Unknown Volumes

JRDAssist
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

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.

Procedure

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

Modeling

  • 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.

Closing

  • 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.

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.)

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