surface areas of RECTANGULAR prisms

Prior knowledge and understanding

Students are assumed to be able to:

• dissect irregular composite shapes into three or more special quadrilaterals
• recall and use area formulas of rectangles and to calculate the total area of a composite shape
• can identify rectangular prisms based off their 3D representation

Have students quickly sketch the net configurations of a closed cube they found for homework on pieces of grid paper. Then, as a class brainstorm, they stick their nets on the whiteboard, grouping together papers that depict the same configuration (including reflections and rotations).

Discuss the most common configurations found and explore the less common examples. Ask students their process of discovering a new configuration for the net of a closed cube. Ask students where we can find rectangular prisms in the real world

10:20 Body activity 1

(15 mins) Calculating the surface areas of rectangular prisms using digital models (ICT)

Individually, students answer the questions below the application to calculate the area of rectangular prisms of specific dimensions. They themselves must manipulate the dimensions of the prism by dragging the sliders or by dragging the cyan dots.

They calculate the area of each face either by visualising its net or by rotating the prism to locate congruent faces. Students can 'open up' the rectangular prism to visualise its net, or they can slide the 'Options' toggle to view separate pairs of congruent faces.

As students are working, roam around the classroom to ensure students are on task and ask questions such as (AFL):

• How are you calculating the surface area? Are you using the net or finding the area of each face?
  • If you were to find the SA using the other method, will this affect your final answer? Explain why/why not.
• How do you think changing the dimensions affects the surface area of the prism?

(EXT.) Ask students if they can summarise the process of finding the surface area of a rectangular prism into a formula using the variables, l (length), w (width) and h (height)

10:35 Body activity 2

(18 mins) Designing a rectangular prism

Drawing upon their understanding of:

• different configurations for the net of a cube (6-sided right prism) [Refer to Orienation]
• congruent faces of a rectangular prism
• calculation of the surface area of rectangular prisms

Students design their own rectangular prism. In pairs, students roll a die three times to determine the prism's length, width and height. Each student then constructs an appropriate net of the prism using its decided dimensions that is different to their partner's by configuration. They then calculate the surface areas of their prisms/area of both nets and should confirm that they are the same. Finally, student cut out their nets, fold and tape them to compare both nets and to confirm they produce the same rectangular prism. If they don't students should review their construction and configuration of their prism and try again.

Students repeat this process at least once more.

Whilst students are working, the teacher roams around the classroom to ensure students remain on task and engaged. Encourage students to look at the 11 configurations for a closed cube for guidance. Ask questions such as (AFL):

• What is the length, width and height of your prism? Show me where they lie on your net.
• Which configuration is your net similar to?
• How could you fix your net such that it
  • matches your partner's surface area?
  • will fold correctly to produce a rectangular prism
• Where are the congruent sides of the rectangular prism? Can you mark them on your net?

10:53 Conclusion

(7 mins) Closing class discussion and pack up. Ask:

• Describe what the surface area of a prism is in our own words.
• How can we find the surface area of a rectangular prism?
• Can we have different net configurations to produce prisms with the same dimensions?

Homework

Find an example of rectangular prisms in your home. Provide a sketch of its 3D representation and label its dimensions (length, width and height). Sketch its net and and calculate its surface area.

Students repeat this process for at least two other rectangular prisms.