This lesson is an introduction to density. Students will explore a variety of materials and learn how density, mass, and volume are related. They will be introduced to how density in liquids affects their behavior. They will learn how to calculate the density of a cube using a scale and a ruler. In addition, they will hear the tale of Archimedes and learn how to use a graduated cylinder to solve for volume via the displacement of water. This lesson also reviews math skills, requiring students to multiply and divide to solve problems. (Most appropriate for grades 5-9, easily adjusted to fit each grade level.)
Standards:
4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole.
5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
5.MD.3: 3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.5: Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with whole number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole number products as volumes, e.g., to represent the Associative Property of Multiplication. b. Apply the formulas V = ℓ × w × h
6.PS.1: Matter is made up of small particles called atoms. Matter has mass, volume, and density and is made up of small particles called atoms. Single kinds of atoms are elements, combinations of two or more atoms joined chemically are called molecules.
PS.M.1: Classification of matter: Heterogeneous vs. homogeneous (alloys are discussed, liquid solutions and the separation of heterogeneous mixtures). Properties of matter (density).
STEM Emerging Technology Connections:
Advanced Materials: Density is a fundamental material property, important for the DoD's research into new materials with specific characteristics.
Hypersonics: Density is crucial for understanding how objects move through air, essential for designing hypersonic vehicles. It also helps in selecting lightweight yet strong materials.