Problems involving Surface area of Triangular prisms

Prior knowledge and understanding

Students are assumed to be able to:

• identify equilateral, isosceles, right-angled and scalene triangles and their features
• recognise that the net of a triangular prism is a composite figure comprised of rectangles and triangles
• recall and use area formulas of triangles and rectangles to calculate the surface area of a rectangular prism
• recall and use Pythagoras' theorem to calculate the length of unknown sides of triangles

10:10 Body activity 1

(20 mins) Calculating the surface areas of triangular prisms using digital models and Pythagoras' theorem (ICT)

Individually, students follow the process of calculating the surface area of a triangular prism demonstrated during the introduction. Students choose their own dimensions using the slider, draw the 3D prism and its net in their workbooks. They use the "Open-Close" slider to aid their visualisation of the net, its edges and areas.

They are to create and find the surface areas of at least two triangular prisms, using Pythagoras' theorem, where the base is a(n)

• right-angled triangle
• isosceles triangle
• scalene triangle (EXT.)

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

• How do you find the surface area of a prism? Is the process different for a triangular prism compared to a rectangular prism? How so?
• Explain to me how you are finding the surface area?
• Which edge lengths do you need to use to calculate the area of a this face?
• How can you find the length if it's not provided for you?
• How do you think changing the dimensions affects the surface area of the prism?

Students then swap their triangular prisms with a partner, providing only the sketch of the 3D prism and dimensions. Their partner sketches the net of the prism and calculates its surface area. Students then check that they came to the same answer. They also compare their nets and process of finding the surface area. Ask:

• Describe any similarities and differences between your nets?
• Explain to your partner how you calculated the surface area?

10:30 Body activity 2

(20 mins) Solving further problems involving the surface areas of triangular prisms

As a class, refer to Question 3 a. Ask students:

• What do we need to find in this question?
• Compare this to previous tasks involving the surface areas of triangular prisms. How is it different? What information has been provided this time?
• What are some strategies we could use to try solve this?
• What have we done during this unit that may help us with finding the missing length?

Take suggestions from the students and use them to explore possible ways to reaching the final answer. Once the class has come up with an appropriate way of finding the missing length, discuss students' thinking and reasons why they came up with a specific strategy, used a certain process, etc.

Allow students to work in pairs to work through the rest of the worksheet. As students are working, ask (AFL):

• What are you trying to find in this question?
• What are some strategies/what could you do to help with solving the problem?
• If you have different approaches to the question, explain how they are different?
• Encourage students to work backwards to solve such problems.

10:50 - Conclusion

(5 mins) Exit card

Provide students with the following exit card. Collect cards before the end of class and look over to gauge students' understanding of the how to calculate the surface area of a triangular prism. (AFL)

(5 min) Take-home assessment task and pack up

Hand out the following assessment task that includes a series of open-ended questions to gauge their understanding of concepts from this area and surface area unit. Student can refer to their notes, but their working out and reasoning must be written in their own words. (AOL)