IP 614

Name:______Block: _____Date:___/____/______

Metric Measurement Activity—

Ratios & Relative Sizes

Introduction:

In 1487, Leonardo da Vinci suggested that the span of a person’s arms is equal to the person’s height. Is this true? What do you think? Do you believe in his hypothesis? What are some other interesting facts you can learn about yourself, your environment, and your lives when you learn about the measurement, metric unit and unit conversion? We will be exploring the idea of sizes and relative sizes of objects in this activity.

In this activity you will be asked to make metric measurements as well as to convert from one metric unit to another. In addition, you will demonstrate your mastery of unit conversion by exploring relative sizes of everyday objects. You’ll also measure the quantities of stuff you use every day and use those measurements to calculate your environmental footprint.

Learning Objectives: By the end of this activity, you should be able to…

  • Measure with reasonable accuracy.
  • Convert length quantities from one unit to another using the Factor Conversion Method (dimensional analysis).
  • Identify appropriate standard international units of measurement of length (meters) and the prefixes milli-, centi-, and kilo-.
  • Calculate averages (mean) and deviations for a set of measurements.
  • Accurately record data, with the correct units, at the time of observation.

New Vocabulary:

  • measurement
  • unit
  • SI units
  • order of magnitude
  • SI base unit
  • SI derived units
  • measurement uncertainty
  • measurement error
  • accuracy
  • mean (average)
  • milli-
  • centi-
  • kilo-
  • metric prefixes
  • meter
  • precision

Activity I: Leonardo da Vinci’s hypothesis

The golden ratio is a number that refers to ratios of distances in simple geometric shapes. During the Renaissance, literature on the aesthetics of the golden ratio inspired architects, painters, and musicians to explore measurements of natural and human-made objects in attempt to understand and incorporate the golden ratio in all aspects of life.

Leonardo da Vinci (April 15, 1452—May 2, 1519), a famous Renaissance artist, scientist, and mathematician, who painted the famous Mona Lisa and The Last Supper, was interested in the proportion of the human body and he made a drawing called the Vitruvian Man, whose arm span is equal to the height of the man.

Activity for you to do—

1)Ask a partner to use a meter stick to measure your height in both centimeters and meters.

My height in centimeters: ______My height in meters: ______

2)Ask a partner to use a meter stick to measure your arm span in both centimeters and meters.

My arm span in centimeters: ______My arm span in meters: ______

3)Make a table of all the students’ names in the class, arm span, heights, and ratio (height / arm span). Report the measurements in meters.

Name / arm span / height / ratio (height/ arm span)

4)Graph height vs. arm span for all the students in the classroom. Use two different color codes on the graph, one for male students and one for female students.

Analysis Questions:

1)What was Leonardo da Vinci’s hypothesis in his drawing of Vitruvian Man presented in Model 1?

2)How closely did your arm span compare with your height?

3)Calculate the average (mean) arm span of students in the class. Show your work!

4)Calculate the average (mean) height of students in the class. Show your work!

5)Do high school male students in the 21st century have the same proportions as the Vitruvian Man?

6)Do high school female students in the 21st century have the same proportions as the Vitruvian Man?

7)Does the arm span increase linearly with height? (i.e. is there a sort of best-fit line through the data that shows that the taller you are the wider your arm span is?)

8)Draw the best-fit lines for male and female students on the graph paper. Calculate the slope of each set of data. SHOW YOUR WORK!

9)What do the slopes tell you about Leonardo’s hypothesis?

10)What is the average arm span of the students in the class? SHOW YOUR WORK.

11)If all the freshmen in the high school held hands and formed a chain, how long would the chain be? Round your answer to the nearest meter. (SHOW YOUR WORK Using Unit Conversion Method)

12)What is the average height of the students in the class? SHOW YOUR WORK.

13)If all students stood on top of each other’s heads, forming a tall pillar, how high would the class reach? Round your answer to the nearest meter. (SHOW YOUR WORK USING Unit Conversion Method)

14)What is an object approximately as tall as this human pillar?

Activity II. Compare the size of centimeters, meters, and kilometers

1) Which measurement is the largest? Circle your answer for each pair.

(a) 2 m or 2 cm / (c) 145 m or 145 km
(b) 50 m or 1 km / (d) 3.4 cm or 2 m

2) Circle the BEST metric unit for each.

(a) The height of a flagpole / cm / m / km
(b) The length of a strand of spaghetti / cm / m / km
(c) The distance from Newton to Framingham / cm / m / km

3)Which of the following measurements are good estimates?

(a) The height of a chicken / 4 cm / 40 cm / 400 cm
(b) The length of a cow / 2 m / 20 m / 200 m
(c) The length of the school / 30 m / 300 m / 3 km

Activity III—Relative Sizes of Objects

How much of the world’s resources do YOU consume? What is human footprint? We will be measuring the size of common consumables and compare them to relative sizes that we know.

Procedure—

1)Use a rule, measure the following objects around the room. Make sure you measurements in whatever units seem convenient and then convert to the other units. (Objects to measure: a) height of a pint of milk b) length of a loaf of bread c) height of a soda can d) length of a pair of jeans e) length of a hot dog f) height of a hamburger

Height of a pint of milk / = ______m / = ______cm
Length of a loaf of bread / = ______m / = ______cm
Height of a soda can / = ______m / = ______cm
Length of a pair of jeans / = ______m / = ______cm
Length of a hot dog / = ______m / = ______cm
Height of a hamburger / = ______m / = ______cm

2)Watch the Human Footprint Video:

Analysis:

1)If you were to stack two bottles of milk on top of each other, how high would the stack measure? SHOW YOUR WORK.

2)The typical American drinks 13,056 pints of milk during a lifetime. If you were to stack these bottles of milk on top of each other, how high would the stack measure? SHOW YOUR WORK.

3)If you were to line up two loaves of bread end to end, how long would the line measure? SHOW YOUR WORK.

4)The typical American eats 4376 loaves of bread in a lifetime. If you were to line this many loaves of bread end to end, how long would the line measure? SHOW YOUR WORK.

5)The typical American drinks 43,371 cans of soda. If you were to stack a lifetime supply of soda cans on top of one another, how high would the stack measure? SHOW YOUR WORK. (How many food Calories does that represent? SHOW YOUR WORK.)

6)The typical American man has 7 pairs of jeans in his closet. If you were to line these jeans up end to end, how far would the line measure? SHOW YOUR WORK.

7)The typical American eats 5442 hot dogs in a lifetime. If you were to line these hot dog buns end to end, how long would the line measure? SHOW YOUR WORK.

8)The average American eats 12,129 hamburgers in a lifetime. If you were to stack these hamburgers on top of each other, how high would the stack measure? SHOW YOUR WORK!

9)Write or draw where the items in the table would fit on the picture below.

lifetime supply of milk / 1 mm
lifetime supply of soda cans / 1 cm
lifetime supply of hamburgers / 1 m
1 km

10)Write or draw where the items in the table would fit on the picture below.

lifetime supply of bread / 1 mm
Jeans in a man’s closet / 1 cm
lifetime supply of hot dogs / 1 m
1 km

Note: The distance from NNHS to the Newton City Hall is approximately 1 km.

Reflection: Write/Type a 1-page reflection to address the following questions

What are some important and interesting insights you have gained through this activity? (Comment on at least three different things you learn, it can be about unit conversion, finding relative sizes, the hypothesis presented, the connection you made after this exercise and watching the Human Footprint Video, etc…) Is there something else you are interested in learning about measurement? Have you wondered about other interesting patterns like femur length to height ratio? Things you could do to reduce your consumption?