Rationale: Students will apply their understanding of how to calculate surface areas of 3-dimensional solids to find the surface areas of composite figures.
- I can determine the surface area of composite 3D objects to solve problems.
- Knowledge and Understanding
Procedural Skills: Calculating surface areas.
Evaluating Reasonableness: Using wrapping paper to check solution
Use of Prior Knowledge: Applying understanding of surface areas of 3D figures to composite figures.
- Experience calculating the surface areas of 2D shapes and 3D objects.
- sets of geometric objects
- wrapping paper
- Review calculating surface areas for a cube and a rectangular prism.
- Display on the board a group of objects arranged collectively, and ask for ideas on how to calculate the surface area of the composite object.
- Give students a few minutes to calculate the surface area on their own.
- Ask students to share and explain their solutions.
- Point out that when objects are combined, there will be areas of overlap. These areas need to be subtracted from the sum of the surface areas of each individual object.
- Alternatively, the surface area of the composite object can be calculated by adding together the areas of each visible side.
- Distribute sets of geometric solids to each group of 2-3 students and have them create any composite figure from them.
- Ask them to measure and calculate the surface area of their composite figure and record it with an explanation.
- Provide each group with wrapping paper, and ask them to cover their composite object and measure the area of the paper they used to check their surface area calculation.
- Have students determine the surface area of another composite object displayed on the board:
- Remind students to show all work.
- Collect student solutions for assessment.
- Provide students with the following problem for homework:
Jamie has built a bird house using a rectangular prism, with a length of 20 cm, a width of 15 cm and a height of 30 cm; and a triangular prism roof with base of 15 cm, height of 10 cm and equal triangle sides of 15cm. How much money will it cost him to paint the bird house if a can of paint covers 500 cm2 and costs $5.75?