Metric Mastery

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Metric Mastery was a Division B event last ran in 2014, which tests the students' ability to quickly and accurately estimate and measure the physical properties of objects in metric units. Properties to be measured can include mass, volume, density, area, force, distance, time, and temperature.

This will usually be a station based event. In the first part of the competition, students will estimate the properties asked for of an object in or in less than 30 seconds, then move on when they are given directions to do so. In the second part, students will usually move back to the same objects with measuring tools, and accurately measure them. In the third part of the competition, students will be given 5 minutes to complete 5 metric unit conversion problems.

During the years between 1984 and 1993, the event was held as Measurement and Metric Estimation. These events were later combined in 1994 to the event Metric Mastery.

Metric Properties

The following are the primary properties that will be used in this event. Other properties are possible (e.g. velocity) but these are the ones that will show up most of the time.

Metric Properties
Property Base Unit
mass grams (g)
distance meters (m)
area square meters ([math]\displaystyle{ m^2 }[/math])
volume cubic meters ([math]\displaystyle{ m^3 }[/math])
density kilograms per cubic meter ([math]\displaystyle{ \frac{kg}{m^3} }[/math])
force newtons (N)
time seconds (s)
temperature degrees Celsius ([math]\displaystyle{ ^{\circ}C }[/math])

Part One: Estimate

In the estimation part of the event, students must estimate the measurements of objects provided by the supervisor. There will usually be between 15-25 stations in this part. The estimations will vary among all of the different properties. About two-thirds of the stations should be direct estimation, while one third will require some sort of calculation.

  • 30 seconds is the recommended time that the event supervisors should give for each estimation.
  • Students may not use any tools to help them estimate.
    • Such "tools" include watches, writing implements, electronic devices, notes, fingers, pieces of paper, pencils, clothing, etc. In the case that some things are impossible to leave behind (fingers, clothing), they cannot be utilized in the competition.
  • The event supervisor will provide pencils.
  • Students may not touch, feel, or "heft" the objects, unless otherwise explicitly stated.
  • Use correct units. The supervisor will identify which units to use.
  • Follow the correct rotation order.
  • No calculators are allowed.

Helpful Tips

  • Practice is key for this event, but especially for this part! Without practice it will be very hard to estimate the measurements to any great deal of accuracy. Practice will let you see how the appearance of certain objects relates to what they actually measure. Also, it will give you a reference point that you can use in competition (i.e. if an object looks shorter than an object you worked with in practice, you know that the length must be smaller)
  • Practice with lots of areas and volumes. This will help you be faster in quickly estimating the calculations at the competition.
  • If they give you a sphere or something else that uses [math]\displaystyle{ \pi }[/math], replace it with a 3. It will be a lot easier to calculate in your head and you will be close enough to the correct value.
  • Make sure students understand that their first station will not necessarily be number one on their paper. They might be starting at any number.
  • Quick conversion: if you can estimate mass well but are not as good at estimating force, you can divide grams by 100 or multiply kg by 10 to get Newtons. You will automatically be off by 2%; however, if their mass estimate is very accurate, they may still be within 10% of the correct measurement of force.

Scoring

Scoring system for the estimation section of the competition:

  • 5 points if within 5% of measured value
  • 3 points if within 10% of measured value
  • 1 points if within 20% of measured value
  • Not in any of the above, 0
    • If in one of the categories, only points for that category are awarded (if you land within 3%, you only get 5 points. You do not get 5+3+1 points)

Part Two: Measure

In the measurement part, students will physically measure the various properties of objects given. Like the first part, there will be between 15-25 stations, and they will be 2/3 direct measurements and 1/3 calculated measurements. Both students are allowed a non-programmable calculator for this section.

  • 60 seconds is the recommended time that the event supervisors should give for each measurement.
  • Use correct units. The supervisor will identify which units to use.
  • Measure to the precision of the instrument plus one estimated digit.
  • For the calculated measurements, significant figures must be used.
  • Follow the correct rotation order. The first station you visit may not necessarily be number one on your paper. You could start at any number.

Helpful Tips

  • Students must realize that not all graduated cylinders are the same, nor are all rulers, or any other measurement instrument. They should practice determining what degree of precision to include in their measurements.
  • Students should practice using a variety of measuring instruments.
    • Practice using a vernier scale such as seen on calipers.
    • Practice using a vernier caliper to find internal diameter (ID), outside diameter (OD) and depth.
    • Practice using micrometers.
    • Practice using instruments with a reversed scale such as on some pipettes.
    • Practice using double pan or Harvard Trip balances.
    • Practice calculating mass by using tare mass (measuring the mass of an empty container and then subtracting it from the mass of the container and the substance it contains).
  • Although it is a good practice to calibrate instruments before they make measurements, do not assume you should at a competition. Check with an event supervisor before adjusting any instrument!
  • Evaluate rulers and meter sticks carefully before you begin measurement, if there isn't a true 0, start measurement at 1 and then subtract 1 from the measurement.

Scoring

  • For direct measurements:
    • Correct if within [math]\displaystyle{ \pm3 }[/math] of the estimated digit
      • For example, if a ruler's smallest increment is 1 mm, the range will be [math]\displaystyle{ \pm0.3 }[/math] mm of the correct answer as determined by the supervisor
  • For calculated measurements:
    • Correct if within the range of calculated values based on [math]\displaystyle{ \pm3 }[/math] of the estimated digits of the direct measurements
  • If correct, the team receives 5 points; if incorrect, no points are awarded

Part Three: Metric Unit Conversion

  • After parts 1 and 2, students will be given 5 minutes to solve 5 metric unit conversion problems.
  • Students will be asked to convert from metric to metric, and will not be required to convert from one measurement system to another. (e.g. centimeters to inches)
  • Conversions typically follow the lines of converting a four or more digit number from a minuscule digit to a large digit, or vise versa.
    Ex. "Convert 3.598x10^3 picometers to kilometers."

Helpful Tips

  • Don't forget your dimensions (e.g., there are 10 decimeters in a meter, but there are 100 square decimeters in a square meter, and 1,000 cubic decimeters in a cubic meter)
  • To perform a conversion, one easy way is to multiply the number they give you by the multiplier of the old unit divided by the multiplier of the new unit. Using the example above:

[math]\displaystyle{ 3.598 \times 10^3 pm * \frac{10^{-12}}{10^3} = 3.598 \times 10^3 * 10^{-15} = 3.598 \times 10^{-12} km }[/math]

  • Since scientific notation always uses a base of 10, you can do this in your head very easily because you can subtract the exponent of the new unit from the exponent of the old unit to get the exponent you need to multiply by. So in the above example, you would take -12 (the exponent for pico) and then subtract 3 (the exponent for kilo) from it. Then when you multiply 10^3 by 10^-15, all you need to do is add the exponents to get 10^-12, which will give you 3.598x10^-12. In almost all conversions, you are only changing the exponent, so you are really only adding and subtracting exponents most of the time.
  • To summarize exponent operations:
    • [math]\displaystyle{ 10^a \times 10^b = 10^{a+b} }[/math]
    • [math]\displaystyle{ \frac{10^a}{10^b} = 10^{a-b} }[/math]

Special Units

  • A metric ton or tonne is 1000 kilograms, or 1 megagram.
  • A Kelvin is degrees Celsius plus 273.15.

Metric Prefix Table

Metric Prefixes
Prefix Symbol Multiplier
yotta Y [math]\displaystyle{ 10^{24} }[/math]
zetta Z [math]\displaystyle{ 10^{21} }[/math]
exa E [math]\displaystyle{ 10^{18} }[/math]
peta P [math]\displaystyle{ 10^{15} }[/math]
tera T [math]\displaystyle{ 10^{12} }[/math]
giga G [math]\displaystyle{ 10^9 }[/math]
mega M [math]\displaystyle{ 10^6 }[/math]
kilo k [math]\displaystyle{ 10^3 }[/math]
hecto h [math]\displaystyle{ 10^2 }[/math]
deca (also deka) da [math]\displaystyle{ 10^1 }[/math]
--- --- [math]\displaystyle{ 10^0 }[/math]
deci d [math]\displaystyle{ 10^{-1} }[/math]
centi c [math]\displaystyle{ 10^{-2} }[/math]
milli m [math]\displaystyle{ 10^{-3} }[/math]
micro [math]\displaystyle{ \mu }[/math] [math]\displaystyle{ 10^{-6} }[/math]
nano n [math]\displaystyle{ 10^{-9} }[/math]
pico p [math]\displaystyle{ 10^{-12} }[/math]
femto f [math]\displaystyle{ 10^{-15} }[/math]
atto a [math]\displaystyle{ 10^{-18} }[/math]
zepto z [math]\displaystyle{ 10^{-21} }[/math]
yocto y [math]\displaystyle{ 10^{-24} }[/math]

Scoring

  • Answers must have the correct unit and correct value to receive points. *Answers must also have the same amount of significant figures as the value teams were given.
  • Correct answers receive 5 points.

Other Precautions

Make sure to:

  • return measuring devices to their original position
  • clean up any spills
  • never alter equipment without first asking an event supervisor (zeroing a balance, etc.-can result in disqualification)

Any of these violations will result in a 10 point penalty, each time.

Practice and Resources

Plastic vernier calipers can be picked up at many hardware stores. Instrument help online: There are many sites available to learning how to use tools such as a micrometer or a vernier caliper. If you use Google to search for a "vernier scale", you will find many usable sites.

A good way to practice this event is to just estimate and measure everything in sight. Make sure to give yourself units that objects wouldn't usually be measured in (e.g. a door in cm and a doorknob in km) and hard properties (e.g. density, mass, force, etc.)!

Links

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