Nets and Surface Area
10 min
Teacher Prep
Setup
Required Preparation
Narrative
This Warm-up prompts students to match nets to polyhedra. It invites them to think about the polygons that make up a polyhedron and to mentally manipulate nets, which helps develop their visualization skills.
Launch
Give students 3 minutes of quiet think time to match nets to polyhedra and then another 2 minutes to discuss their response and reasoning with a partner. Encourage students to use the terminology that they learned in prior lessons.
To support students who need more time or help in visualization, prepare physical models of the polyhedra and copies of the nets from the blackline master. Pre-cut the nets or have scissors available so that students can assemble the nets and test their ideas.
Advances: Conversing, Reading
Student Task
Each of the nets can be assembled into a polyhedron. Match each net with its corresponding polyhedron, and name the polyhedron. Be prepared to explain how you know the net and polyhedron go together.
Sample Response
Students are likely to give similar reasoning for each figure as in the given sample reasoning.
Net A is a square pyramid (3). Sample reasoning: It has five faces: one square and four triangles, just like the square pyramid.
Net B is a rectangular prism (2).
Net C is a triangular pyramid (4).
Net D is a triangular prism (5).
Net E is a cube or square prism (1).
Activity Synthesis (Teacher Notes)
Invite a few students to share their matching decisions and reasoning with the class. Ask students: “What clues did you use to help you match? How did you check if you were right?” If there is not unanimous agreement on any of the nets, ask students with differing opinions to explain their reasoning. Discuss to come to an agreement.
Anticipated Misconceptions
If students have trouble distinguishing between Figures A, C, and D, remind them that prisms and pyramids can both contain faces that are triangles. In a pyramid, all triangular faces that are not the base meet at a one vertex and have shared edges. In a prism, there can be a triangular base, but the other faces are quadrilaterals.
Standards
- 6.G.4·Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.A.4·Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Nets and Surface Area
10 min
Teacher Prep
Setup
Required Preparation
Narrative
This Warm-up prompts students to match nets to polyhedra. It invites them to think about the polygons that make up a polyhedron and to mentally manipulate nets, which helps develop their visualization skills.
Launch
Give students 3 minutes of quiet think time to match nets to polyhedra and then another 2 minutes to discuss their response and reasoning with a partner. Encourage students to use the terminology that they learned in prior lessons.
To support students who need more time or help in visualization, prepare physical models of the polyhedra and copies of the nets from the blackline master. Pre-cut the nets or have scissors available so that students can assemble the nets and test their ideas.
Advances: Conversing, Reading
Student Task
Each of the nets can be assembled into a polyhedron. Match each net with its corresponding polyhedron, and name the polyhedron. Be prepared to explain how you know the net and polyhedron go together.
Sample Response
Students are likely to give similar reasoning for each figure as in the given sample reasoning.
Net A is a square pyramid (3). Sample reasoning: It has five faces: one square and four triangles, just like the square pyramid.
Net B is a rectangular prism (2).
Net C is a triangular pyramid (4).
Net D is a triangular prism (5).
Net E is a cube or square prism (1).
Activity Synthesis (Teacher Notes)
Invite a few students to share their matching decisions and reasoning with the class. Ask students: “What clues did you use to help you match? How did you check if you were right?” If there is not unanimous agreement on any of the nets, ask students with differing opinions to explain their reasoning. Discuss to come to an agreement.
Anticipated Misconceptions
If students have trouble distinguishing between Figures A, C, and D, remind them that prisms and pyramids can both contain faces that are triangles. In a pyramid, all triangular faces that are not the base meet at a one vertex and have shared edges. In a prism, there can be a triangular base, but the other faces are quadrilaterals.
Standards
- 6.G.4·Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
- 6.G.A.4·Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.