# Submarines: Using mass, volume and density to create a working submarine

The students will design a submarine that will float, subsurface, sink, and return once again to the water's surface by external manipulation of the submarine outside of an aquarium. In order to accomplish this, the students will use not only the concepts of mass, volume, and density but will also integrate buoyancy and ballast in their submarine design.

**A lesson plan for grades 8–12 Mathematics and Science**

## Learning outcomes

- The students will first explore the concept of mass. They will learn how to mass objects and will compare various objects according to their mass.
- The students will explore the concept of volume. They will learn how to find the volume of regular as well as irregularly shaped objects and will compare these objects according to their volume.
- The students will manipulate the formula for density (Density = mass/volume). They will find the density of various objects and experiment with how density affects the floating and sinking capabilities of these objects.
- The students determine that in tap water (which has a density of one gram/ml), that floating objects have a density less than one gram/ml and that sinking objects have a density greater than one gram/ml.
- The students learn that ballast is any material added to an object to cause it to sink, and that buoyancy is an object’s ability to float. The amount of ballast an object holds determines its capability to remain floating or sinking.
- The teacher will conduct a series of lab experiences that will reinforce the above mentioned objectives. At the end of the unit, the teacher will assign the submarine project. The students should realize that their submarine must have a means to take water (ballast) in, causing it to sink, and then removing the water, causing it to float. They should know through lab experiences that when an object’s mass is less than its volume that it will float, when mass is equal to volume, it will subsurface, when mass is greater than volume, it will sink. They will determine the materials to build the submarine as well as the procedure to aid it in floating and sinking.

## Teacher planning

### Time required for lesson

4 weeks

### Materials/resources

- triple beam balance
- metric ruler
- overflow containers (volume of irregular objects)
- aquarium (minimum ten gallon in size)
- fifteen dishpans
- fifteen graduated cylinders
- water
- fifteen objects of varying mass
- fifteen objects of varying volume
- fifteen regular shaped objects to practice cubic volume
- fifteen irregular shaped objects (use overflow container)
- fifteen objects to use to determine their density
- various objects that either float or sink in water

## Pre-activities

The students should have a working knowledge of basic science laboratory skills such as how to use a triple beam balance, a graduated cylinder, a metric ruler, and an overflow container to determine the volume of an irregularly shaped object.

## Activities

This unit consists of a series of laboratory experiences outlined as follows:

- To give the students practice in determining mass, place the students in groups of two, allow them to first predict the mass of fifteen different objects. Once this is complete, they should actually determine the mass of the objects, rotating these objects until every group has measured every object. Discuss the data and any inconsistencies between their predictions and the actual data. They should discover that often the mass of an object can be deceiving and that often a small object may have a large mass or a large object may have a small mass.
- To give the students practice in determining volume, again place the students in groups of two, and allow them to predict the volume of fifteen different objects. Teach the students the three different ways to determine the volume of objects (capacity—how much the object holds, formula method—length × width × height for cubical shapes, and overflow method for objects with irregular shapes. Repeat procedures as with the mass lab and discuss any inconsistencies such as variances in volume and how size and shape can deceive perceived volume.
- Placing the students in groups of two, practice determining the density of various objects using a triple beam balance, a metric ruler, and an overflow container (these objects should consist of some that will float and some that will sink). Discuss how density changes according to the mass or volume of each object and explore the concept of density in relation to mass per unit volume (one gram per cubic centimeter).
- Using the floaters and sinkers from the density lab mentioned above, explore further what causes this phenomena to occur. Using the density data on these objects, students should discover that the relationship of mass to volume determines the floating and sinking ability of objects. Also, they should experiment with ballast and how much ballast an object can hold before it loses buoyancy and begins to sink.
- To introduce the submarine project, the students may experiment with Cartesian divers made from an eyedropper and a sealed plastic soda bottle filled with water. When the dropper is started from a floating position and the bottle is squeezed, it forces water into the dropper adding mass to it and causing it to sink. When the bottle is not being squeezed, the water escapes from the dropper, decreasing its mass, and causing it to float once again. Students should deduce that their submarines should operate in the same manner, and incorporating unit concepts, tie this information together into the design and creation of their submarine.

## Assessment

- At the end of this unit, the students will be given a unit test that will cover all unit concepts. The students will be given a handout with a chart identifying various objects for which the mass, volume, and density of the objects to be determined and recorded on the chart. Though I used the test with my Advanced Learners, segments may be modified to use with all ability levels.
- The students should be given approximately one month to complete their submarines. A teacher-made rubric determines their grade.

## Supplemental information

This unit also has interdisciplinary possibilities by connecting the concept of density and floating objects into icebergs and the Titanic. Students read the Titanic in the Language and Literature text used in seventh grade. There is an excellent National Geographic video called “Secrets of the Titanic” which shows actual footage of Dr. Robert Ballard discovering the Titanic wreckage two miles under the sea. Also, the internet is a very good resource for not only Titanic research but many of my students have used it to research ideas for submarine design and construction.

### Comments

I often videotape my students presenting their submarines and allow my students to “show-off” at events such as Family Science Night or PTSA Parent Night. This is a very challenging unit as well as culminating project and I have implemented this with students from all ability levels. It is truly amazing to see the pride the students have in their projects once complete and the joy they experience as they rise to the challenge!

- Common Core State Standards
- Mathematics (2010)
#### Grade 8

- Geometry
- 8.G.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

- Geometry
#### High School: Geometry

- Geometric Measurement & Dimension
- GEO.GMD.3Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

- Geometric Measurement & Dimension
- North Carolina Essential Standards
- Science (2010)
#### Physical Science

- PSc.1.1 Understand motion in terms of speed, velocity, acceleration and momentum. PSc.1.1.1 Explain motion in terms of frame of reference, distance, and displacement. PSc.1.1.2 Compare speed, velocity, acceleration and momentum using investigations, graphing,...

#### Physics

- Phy.1.1 Analyze the motion of objects. Phy.1.1.1 Analyze motion graphically and numerically using vectors, graphs and calculations. Phy.1.1.2 Analyze motion in one dimension using time, distance, displacement, velocity, and acceleration. Phy.1.1.3 Analyze...

## North Carolina curriculum alignment

### Science (2005)

#### Grade 8

**Goal 1**: The learner will design and conduct investigations to demonstrate an understanding of scientific inquiry.**Objective 1.01**: Identify and create questions and hypotheses that can be answered through scientific investigations.**Objective 1.02**: Develop appropriate experimental procedures for:- Given questions.
- Student generated questions.

**Objective 1.05**: Analyze evidence to:- explain observations.
- make inferences and predictions.
- develop the relationship between evidence and explanation.

**Goal 3**: The learner will conduct investigations and utilize appropriate technologies and information systems to build an understanding of the hydrosphere.**Objective 3.01**: Analyze the unique properties of water including:- Universal solvent.
- Cohesion and adhesion.
- Polarity.
- Density and buoyancy.
- Specific heat.