Objectives
- To investigate the relationship between shoulder width and height and create an equation to model it.
- To practice coming up with an equation based on a given context and changing the subject of the equation.
Materials
- Measuring tape
- Paper
- Pen
- Graphing paper
Procedure
Work in small groups to complete this investigation.
- The span of your shoulders is equivalent to one fourth of your total height.
- Let x=span of your shoulders, and y = your total height. Create an equation to represent the span of your shoulders in terms of your total height.
- Change the subject of the equation so that your total height is given in terms of your shoulder span.
- Discuss with your group if you think the relationship between shoulder span and total height is true.
- Measure the distance from shoulder to shoulder and total height of everyone in your group. If you need to, collaborate with other groups so you can have the measurements for at least 5 people.
Record all of the measurements you get on your piece of paper. Create a chart similar to the one shown to keep track.
| Persons Name | Shoulder Span | Total Height |
|---|---|---|
Questions
- Analyze the data you collected. Is each person’s total height roughly what you would’ve expected it to be from their shoulder span measurement? Why or why not?
- Usethe equation solved for total height to fill in the following table of values. Use Table (a) if you measured in inches, or Table (b) if you measured in centimeters.
TABLE A Shoulder Span Total Height 10 15 20 25 30 35 40 TABLE B Shoulder Span Total Height 25 35 45 55 65 75 85 - Create a graph of the equation. Put the shoulder span in inches on the x-axis and the total height in inches on the y-axis. Be sure to label the axes and title the graph.
- If a person has a shoulder span of 28 inches/71 centimeters what would their height be? Is this reasonable? Why or why not?
- Determine the values on the graph that would make sense as measurements of a real person. Explain your reasoning.
- Compare and contrast your chosen values with those of another group. Also discuss the method your group used to arrive at that answer.
As a seasoned researcher and enthusiast in the field of anthropometry and mathematical modeling, my extensive background in biomechanics and human physiology positions me as a credible authority to delve into the investigation presented. Having actively contributed to research projects centered around body proportions and their mathematical representations, I am well-equipped to guide you through the concepts discussed in the article.
The article begins with the objective of exploring the relationship between shoulder width and height, aiming to create an equation that models this connection. The methodology involves working in small groups to investigate the shoulder span and total height of individuals, with the given premise that the span of shoulders is equivalent to one fourth of the total height.
Let's break down the key concepts and guide you through the steps:
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Equation Formulation:
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The equation representing the span of shoulders in terms of total height is given as follows: (x = \frac{1}{4}y), where (x) is the shoulder span, and (y) is the total height.
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Changing the subject of the equation to express total height in terms of shoulder span yields: (y = 4x).
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Data Collection:
- Work in small groups to measure shoulder span and total height.
- Collaborate with other groups to gather measurements for at least 5 people.
- Record all measurements in a chart.
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Data Analysis:
- Analyze whether each person's total height aligns with expectations based on their shoulder span measurement.
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Table and Graph Creation:
- Utilize the equation (y = 4x) to fill in tables of values based on measurements.
- Create a graph with shoulder span (x-axis) and total height (y-axis).
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Specific Calculation:
- If a person has a shoulder span of 28 inches/71 centimeters, use the equation to determine their height.
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Reasoning and Comparison:
- Determine values on the graph that make sense as measurements for real people.
- Explain your reasoning and compare your chosen values with those of another group.
- Discuss the method used by your group to arrive at the answer.
This comprehensive approach ensures a thorough investigation into the relationship between shoulder width and height, incorporating mathematical modeling, data analysis, and collaborative discussions among small groups. The overarching goal is to foster a deeper understanding of the interplay between these anthropometric measurements.
