Measurement and Data: Unit Conversion, Line Plots, and Volume
Measurement and Data in Grade 5 tests unit conversion within a measurement system, line plots with fractional data, and volume of right rectangular prisms, including composite solids.
Converting measurements
Within a system, multiply when converting a larger unit to a smaller unit and divide when converting a smaller unit to a larger one. Useful Grade 5 equivalences: 1 km = 1,000 m; 1 m = 100 cm; 1 kg = 1,000 g; 1 L = 1,000 mL; 1 hour = 60 minutes; 1 foot = 12 inches; 1 yard = 3 feet; 1 pound = 16 ounces. So 3.5 m = 3.5 × 100 = 350 cm, and 250 mL = 250 ÷ 1,000 = 0.25 L.
Line plots
Each X represents one data value; fractional values such as 1/4, 1/2, and 3/4 are common. To find a total, multiply each value by its number of X’s and add; to find a difference, subtract the values asked about. The number of X’s is a count, not the data value.
Volume
Volume is the number of cubic units that fill a solid. For a right rectangular prism, V = length × width × height, or V = area of the base × height. A prism 4 cm by 3 cm by 2.5 cm has V = 4 × 3 × 2.5 = 30 cm³. A composite solid made of two non-overlapping prisms is handled by finding each volume and adding.
Worked example
A fish tank is 10 in long, 6 in wide, and 8 in tall. The base area is 10 × 6 = 60 in². The volume is 60 × 8 = 480 in³. If the tank is filled to a depth of 5 in, the water volume is 60 × 5 = 300 in³.
Traps that cost marks
- Multiplying when the conversion requires dividing, or the reverse.
- Writing volume in square units or area in cubic units.
- Adding side lengths instead of multiplying dimensions.
- Reading a line plot’s X count as the data value.
- Forgetting that the parts of a composite prism must not overlap.