Measurement and Data
The Measurement and Data domain tests converting units within a measurement system, solving problems involving perimeter and area, and interpreting data on line plots. Questions expect accurate unit labels and attention to whether a measurement is a length, a liquid volume, a mass, or a time interval.
Unit conversions
- Length: 1 kilometer = 1,000 meters; 1 meter = 100 centimeters; 1 centimeter = 10 millimeters.
- Mass: 1 kilogram = 1,000 grams. Liquid volume: 1 liter = 1,000 milliliters.
- Time: 1 hour = 60 minutes; 1 minute = 60 seconds.
- Converting from a larger unit to a smaller unit multiplies. Converting from a smaller unit to a larger unit divides.
Perimeter and area
- Perimeter is the distance around a figure and is measured in linear units. For a rectangle, P = 2 × (length + width).
- Area is the number of square units covering a figure. For a rectangle, A = length × width.
- The same dimensions can produce different numerical perimeter and area values, so keep the units and the formulas separate.
Line plots
- Each mark on a line plot represents one data value. Count marks carefully, especially when several marks stack above the same fraction.
- Read the scale before counting. A line plot may be divided into halves, fourths, or eighths.
- Use the line plot to answer questions about the most common value, the difference between the greatest and least values, or the total number of observations.
Worked example
A jug contains 3.25 liters of juice. How many milliliters is that? Since 1 liter = 1,000 milliliters, multiply by 1,000. 3.25 × 1,000 = 3,250 milliliters. Reason it out: 3 liters = 3,000 milliliters, and 0.25 liter = 250 milliliters, for a total of 3,250 milliliters.
Traps that cost marks
- Mixing units, such as subtracting centimeters from meters without converting first.
- Labeling area in linear units or perimeter in square units.
- Using the area formula when the question asks for distance around a figure.
- Miscounting stacked marks on a line plot or reading the wrong fractional interval.
- Multiplying when converting from milliliters to liters instead of dividing.