Unknown Volumes

Middle School and High School Teacher

Finding the volumes of miscellaneous-sized containers using a known total measurement of one container.  They will do this in as few steps as possible.

Grade Level: 4 - 6th

Subject: Math

Length of Time: About 2-3 Class Periods

Featured Programs:
Sponsored School(s)

Common Core Alignment

CCSS.Math.Content.5.MD.A.1 - Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Objectives & Outcomes

The students will be able to determine the volume of unknown-sized containers using one known-sized measuring cup or other container in as few steps as possible.

Materials Needed

One 8 or 16 ounce (or other size) container, at least 5 other miscellaneous containers, access to water, ruler, handout

Prepare ahead of time:  Empty containers for every three students:  One empty symmetrical container with a total measurement of 8 or 16 ounces (It cannot have lines showing individual ounces.), plus at least 5 containers without its size shown.  The containers do not necessarily have to be for a liquid.  For example, using a plastic container from any product would be useful, as long as it can hold water.  Large water containers students to use to access water, dump water, etc., especially if a sink is not near.  One measuring cup, or similar, to check for exact volumes in miscellaneous containers following activity.  Prepare a handout for students to sketch each container and to show its volume in ounces.  You may decide to label every container with letters/numbers.


Opening to Lesson

  • Display two of the same containers, one full of water, the other empty.  Tell students there are X ounces of water in the full container.  Ask students:  How can we make sure both containers have the same number of ounces?
  • Allow for responses and discussion.  Most students should discover that pouring half the liquid into the empty container would solve the problem.
  • Next, ask what one could do if the containers were not the same size.
  • Allow for responses and discussion.

Body of Lesson


  • Pour half the water into the second container.
  • Tell students they will also try and determine the volumes of different sized containers using a single container of water.
  • They will pour water into, out of, exchanging amounts, recording amounts, etc.
  • The goal is to determine the volumes of each empty container in as few steps as possible.

Guided Practice

  • Place students in groups of three.  Assign one student to record information, but he or she is also participating by sharing ideas, etc.
  • Distribute a chart showing volumes: ounces in a cup, etc.
  • Review the chart with the class.
  • Distribute the empty containers along with the chart for recording information.
  • Tell students to brainstorm ideas to determine volumes of each container.  They should not need to guess.
  • Distribute the known container with the water and a ruler.  Allow access to a dumping bucket, additional water.  Tell students to be as neat as possible.
  • Allow students a sufficient amount of time to solve the problem in as few steps as possible.
  • Once they have determined volumes of each container, remind the recorder to also sketch pictures on the chart showing the volume of each.

Independent Practice

  • Students will use teacher-created materials or commercial worksheets to enhance their understanding of volume.


  • Use the measuring cups or similar containers to determine exact measurements of each unknown container.
  • Ask students if they would do anything different if they began the activity again.
  • Allow for responses and discussion.
Sponsored Content

Assessment & Evaluation

Evaluate the students as they work together using a prepared rubric.  Test or quiz students’ knowledge on volume measurements: ounces in a cup, cups in a pint, etc.  Students write a short paragraph of steps involved in determine the volume of an unknown-sized container.

Modification & Differentiation

Give each group more than 5 containers to guess their volumes.  Plan a similar activity using weight.  Students work in pairs or alone (more containers needed.)

Related Lesson Plans

Graph Smile

Pairs of students will survey other students in the school and then graph the results, as well as come to conclusions based on the information.  

Order in the Math Class

The students will physically review the order of operations.

Exchanging Time

The lesson is used for students to practice basic time measurement, and understanding the basic units of time.

Silent Geometry

The students will practice using geometry formulas measuring items in the classroom to find area and volume, radius and circumference, and identify the types of angles.