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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Related pages

  • Investigating surface area: This is a hands on lesson best used to introduce geometry students to 3-dimensional figures. Students will have the opportunity to draw 3-dimensionally and create collapsible figures which can be used to develop the standard surface area formulas.
  • Building a paper bridge: An introduction to problem solving: This activity allows the student to explore problem solving strategies while working with a partner. This activity (building a paper bridge), requires students to question word definition and the application of those definitions. Through problem solving strategies, students discover the need for applying math skills.
  • Giving meaning to volume and surface area: This lesson is designed to help students give meaning to volume and surface area by solving problems using a meaningful situation rather than formulas.

Related topics


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Learning outcomes

Students will:

  • learn the concepts of lateral area and total surface area as applied to rectangular solids and cylinders, and how mathematical formulas for surface areas of solids relate to these concepts.
  • discuss application of these concepts and formulas in real life.

Teacher planning

Time required for lesson

1.5 hours


  • Twelve pack box of soft drink cans
  • Measuring device(ruler or tape measure)
  • Graph paper or plastic graph sheet (can be purchased at Wal-Mart; about the size of a placemat)

Technology resources



Formulas for area of a rectangle and circle.


  1. Students gently tear open the carton surrounding the cans, opening all the seams until the cardboard will lie flat.
  2. Students measure the carton one piece at a time, recording the dimensions of each piece.
  3. Students transfer the measurements to the graph paper and count the units on the graph paper, then find the total area of the solid by using individual area formulas for rectangle, square, circle, etc.
  4. Students use established formulas for surface area and lateral area of solids to find the area of the carton another way.
  5. Students compare the answers obtained by the two different methods.
  6. Students compare answers with each other.
  7. Repeat the same procedure for the soft-drink cylinders (as an alternative, use a cardboard cylindrical container, such as an oatmeal container).
  8. Let the students figure out the amount of cardboard and/or aluminum needed and the approximate cost of producing the containers (you can assume a per-square-foot cost of each material, or have curious students research this on the internet or by contacting soft-drink companies). Discuss how this affects the cost of the drinks.


Students must turn in their graphs and worksheets showing the formula problems. Also, one student from their group would make an oral presentation.

Supplemental information


Lessons similar to this are found in the Cord material.

  • Common Core State Standards
    • Mathematics (2010)
      • Grade 6

        • Geometry
          • 6.G.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
        • Grade 7

          • 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.
      • High School: Geometry

        • Modeling with Geometry
          • GEO.M.1Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).★

North Carolina curriculum alignment

Mathematics (2004)

Grade 7

  • Goal 2: Measurement - The learner will understand and use measurement involving two- and three-dimensional figures.
    • Objective 2.02: Solve problems involving volume and surface area of cylinders, prisms, and composite shapes.

Grade 8

  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.01: Represent problem situations with geometric models.

Grade 9–12 — Geometry

  • Goal 2: Geometry and Measurement - The learner will use geometric and algebraic properties of figures to solve problems and write proofs.
    • Objective 2.04: Develop and apply properties of solids to solve problems.

Grade 9–12 — Integrated Mathematics 1

  • Goal 2: Geometry and Measurement - The learner will use properties of geometric figures to solve problems.
    • Objective 2.01: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Grade 9–12 — Technical Mathematics 1

  • Goal 2: Geometry and Measurement - The learner will measure and apply geometric concepts to solve problems.
    • Objective 2.03: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.