High School Mathematics Problems from Alaska
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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
decisionmaking 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 3mile 45pound 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 3mile 45pound 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

 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 3mile 45pound
pack test.
 Find the mean, median, and
mode for the number of years of firefighting experience.
 Find the mean, median, and
mode for the age in years.
 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.
 Find the mean, median, and
mode for the 3mile 45pound pack test.
 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.
 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.
 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.
 Using the graphs and the
measures of central tendency (mean, median, and mode), pick 5 of the best
firefighters to form a crew.
 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
For the Teacher's Guides, please email Alaska
Native Knowledge Network
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." 