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

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  • Modeling volume: This activity helps the students see how the volume of something includes the third dimension (width or depth) which is different from area. This activity also helps the students "prove" that the volume formula actually works. Students will already know that the volume of a rectangular prism is found by multiplying the object's length, width, and height. By using the blocks as models of volume, the students should come to realize that volume can be calculated simply by multiplying the area of the base by the height of the rectangular prism. Thus, they will come to realize that there is no need to try and fill the entire box with the tiny 1cm cubes, they can simply fill the bottom (to see how many cubes are there) and figure out how many rows there will be and multiply.
  • Inside, outside, and all around: Students will distinguish between perimeter, area, and volume. They will use tangrams and graph paper to create two-dimensional figures that will be measured for area and perimeter. By creating layers of centimeter cubes, the students will explore the concept of volume.
  • Flying saucers: Circles: Students will apply what they have learned about circles and finding averages with this lesson. This lesson should be broken up into 3 class periods of an hour for each class.

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Learning outcomes

Students will be able to display their knowledge of surface area and volume. This will be accomplished by measuring the volume of a cylinder and constructing/designing a rectangular prism with the same volume.

Teacher planning

Time required for lesson

3 Days

Materials/resources

  • Scissors
  • Construction paper
  • Grid paper
  • Glue/tape
  • Calculators

Technology resources

  • One computer
  • Claris Works
  • Label-ology software (optional)

Pre-activities

Students should be familiar with the formulas necessary to find the:

  • Volume of a cylinder
  • Volume of a rectangular prism
  • Surface area of a rectangular prism

Activities

I have this letter on the overhead so that all students can see. It states:

HELP! Fruit Tree Juice Co. is losing sales fast to the Prune People Juice Co. Ms. Fruity Tuity, the CEO of Fruit Tree, believes this decline has occurred due to the fact that their juice is currently sold in cylinder cans. The Prune People Juice Co. have cool rectangular prisms that fit perfectly into kids’ lunch bags and their sales have been booming! Now it is up to you to design a rectangular prism in order to compete with the Prune People. Remember that it must have the same volume as the cylinder so that it can fit the same amount of juice in it. Good luck and be creative! Thanks, Ms. Fruity Tuity, CEO.

  1. Measure the volume of the cylinder can. The dimensions have the following measurements: diameter-6.5 cm, height-12.5 cm
  2. Through trial and error, find the dimensions of a rectangular prism that will have as close to the same volume as the cylinder. The volume of the prism must not be less than the volume of the cylinder because all of the juice needs to fit in.
  3. Check with Ms. Fruity Tuity to approve of your design. Your final product must have the surface area and the volume labeled on your rectangular prism.
  4. Make it attractive to the eye so that you would choose it from the grocery store aisle.

Students spend day one working with their calculators to find the volume of a rectangular prism that would be the same as the cylinder. Day two will be the construction of the prism. Day three should be the final production which includes the volume and surface area listed, graphics, nutrition label and extras.

The actual label for the juice box can be made through Label-ology computer software program. Once into the program, select Label Maker. Select name and edit food label from the LABEL listed in the menu bar. Input your information and print it out for your juice box.

Assessment

The actual juice box will be the final product of this lesson. I assess the box in the following manner:

  1. Juice box in solid constructed form = 30 points
  2. Correct volume listed = 20 points
  3. Correct surface area listed = 20 points
  4. Nutrition label = 20 points
  5. Extras (straw, website of the company listed, graphics, crossword puzzle, etc …) = 10 points

As an overall summary I have my class plot their boxes’ height, length, width and volume into a Claris Works spreadsheet. Input A1 as height, B1 as length, C1 as width and D1 as volume. Have all students type in their measurements. Click and drag (highlight) from the A1 cell down to the bottom right end of your document until all information is highlighted. Choose Options from the main menu bar and select Make Chart and choose the graph desired. Through the graph students can see visually the different variations of measurements. Discuss how a large measurement of either the height, length or width will affect other measurements in order to achieve the desired volume.

Supplemental information

Comments

I actually dress up and wear a name tag of Ms. Fruity Tuity, CEO, when I am introducing this lesson. The students get a kick out of it and it makes them more excited for the project.

  • 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 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.