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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.

Fire Fighting Crew

 

Beth Sukraw

 

MS Word Download

Standards: Probability and Statistics.

Performance Standards: A6.3.1, A6.3.2, A6.3.3, A6.4.1, A6.4.3

Concepts: Bar Graph, Measures of Central Tendency, and Representation of Data.

Carnegie Chapter: Analyzing Data and Making Predictions.

Overview: The following unit explores the use of statistics to make decisions. Calculations for the mean, median, and mode must be accurate and then used to compare one fire fighter to another. The decision as to when to use the mean, median, or mode to pick a fire fighter is made and then justified. For example, someone might choose a firefighter whose test score is closest to the mode test score. Then that decision must be explained using reason. The use of the bar graphs when comparing the mean, median, and mode will help with the justification. This emphasizes how geometrically humans think and how important it is to graph information in order to understand it.


 

This unit is flexible and can be completed individually or as a group. Please note that the numbers in the table were generated to make the decision-making difficult. They could be changed and the unit completed again.

A big thank you to our local area fire fighters for information about the safety test and times on the 3-mile 45-pound pack test. We truly appreciate our firefighters everywhere.


 

Fire Fighting Crew

The following are the physical fitness scores, ages, safety test scores and firefighting experience of 10 firefighters. You are to pick 5 of the best for a crew using the statistics you calculate. Below is a table of data for each firefighter.

Firefighters
Number of years of firefighting experience
Age in years
Safety test score
Time on the 3-mile 45-pound pack test in minutes
A
10
30
Minimum
35
B
5
45
Minimum
40
C
2
22
Above minimum
35
D
2
28
Maximum
30
E
15
44
Minimum
35
F
4
38
Above minimum
38
G
11
45
Maximum
42
H
8
35
Maximum
40
I
8
30
Maximum
38
J
1
19
Minimum
32

 

  1. Graph the data given on 4 separate graphs. Create one bar graph for each category: number of years firefighting experience, age in years, score on safety test, and time for the 3-mile 45-pound pack test.

 

graph

 

 graph

graph

graph

 

 

  1. Find the mean, median, and mode for the number of years of firefighting experience.

 

 

 

 

  1. Find the mean, median, and mode for the age in years.

 

 

 

 

  1. Find the mean, median, and mode for the score on safety test. Note: Use 1, 2, and 3 to calculate for minimum, above minimum, and maximum.

 

 

 

 

  1. Find the mean, median, and mode for the 3-mile 45-pound pack test.

 

 

 

 

  1. Designate the mean of each category on the correct category’s grid by marking the mean with an X and then drawing a horizontal line parallel to the horizontal axis through the X across the entire graph. Include this symbol X in the legend of your graph. An example is X = arithmetic mean.

 

  1. Designate the median of each category on the category’s grid by marking the median with an O and then drawing a horizontal line parallel to the horizontal axis through the O across the entire graph. Include this symbol O in the legend of your graph. An example is O = median.

 

 

  1. Designate the mode of each category on the category's grid by marking the mode with a _ and then drawing a horizontal line parallel to the horizontal axis through the _ across the entire graph. Include this symbol _ in the legend of your graph. An example is _ = mode.

 

 

  1. Using the graphs and the measures of central tendency (mean, median, and mode), pick 5 of the best firefighters to form a crew.

 

 

 

 

  1. Explain why you picked those 5 firefighters as the best using the graphs and measures of central tendency to defend your choices.

 

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