Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Modeling density
Model density using area or volume with consistent units
Problem types
- Density from area and volume
- Rank regions by population density
Builds on
- Modeling with geometry
- Choosing units and a sensible precision
- Cavalieri's principle · Useful idea
Solids with equal cross-sections have equal volumes, so a slanted and a straight block of the same material have equal mass.
- Volumes of cylinders, cones, pyramids, spheres · Useful idea
Mass is density times volume, so a solid's volume formula gives the mass of a rod or block of known density.
- Volume with fractional edge lengths · Useful idea
Mass is density times volume, and volume of a prism with fractional edges gives the mass of a block.
- Mass and liquid volume · Useful idea
Density compares the mass of a material with its volume, both measured with the tools used for mass and volume.
Leads to
- Systems that model two constraints · See it applied
Mixing two materials of known densities to get a given total mass and volume is solved with a system of equations.
- Linear models of a situation · See it applied
A graph of mass against volume is a line whose slope is the density.
Related skills
- Designs that meet geometric constraints · Related idea
Mass is density times volume, and the cost of painting a wall is a price per square meter times the painted area. Both multiply a rate per unit by a measured amount, which is how a design is priced.
- Naming the quantities in a model · Shared foundations
Open the interactive map to explore lessons and skill connections.