Lesson 1: The Feet Can Measure The Height
The bones of the feet can tell you a lot about a person. When you divide the length of
each person's left food by his/her height, and then multiply the quotient by 100, the
results of your calculations should be about 15, illustrating that the length of a
person's foot is approximately 15 percent of his or her height.
Learning Standards: A1.N.4, A1.P.1, A1.P.2, A1.P.9, A1.P.11, A.1.D.1, A1.D.3
Guiding Principles: Students will be able to calculate their foot size as a percentage
of their height.
Materials:
1. paper
2. rulers
3. pencils
4. calculators
Activity (35 MINUTES):
Students will make a table with the following categories: name, height,
15% of height, and foot length. Students will work with a partner to
measure each other's heights in cm. They will record their results in the
table. Then students will multiply their height by 15% to get the expected
size of their foot, and then they will actually measure their foot and record
that data in the table.
Assessment: Student’s tables will provide a means of assessment.
Discussion:
Prior to beginning the activity, a review lesson on percents may be
appropriate. When the activity is completed, students should share any
disparity between the expected foot size and the actual foot size.
Conversation should lead the class to discuss how continued growth versus
someone who has stopped growing influences their results.
Conclusion/Next Step:
Forensic scientists are able to determine a person's height based on the
measure of a footprint. This works best on full grown individuals for the
ratio of body parts is slightly different in growing children.
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Lesson 2: Determine The Foot Size of The Four Suspects
At approximately 7 15am, Friday morning, Mrs. King, the seventh grade science
teacher, thought something was fishy as she walked down the hall and noticed that
her door was open. She walked into her classroom and immediately discovered that
the small aquarium had been broken and her prized gold fish were gasping in the
sink. Beside the broken aquarium were the shattered remains of the pinky piggy
bank that had been on the shelf above the aquarium. A can of blue paint was spilled
on the floor. Footprints of a barefooted burglar led to an open window. Bits of a
white powdery substance were found next to the broken, empty, piggy bank. The
only other item found was a half eaten large chunk of chocolate candy.
When the police arrived they immediately began to gather the following evidence:
1. sticky fingerprints were lifted from the aquarium and piggy bank
2. the painted footprints were measured; the footprint measured 10.5 inches
3. the chunk of chocolate candy was collected for examination; it appeared there
were teeth imprints
4. the white powdery substance by the piggy bank was carefully placed in a plastic
bag and taken to the forensic chemist for identification
Police found four suspects to the crime. Their names and information is as follows:
1. Lou Lou is 5'3''
2. Dan the Man is 5'10''
3. Peg the Leg is 5'
4. Jake the Jock is 6'6''
Learning Standards: A1.N.4, A1.P.1, A1.P.2, A1.P.9, A1.P.11, A1.D.1, A1.D.3
Guiding Principles: Students will be able to identify the prime suspect in the crime
based on calculating each suspect’s foot size as a percentage of their heights.
Materials:
1. paper
2. rulers
3. pencils
4. calculators
Activity (35 minutes):
Students will put each of the four suspects information on the board.
Students will convert each suspect's height to inches and then calculate
each suspect's foot size based on their height (multiply by 15%). Students
may then discuss which of the suspects match the footprint found at the
scene of the crime. Recall that the footprint at the scene of the crime
measured 10.5 inches. From there, students should convert the data they
calculated from inches to centimeters. A review lesson on proportions may
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be appropriate. For example, to calculate Peg the Leg's height in
centimeters:
30 cm
x
____ _ = _____
12 in 60 in
Student's should do this for each of the suspect's height as well as foot size
so all the data is in terms of centimeters, as they were measured in the first
lesson. Students should organize this data in a small table or chart.
Assessment: Student’s chart will provide a means of assessment.
Conclusion/Next Step: Students should be able to identify the suspect who
committed the crime based on their analysis of the data. A conversation
could ensure about other potential suspects given particular data at hand.
Lesson 3: Suspect's Data To Teach Statistics
Now that all the data on the suspects has been calculated, its time to put that data to use.
The statistics reviewed for this lesson are mean, median, mode, and range.
Learning Standards: A1.N.4, A1.P.1, A1.P.2, A1.P.9, A1.P.11, A1.D.1, A1.D.3,
Guiding Principles: Students will be able to look at the suspect’s data in terms of the
algebraic statistics presented.
Materials:
1. paper
2. pencils
3. calculators
Activity (35 minutes):
Students will put each of the four suspect's information on the board. The
suspect's height and foot size should be presented in centimeters:
Lou Lou
-height: 157.5 cm
-foot size: 23.63 cm
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Peg the Leg
-height: 150 cm
-foot size: 22.5 cm
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Dan the Man
-height: 175 cm
-foot size: 26.25 cm
Jake the Jock
-height: 195 cm
-foot size: 29.25 cm
A review of the following statistics should be discussed: mean, median,
mode, and range. Students should discuss definitions for each of these
statistics and put them on the board and in their notes:
mean: the average
median: the middle number after the data set has been put in numerical
order
mode: the data that appears most frequently
range: the difference between the largest and smallest data
Starting with height of the four suspects, students should calculate the four
statistics. After a review and discussion of those results, students should do
the same for the suspect's foot size.
For height:
mean: 169.38
median: 166.25
mode: no mode
range: 45
For foot size:
mean: 25.41
median: 24.94
mode: no mode
range: 6.75
Assessment: Student’s analysis of the suspect’s data should be organized
in a spreadsheet, matrix, or a simple table.
Conclusion/Next Step: there’s potential for an extension to this lesson, or a
fourth lesson for this module:
Lesson 4: Suspect's Data To Teach Graphing (Optional)
Now that all the data on the suspects has been calculated, its time to put that data to
use.
Materials:
1. paper
2. pencils
3. calculators
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Activity:
Students will put each of the four suspect's information on the board. The
suspect's height and foot size should be presented in centimeters:
Lou Lou
-height: 157.5 cm
-foot size: 23.63 cm
Peg the Leg
-height: 150 cm
-foot size: 22.5 cm
Dan the Man
-height: 175 cm
-foot size: 26.25 cm
Jake the Jock
-height: 195 cm
-foot size: 29.25 cm
The suspect's data will be graphed on the coordinate plane. Students
should discuss the independent vs. dependant axes and determine which
data should go on which axis. Students should set up their axes then plot
the coordinates. From there, conversations regarding slope, line of best fit,
distance, and midpoint could be pursued.
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