Watch Measure for Measure: Lengths and Heights , and point out that the narrator says, "Measurement rules our lives. It has sliced up our world and helped us impose order and logic on our restless universe." Ask students what they think this means. Ask what a world with no measurements would be like. Then have students discuss how people featured in the program (below) used measurements.
Ask students why accurate measurements were so important to these people. ( Sailors needed to know the time to determine longitude or they could be off course by hundreds of miles. Accurate measurements allow scientists to predict tsunamis and give warnings. The rower must know how well his heart is pumping blood. )
The video segment "Going the Distance" reviewed the history of measurements and noted that different countries once used their own measurement systems. How have units of length been determined? ( People used the length of their own foot, hand, fingertip, pace, or the distance from the elbow and fingertip. In England, the distance from the ruling monarch's nose to fingertip was one yard and three barleycorns made up one inch. ) What was the problem with using the human body or natural products as a standard of measurement? ( They always differ. ) Who first called for standard measurements, and why? ( Traders needed to know how much they were buying or selling. )
The foot has long been a unit of measurement, but it has ranged between 10 and 27 inches. Explain to students that in this activity, they will use their own feet as a standard measurement and then measure and compare distances.
Have students work with a partner to measure the length of their feet without shoes. Have them record this measurement in standard inches.
Length of my foot in standard inches: _____________
Using their personal unit measurement, have students determine the length of a personal non-standard inch. They should divide the length of their foot by 12. (Example: If a student's foot measures 8 inches, a non-standard inch would be 8 divided by 12 = .6.) Students may round their answer to the nearest eighth.
Length of my personal inch in standard inches: _____________
Have students draw two squares with four-inch sides, one using standard inches, the other using personal inches. (Using the example above, the second square would have 2.5-inch sides.)
Have students attach their personal squares to the board. Discuss the consequences of countries using non-standard measurements. For example, what if one country supplied parts for a machine to be produced in another country?
Now students will consider their personal units of measurement on a larger scale. How many personal feet would go into a mile? (5,280 standard feet = one mile) When comparing feet to miles, the numbers are very large, so it will be easier to compare standard miles and new miles using a ratio. First, determine the ratio of the standard foot to a personal foot. For example, 12 inches to 8 inches is 12: 8, or 1.5. In other words, a standard foot is 1.5 times larger than the new foot. Since ratios are constant, you can also say that a standard mile is 1.5 times longer than a personal mile. That means a distance of 100 standard miles would measure 150 personal miles. (They will multiply the distance times 1.5: 100 X 1.5 = 150))
Give students a chart to show distances between your school or town and different locations. Then have them use the ratio to determine the distances with their personal measurement system. For example, your chart might look like this:
|Distance||Standard Miles||Personal Miles|
|from school to mall||5 miles||7.5 miles|
|from Charlotte, North Carolina, to Asheville, North Carolina||130 miles||195 miles|
|from Charlotte to New York, New York||630 miles||945 miles|
|from Charlotte to Paris, France||4,165 miles||6,247.5 miles|
Have students share some of the distances they determined. Then discuss the consequences of using non-standard units of measurement. Pose these questions to the class: What would happen if you gave directions to the mall using personal miles? What if a pilot used personal miles to calculate the distance on an international flight to Paris? Why are standard measurements so important? Ask students to share other examples of why accurate measurements are critical.
Definition: a decimal system of units based on the meter as a unit length
Context: Most countries use the metric system.
Definition: a unit of length equal to 12 inches
Context: Although the standard length of a foot is 12 inches, it has ranged throughout history between 10 and 27 inches.
Definition: the relation of one part to another or to a whole
Context: In the group are four boys and three girls, so the ratio of boys to girls is 4 to 3, or 4: 3.
This lesson plan addresses the following national standards: