Lesson plan - Study Island
|Math Lesson: Area, Volume, and Surface Area |Grade Level: 7 |
|Lesson Summary: Students find the volume and surface area of various rectangular prisms. They then create cubes and right prisms from nets, calculate volume and |
|surface area, and design a box to contain a set of six figures. Next, students determine the dimensions of a building with surface area requirements. Advanced |
|students design a container to ship 100 DVDs with fractional measurements. Struggling students calculate the volume and surface area of the classroom. |
|Lesson Objectives: |
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|The students will know… |
|the formulas used to determine measurements of area, volume, and surface area. |
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|The students will be able to… |
|solve problems involving area, volume, and surface area of two- and three-dimensional figures. |
|Learning Styles Targeted: |
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|Visual |
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|Auditory |
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|Kinesthetic/Tactile |
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|Pre-Assessment: |
|Determine whether students understand the difference between surface area and volume. |
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|Present a cube. Ask students to describe the concepts of surface area volume. Make sure students note the differences. |
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|Note students who cannot describe the differences among area, surface area, and volume. |
|Whole-Class Instruction |
|Materials Needed: Centimeter cubes, Cube and right prism nets*, rulers, scissors, tape or glue |
|Procedure: |
|Presentation |
|Have students create a 2 ( 4 ( 3 stack of 24 cubes. |
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|As a class, discuss the definition of area and surface area. Students suggest some reasons to find surface area. |
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|Students create a chart with the headings: area, surface area, and volume. |
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|Using their stack of cubes, student calculate and record, area, surface area and volume. |
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|Next, students reconfigure the dimensions of the stack of cubes in another way (for example 2 ( 2 ( 6) and record each of the measurements (area of a side, surface|
|area, and volume). Repeat with at least three other configurations. |
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|Review student results. Discuss why the volume remained the same but the area and the surface area may have changed with different configurations. |
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|Have students suggest why designers and engineers might prefer a package of one configuration over another (More surface area allows for cooling. Less surface area|
|allows for temperature retention, ability to carry, pack, or ship in a particular configuration). |
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|Guided Practice |
|Divide the class into groups of four. Distribute six sets of the cube and right prism nets to each group. |
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|Students calculate the surface area of each figure. |
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|Students construct six figures of each shape and calculate the volume. |
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|Students design a shipping package that would most effectively ship a set of six of each type of figure. |
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|Have students describe their designs and explain their reasoning. |
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|Independent Practice |
|Present this engineering problem: A builder would like to build a storage facility with a volume of 8,000 cubic meters and the least possible surface area. What |
|should the length, width, and height of the building be? [l = 20m, w = 20m, h = 20m, a cube] |
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|Closing Activity |
|Review the formula students used to determine volume, and ask them to explain the difference between volume and surface area. |
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|Make a list of applications for finding volume and surface area (storing boxes, packaging). |
|Advanced Learner |
|Materials Needed: Notebooks, pens, and pencils |
|Procedure: |
|Challenge students to design a box to ship 100 DVD packages that each measure 7 ½ inches by 5 ½ inches by ½ inch. |
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|Have them present their designs to the class and explain how the DVDs will fit and why it is a practical design. |
|Struggling Learner |
|Materials Needed: Meter sticks and calculators |
|Procedure: |
|Work with students to measure or estimate the height, length, and width of the classroom. |
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|Students use the measurements to calculate the volume and surface area of the room. |
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|Students describe their results and explain their reasoning. |
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|Students complete the independent practice activity. |
*see supplemental resources
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