Distinguishing Volume and Surface Area

5 min

Narrative

The purpose of this Warm-up is for students to reason, within a context, about two objects that have the same volume but different surface areas. 

Launch

Give students 1 minute of quiet think time, followed by a whole-class discussion. 

Student Task

Mai’s science teacher told her that when there is more contact between the ice and water in a glass, the ice melts faster. She wants to test this statement so she designs her science fair project to determine if crushed ice or ice cubes will melt faster in a drink.

She begins with two cups of warm water. In one cup, she puts a cube of ice. In a second cup, she puts crushed ice with the same volume as the cube. What is your hypothesis? Will the ice cube or crushed ice melt faster, or will they melt at the same rate? Explain your reasoning.

Sample Response

The crushed ice will melt faster because there are more parts touching the warm water. The increased surface area will make the crushed ice melt faster.

Synthesis

The goal of this discussion is to focus on the role of surface area in the speed of ice melting in water. Poll the students on their hypotheses. Record and display their responses for all to see. If all students agree that the crushed ice will melt faster, ask them to share their reasoning. If there are different hypotheses, ask students to explain their choice and ask questions of one another. Continue the discussion until the students reach an agreement on the crushed ice. Important ideas to highlight during the discussion are:

  • Since the crushed ice has more places touching the warm water, it should melt faster.
  • The center of the cube is surrounded by cold ice and will not melt until it is touching the water.
  • The surface area of the crushed ice is greater, so it will melt faster than the ice cube even though they have the same volume.

If any of these ideas are not mentioned by students, bring them to their attention at the end of the discussion. 

Standards
Addressing
  • 7.G.6·Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
  • 7.G.B.6·Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

10 min

15 min

5 min