Nets of Triangular prisms

Prior knowledge and understanding

Students are assumed to be able to:

• can identify triangular prisms from their 3D representation
• identify, visualise and draw right prisms
• recognise that the net of a triangular prism is a composite figure comprised of triangles and rectangles
• dissect irregular composite shapes into three or more special quadrilaterals and triangles

10:00 Introduction

Collect students' homework as students settle into class (AFL)

• Check if completed/attempted
• Assess if students can recognise the nets of rectangular prisms and calculate its surface area

(10 mins) The triangular prism

Hold up a model of a triangular prism. Ask students to identify the (AFL: Diagnostic assessment)

• Name of the prism (triangular prism)
• Number of faces (5)
  • Shapes of each face, and are they the same? (2 triangles and 3 rectangles; no)
• Number of edges (9)

Point out the features of the triangular prism including its:

• pair of congruent triangular faces (bases)
• the edges of the prism, perpendicular to the triangular bases ("height")

Ask students in pairs, to compare this to a rectangular prism.

• What are the similarities and differences?
• How do you think the net of a triangular prism will differ to from that of the rectangular prism?
• What shapes will be present in the net?/How many faces does it have?
  • What do we call a figure that is comprised of smaller, basic shapes? (Link to composite figures)

Finally brainstorm where we can find triangular prisms in the real world (Toblerone, tents, roofs, etc.).

10:10 Body activity 1

(20 mins) Exploring the nets of triangular prisms

(13 mins) Segue from the brainstorm of real-life examples of triangular prisms. Provide pairs of students with Toblerone boxes. Ask students to note the (AFL):

• number and shapes of faces
• number and shapes of congruent faces
  • placement of congruent faces on the 3D object (students hold up their boxes and point to the pairs of congruent triangles/ the trio of rectangles)

Using a marker, students mark along each distinct edge with a different colour. Students lay the Toblerone on a piece of butcher's paper and trace around the face in contact with the paper. They then flip the Toblerone box onto another adjacent face and trace around this. Students continue until they construct a net of the triangular prism. As students are tracing the faces, they should mark the edges on the net with its corresponding colour that appears on the 3D prism.

Students need to:

• measure the lengths of the edges on the net, and note which are the same.
• identify what the same lengths of edges means in terms of the length of the prism (the constant edge lengths of the rectangles is the length of the triangular prism)
• ensure that the number and shapes of faces they have drawn on the butcher's paper corresponds to the number of faces of a triangular prism

Students then cut out their outline of the Toblerone and fold it to check it is a valid net of a triangular prism. As students are working, ask (AFL):

• How many faces does your net include? Does this match to the number of faces on a triangular prism?
  • How are you ensuring you do not double up on a face?
• How many edges does the Toblerone box have? How many edge lengths are on your net? Does the number match? Why/why not? (No, some edges appear twice because they are shared between two faces)
• How are the faces connected? Which edges are being shared on your net?
• What can change when you create a new configuration for the net of the prism? Lengths? Position of faces? Number of faces?
• Are some edge lengths the same? Which edges are they?
  • Can you show me on your net and on the box where these equal edges are?

Students repeat this process, flipping the Toblerone box in a different order, to find another configuration for the net of a triangular prism. Ask:

• Describe to me how this configuration is different to your previous one.
• How are the faces connected? Which edges are being shared on your net?

(7 mins) Students stick their nets on the board. As a class, group similar net configurations together. Reaffirm that all nets are comprised of 2 triangles and 3 rectangles. Discuss how the changes in configurations arise from the faces being connected by different edges in their nets.

10:30 Body activity 2

(20 mins) Visualisation of nets of triangular prisms using digital models (ICT)

By dragging the slider from 'Close' to 'Open' students can visualise the 3D object 'opening up' to create a 2D net.

10:50 Conclusion

(5 mins) Class review Ask:

• What did we cover today?
• How is a net of a triangular prism a composite shape? What basic shapes can it be dissected into?
• Are there multiple ways of forming the nets of a triangular prism?
• How many edges of a triangular prism are the same? Where are they situated on the prism?

(5 mins) Homework and pack up

Using the possible configurations of the nets of triangular prism the discovered in Activity 1, students sketch another configuration for their nets created in Activity 2. Students must keep the same dimensions and edge lengths such that their new configurations produce the same triangular prism.