Geometry and Measurement
The Geometry and Measurement domain on Grade 5 FAST Math covers volume of rectangular prisms, classification of two-dimensional figures, the first quadrant of the coordinate plane, and unit conversions. Items often combine two ideas, such as finding the volume of a composite solid made from rectangular prisms or plotting points that form a rectangle and finding its side lengths.
Volume
- Volume is the number of unit cubes that fill a solid, measured in cubic units.
- For a rectangular prism, V = length × width × height, or V = area of the base × height.
- A composite solid can be split into rectangular prisms; find each volume and add.
- Volume and surface area are different: volume measures space inside, while surface area measures the outside faces.
Classifying figures
- Quadrilaterals are classified by parallel sides, right angles, and equal sides. A square is also a rectangle and a rhombus, but a rectangle is not always a square.
- Triangles can be classified by angles (acute, right, obtuse) or by sides (equilateral, isosceles, scalene).
Coordinate plane
- An ordered pair (x, y) gives the horizontal distance first, then the vertical distance.
- The origin is (0, 0); the Grade 5 grid uses positive coordinates only.
Conversions
Use relationships such as 1 foot = 12 inches, 1 yard = 3 feet, 1 meter = 100 centimeters, and 1 liter = 1,000 milliliters. Multiply when converting from a larger unit to a smaller unit; divide when converting from a smaller unit to a larger unit.
Worked example
A fish tank is 6 feet long, 4 feet wide, and 2.5 feet high. Find its volume. V = 6 × 4 × 2.5 = 24 × 2.5 = 60 cubic feet. The answer is in cubic feet because three length measurements are multiplied.
Traps that cost marks
- Adding length, width, and height instead of multiplying.
- Reporting square units for a volume answer.
- Reversing coordinates when plotting or reading an ordered pair.
- Multiplying when converting from a smaller unit to a larger unit.
- Classifying a square as “only a square” and denying that it is also a rectangle.