K-12 Teaching and Learning From the UNC School of Education

Important Announcement about Online Courses and LEARN NC.

Important Message about LEARN NC

LEARN NC is evaluating its role in the current online education environment as it relates directly to the mission of UNC-Chapel Hill School of Education (UNC-CH SOE). We plan to look at our ability to facilitate the transmission of the best research coming out of UNC-CH SOE and other campus partners to support classroom teachers across North Carolina. We will begin by evaluating our existing faculty and student involvement with various NC public schools to determine what might be useful to share with you.

Don’t worry! The lesson plans, articles, and textbooks you use and love aren’t going away. They are simply being moved into the new LEARN NC Digital Archive. While we are moving away from a focus on publishing, we know it’s important that educators have access to these kinds of resources. These resources will be preserved on our website for the foreseeable future. That said, we’re directing our resources into our newest efforts, so we won’t be adding to the archive or updating its contents. This means that as the North Carolina Standard Course of Study changes in the future, we won’t be re-aligning resources. Our full-text and tag searches should make it possible for you to find exactly what you need, regardless of standards alignment.

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Learning outcomes

Students will be able to determine the volume and surface area of rectangular prisms.

Teacher planning

Time required for lesson

2 days


  • Transparencies of the 3 activity sheets
  • Copies of the 2 activity sheets found in Vol & S A.pdf
  • Unlined paper
  • Cubes would be useful, e.g., cm cubes (students could use enough cubes to help their thinking, but not enough to solve the problem - no more than 30 cubes per pair)

Technology resources

Overhead projector


  1. Begin the lesson using the two figures in the Quick Draw file (10 min). “I will show you a figure for two seconds. Draw what you saw.” Show the figure a second time after they have made their attempt. Then uncover the figure and ask students to describe what they saw. There are no “wrong” answers. Show enthusiasm for all responses.
  2. “If we had a box that was 3 cm wide, 4 cm long and 5 cm high, how many one cm cubes would fit in the box?” Ask student to explain how they decided on their answer. After several explanations, organize the class into pairs, putting students of a similar mathematical level together. Distribute the first page of the Vol&SA activity sheet and ask the pairs to solve the problems and be prepared to explain their solutions to the class.
  3. While students are solving the problems, move around the room listening to the discussions but avoid answering questions directly. Do not tell students whether they are right or wrong and don’t give hints. This is an important learning time for you.
  4. When a pair has finished the first activity sheet, give them page two. Some pairs may not get to page two.
  5. Allow 15-20 minutes for discussion. Have the class come together and call on pairs to explain how they solved the problems. Feel free to ask clarifying questions but do not judge or tell students they are right or wrong. You may not have time for all problems to be discussed. The lesson could be spread over two days. There are many ideas to be discussed.


Give them the dimensions of a rectangular prism and have them find its volume and surface area.

Supplemental information



This lesson utilizes an instructional strategy called Problem Centered Learning. The teacher does not explain but students develop their own solution methods.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 7

        • Geometry
          • 7.G.6Solve 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.

North Carolina curriculum alignment

Mathematics (2004)

Grade 8

  • Goal 2: Measurement - The learner will understand and use measurement concepts.
    • Objective 2.01: Determine the effect on perimeter, area or volume when one or more dimensions of two- and three-dimensional figures are changed.
  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.01: Represent problem situations with geometric models.
    • Objective 3.02: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.