Lesson: Surface Area
Length: 45 minutes
Age or Grade Level Intended: 6th Grade
Measurement Standard 5
6.5.7 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to compute the surface area of the objects.
The sixth graders will correctly compute the surface area of eight out of ten different cube and rectangular boxes when given a corresponding worksheet.
Students will be given a worksheet with ten math problems. They will be assessed by the completion and correction of each problem on the worksheet. They will be evaluated by the amount of problems that are answered correctly. If the student correctly answers the problems on the worksheet, full credit will be given. Students will be expected to answer eight out of the ten problems that they are given.
Advance Preparation by Teacher:
Dry erase board
Dry erase markers
Before the students arrive, write the definition and formula for the surface area of different rectangular prisms on the board (given below in the Step-by-Step). You will use these to explain how to compute the surface area. Make sure that there are enough copies of the worksheet (worksheet is attached), cutouts, scissors, and tape for each student.
Begin the lesson by reviewing the previous lesson about translating and reflecting different shapes on a graph. Refresh the students’ memories by reminding them how to do each one.
- Translating a figure means sliding it without turning or flipping it.
- Reflecting a figure means flipping it across a line of reflection. It is positioned the same distance from the line as the original shape.
- Translating and reflecting figures does not change the shape.
Explain to the students that surface area is the sum of the areas of each face. Give them the definition and formula for the surface area of rectangular prisms (given below in the Step-by-Step). Answer any questions they may have regarding surface area or the information that you covered.
- Write down the definition and formula for the surface area of different rectangular prisms on the board (Bloom Level I Knowledge).
Definition: The surface area S of a rectangular prism with length l, width w, and height h is the sum of the areas of the faces.
Formula: S = 2lw + 2lh + 2wh
- Using the definition and the formula on the board, explain to the students that in order to find the surface area of a rectangular prism, they must find the area of each face and add up all of those areas together.
- Do a couple of examples of finding the surface area with the students so that they understand the concept. Allow them to work with a partner, if needed (Gardner Interpersonal) (Gardner Logical/Mathematical).
EX 1: Find the surface area of the cube with dimensions:
l = 5cm h = 5cm w = 5cm
2(5)(5) + 2(5)(5) + 2(5)(5) =
50 + 50 + 50 =
EX 2: Find the surface area of the rectangular prism with dimensions:
l = 3in h = 4in w = 5in
2(3)(5) + 2(3)(4) + 2(5)(4) =
30 + 24 + 40 =
EX 3: Find the surface area of the rectangular prism with dimensions:
l = 4in h = 7in w = 6in
2(4)(6) + 2(4)(7) + 2(6)(7) =
48 + 56 + 84 =
- Pass out the 2 different cutouts to each student.
- Show the students that the 2-dimensional cutout is a way to see each face of the 3-dimensional figure separately. Tell them that the areas of the individual faces must be added together in order to find the surface area.
- Have the students compute the surface area for each of the three 2-dimensional cutouts. Help those who have questions on computing any of the surface areas (Bloom Level III Application).
- Once the students are all finished, go over the answers to the surface area of each cutout.
- Ask the students if they have any questions on how to find the surface area of rectangular prisms.
- Allow the students to cut out the 2-dimensional figures and fold/tape them together so that they can see how it transforms into a 3-dimensional figure (Bloom Level V Synthesis) (Gardner Spatial).
- Pass out the worksheets to the students and go over the directions with them so they know what is expected.
- Have the students complete the worksheet problems based on what they have learned and assist those who need help (Bloom Level III Application) (Gardner Logical/Mathematical).
At the end of class, ask the students if they have any questions or need help with understanding surface area. If they do need help, spend the last amount of class time working with them. If they do not need help, review what the students learned throughout the class by asking them questions help (Bloom Level II Comprehension).
- What is the definition of surface area of a rectangular box?
- What is the formula for the surface area of a rectangular box?
Was I prepared for the lesson?
Were the students engaged?
What could I have done to improve the lesson?
Did the students easily understand the instructions?
Was there enough time given to complete the lesson?
Did the students learn from the lesson?
Do the students understand the concept of finding the surface area of rectangular box?
- This lesson may be adapted for students with autism. Optimal communication patterns and strategies will be designed in order to keep those students prepared and ready for the lesson.
- If needed, behavior analysis will be applied and reinforcement will be used to display the appropriate behaviors that are expected.
- The direct instruction that is structured according to the students’ needs will help make the lesson more understandable.
- The lesson will be prepared in a way that will fit the normal routine that the students are used to avoid any added stress.
Directions: Compute the surface area of the rectangular box from the given dimensions.
- l = 6cm
h = 2cm
w = 4cm
- l = 7in
h = 3in
w = 3in
- l = 9ft
h = 12ft
w = 2ft
- l = 8in
h = 8in
w = 8in
- l = 10ft
h = 5ft
w = 12ft
- l = 20cm
h = 1cm
w = 7cm
- l = 22ft
h = 4ft
w = 3ft
- l = 9in
h = 5in
w = 9in
- l = 11cm
h = 18cm
w = 6cm
- l = 3ft
h = 14ft
w = 16ft