 

1989

 

11,700

 

12,135

 

9.36

 

6AM, 3/22

 

3/31 - 4/8

 

88:00

 

19-Mar

 

66

 

27,200

 

39,335

 

58,500

 

35,668

 

2

 

1990

 

4,150

 

3,804

 

10.6

 

6AM, 4/4

 

4/5 - 4/6

 

3:30

 

31-Mar

 

39

 

22,750

 

26,554

 

27,200

 

26,145

 

 

 

1991

 

3,200

 

1,908

 

8.88

 

7AM, 3/29

 

4/10 - 4/13

 

78:30

 

1-Apr

 

45

 

23,450

 

25,358

 

22,750

 

38,462

 

2

 

1992

 

3,356

 

5,368

 

9.38

 

8AM, 3/30

 

4/6

 

1:23

 

28-Mar

 

73

 

48,600

 

53,968

 

23,450

 

70,778

 

 

 

1993

 

9,700

 

10,186

 

10.67

 

8AM, 3/26

 

3/27 - 4/3

 

52:20

 

24-Mar

 

55

 

35,500

 

45,686

 

48,500

 

41,825

 

2

 

1994

 

4,432

 

4,758

 

11.03

 

8AM, 3/28

 

3/29, 3/31

 

6:45

 

28-Mar

 

58

 

14,050

 

18,808

 

28,450

 

32,081

 

 

 

1995

 

2,609

 

2,908

 

11.8

 

8AM, 3/23

 

3/25, 3/27

 

3:30

 

21-Mar

 

37

 

40,150

 

43,058

 

19,700

 

35,441

 

 

 

1996

 

8,144

 

8,144

 

9.6

 

8AM, 3/23

 

3/23, 3/31 - 4/8

 

159:00

 

22-Mar

 

46

 

36,372

 

44,516

 

42,265

 

42,263

 

2

 

1. First year using spawn deposition

2. Coop fishery

 

Investigation of Herring Statistics

 

Using the information from Sitka Sound Herring Sac Roe Fishery Effort and Value, 1975-1996, answer the following questions. If any mathematics is required to find the solution, show all the work that you did to arrive at your answer.

  1. In what year was the quota the highest? What was that quota?

 

 

  1. What year (other than 1977 and 1978) had the lowest quota? What was it?

 

 

  1. What is the range for the harvest in tons?

 

 

 

  1. What percent of the quota was harvested in 1989?

 

 

  1. In which year was the percent of harvest at its lowest?

 

 

  1. Find the mean for the ROE Percentage between the years of 1975 and 1996.

 

 

 

 

 

  1. What year had the longest amount of total time fished? Why did this occur?

 

 

 

  1. Which year had the earliest fishing dates? How could the fishermen use the information in the chart about fishing dates?

 

 

 

  1. Make a histogram showing the dates of fishing.

 

 

 

 

 

  1. What do the footnote numbers indicate?

 

  1. In 1996, the fishery was worth 13.86 million dollars. Write this number in standard form.

 

 

 

 

  1. Using your answer in #11, if each of the 52 boats caught the same amount of herring, how much money would each boat make?

 

 

 

 

  1. Under what conditions might the dominant age of the herring be important?

 

 

 

 

  1. In what year, between 1990 and 1996 was the most money made per minute? How much money was made each minute of fishing?

 

 

 

  1. Does there appear to be a connection between the dominant age of herring, percentage at that age, and the percent of roe content? Explain.

 


Extensions

  1. Create a box plot of the data showing fishery value in millions of dollars. Begin with 1976. Be sure to label axes, indicate intervals, and create a title for the graph.

 

 

 

 

 

 

 

Answer the following questions.

  1. What is the median of the data?

 

 

 

 

 

  1. What are the extremes?

 

 

 

 

 

 

  1. What are the upper and lower quantities?

 

 

 

 

 

  1. Are there any outliners?

 

 

 

 

 

  1. How do you find them?

 

 

 

 

 

  1. Write a general description about the herring value from the graph that you made. Write in complete sentences.

 

Table of Contents

 

AL-CAN Highway Problem

Cigarette Smoking

Commercial Salmon Fishing

Cutting Cordwood

Dog Lot Math

Firefighting Crew

Firewood Problem

Investigation of Herring Statistics

Jesse Thomas Moose Hide Problem

Predicting Plant Coverage

Problem 1 - Converting the Date to the Day of the Year

Problem 2 - Azimuth and Arc Length

Problem 3 - Reading a Graph: Azimuth Range vs. Day in Barrow, Alaska

Problem 4 - Writing an Equation: Altitude Range vs. Day in Barrow, Alaska

Problem 5 - Problem Setup and Pattern Recognition: Sunrise in Barrow, Alaska

Problem 6 - Extensions of Data: Barrow, AK Sunrise/Sunset Information

Problem 7 - Writing an Equation: Fundraiser

Problem 8 - Writing an Equation: Fundraiser Choosing a Distributor

Stanley Jonas Travel Problem

Subsistence Fishing on the Kenai

Tourist and Traveler Information

 

 

For the Teacher's Guides, please email Alaska Native Knowledge Network

Whouy Sze Kuinalth
"Teaching Our Many Grandchildren"
Tauhna Cauyalitahtug
(To Make a Drum)
Math Story Problems
St. Lawrence Island Rain Parka Winds and Weather Willow
Driftwood Snowshoes Moose
Plants of the Tundra Animal Classification for Yup'ik Region Rabbit Snaring
The Right Tool for the Job
Fishing Tools and Technology
Blackfish Family Tree
Medicinal Plants of the Kodiak Alutiiq Archipelago Beaver in Interior Alaska Digging and Preparing Spruce Roots
Moose in Interior Alaska Birds Around the Village  

 

Handbook for Culturally Responsive Science Curriculum by Sidney Stephens
Excerpt: "The information and insights contained in this document will be of interest to anyone involved in bringing local knowledge to bear in school curriculum. Drawing upon the efforts of many people over a period of several years, Sidney Stephens has managed to distill and synthesize the critical ingredients for making the teaching of science relevant and meaningful in culturally adaptable ways."

 

 

Go to University of AlaskaThe University of Alaska Fairbanks is an affirmative action/equal opportunity employer and educational institution and is a part of the University of Alaska system.

 


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Last modified August 18, 2006