gr9_Surface+Area

= Surface Area =

//It is expected that students will://
 * **Prescribed Learning Outcomes**


 * C2** determine the surface area of composite 3-D objects to solve problems [C, CN, PS, R, V] ||
 * **Planning for Assessment** || **Assessment Strategies** ||
 * Provide groups of students with small groups of blocks (cylinders, rectangular prisms, and triangular prisms) and have them measure and calculate the surface area of each block. Have each group determine the total surface area of their block collection.

Have each group construct a structure out of the blocks, such as a building or an animal. Explain that this is called a composite object because it is composed of several simpler objects. Ask them if the surface area of this new composite object is the same as the total surface area of the blocks. Discuss why the two might be different.

Ask students to suggest a way of measuring the surface area of their structure. Ask how they could simplify their calculation of the surface area of their structure using what they already know about the total surface area and the overlapping faces. || In discussion, verify that students are able to determine the overlap in a given composite 3-D object and to explain its effect on the surface area.

Assess students' ability to develop a strategy for determining surface area of a 3-D object. ||
 * With or without the use of technology, have students design either a skate park or a swimming pool composed of prisms (circular, rectangular, triangular). The use of computer software for this is encouraged, as it increases student interest, develops important skills, and simplifies the design process. If students are not working with technology, a physical model could be constructed.

Note that the swimming pool design involves working with objects that are composed of empty space "cut out" of the ground. In art and design, this is called negative space. Some students may have trouble visualizing composite objects in negative space, and would be better able to work with a "positive space" design.

Give the task of determining the surface area of the design in question. This is required to determine the cost of concrete sealant for the skate park, or tiling for the pool interior.

Have students identify how the real-life parameters of their scenario affects the total surface area. For example, the top surface of a swimming pool is open water, and does not require finishing. Likewise, the bottom surface of every object or composite object in a skate park does not require finishing, and there may be a large 2-D surface of concrete that may need finishing in addition to any objects in the design.

Have students measure the surface area of their design. Ask students to organize their calculations in a spreadsheet, labeling each face in their design and referencing its calculation in the spreadsheet. For the pool example ask students to calculate costs such as: a) tiling the pool given a fixed price per square unit of either material. b) tiling the sides of the pool given a fixed price per square unit of tile and to tile the bottom of the pool with a tile of different price per square unit. c) tiling the pool given the price per tile and the dimensions of each tile.

For the skate park example ask students to calculate costs such as a) sealing the concrete given a fixed price for cost of a bottle of sealant and the total area each bottle can be expected to seal. b) seal the concrete and paint various objects in the park given a fixed price per can of paint and the total area each can be expected to cover.

There are many opportunities for extension. Students could go on to determine the volume of concrete required or water capacity of their pool. Complex designs, such as circular quarter-pipes for the skate park, could be included for more advanced students. || Assess students ability to determine the surface area of a given composite 3-D object.

Verify that students are able to identify overlapping surfaces in a composite 3-D object, and to relate real-life considerations to surface area calculations when solving a problem involving surface area. ||