Volume of Right Rectangular Prisms

Version 5



    Students have previously learned about the formula for volume of a rectangular prism by experimenting with cubes and filling prisms and drawing conclusions about the relationship between the cubes and measurement of the volume of a prism.


    At a Glance

    Subjects: Math

    Grades: Middle School

    Lesson Duration: One 50 minute class period


    Learning Objectives

    Students will:

    • Determine the volume of two non-overlapping right triangles and prisms; and,
    • Use the ArtRage app to represent volume.


    Materials and Resources

    Student Devices

    • Laptop, 2 in 1, or tablet with internet connectivity
    • Digital camera (optional)



    • A variety of differently-shaped rectangular prisms
    • Ruler


    Inquiry Process

    The inquiry process with guide students through and investigation of determining the volume of rectangular prisms. In small groups or as a whole class they will experiment with different methods of organization. Students will use ArtRage to create visual representation of the prisms in order to determine the volume.


    Technology Benefits

    Working with both hands-on objects, such as the boxes and the images thought technology helps students connect and transfer their understanding to a more abstract level. Making decisions about how to show their thinking allows students to use their creativity while thinking meta-cognitively.




    Review the volume of a prism by introducing the following scenario:


    Queen Greedina Goldlover has a room in her castle that is filled with 10,000 gold cubes with sides 1 "pligit" in length. Her generals have told her that her fortress is about to be invaded by peasants, and she needs to move her gold to a nearby cave. She has prepared for this eventuality by having her royal blacksmith make 500 iron boxes that are 10 pligits high and 5 pligits wide and 3 pligits deep. How many gold cubes can she fit in each box? How many will she have left over?



    1. Ask pairs of students to work with two different sized prisms. They can find rectangular prisms around the classroom or make them out of paper and tape. Alternatively, provide pairs of boxes to students.
    2. Have students place the boxes next to each other, take a photo, and upload it to the ArtRage app. Or, alternatively, distribute different photos of two non-overlapping boxes to the students.
    3. Ask students to measure the boxes.
    4. Have students label the measurement of the rectangular prisms
    5. Ask students to use the ArtRage app to annotate and sketch on the image to show how they determine the volume of the two combined rectangular prisms.



    Continue the scenario:


    Our greedy queen has some other iron boxes of different shapes that she can put some cubes in. Hopefully, she can fit the remaining cubes in those boxes. She has 1 box that is 4 pligits wide, 3 pligits tall, and 6 pligits deep and another box that is 2 pligits wide, 11 pligits tall, and 10 pligits deep.


    Show a diagram with the two prisms next to each other without overlapping with the measurements (in pligits) labeled.


    Ask students in small groups to brainstorm how they might figure out how many gold cubes Queen Greedina could fit in those two boxes together.


    Review suggestions and draw conclusions about how to determine the volume of the figure.




    Ask students in a small or large group to brainstorm examples of objects made up of two non-overlapping rectangular prisms (e.g., a wall with a bookshelf attached or a stool with legs). When might it be useful to know the area or the volume of these shapes? Make sure students’ responses reflect that they understand the differences between area and volume. Clarify as necessary.


    Ask students to repeat the exercise trading boxes or using different measuring systems, such as metric, body parts such as fingernails, or even pligits!



    Observe students as they measure their boxes to make sure they are labeling their images correctly and intervene with prompts to get students back on track, if necessary. Check the final products for accuracy and clear mathematical explanation.



    This lesson was created by Dr. Margaret Grant, Senior Content Developer for Clarity Innovations, Inc. in Portland, Oregon

    Students will use ArtRage to create visual representation of the prisms in order to determine the volume.