Authentic Problems: Pyramids in a Box


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What is the best box to hold 2 different sized items that are packaged as pyramids?

This unit is for students in Year 6 who are building an understanding of constructing and manipulating three-dimensional objects (prisms and pyramids). The context of this inquiry could be packaging a gift for a classmate or a family member, or sending gifts overseas. Students work flexibly as they construct simple prisms and pyramids from nets they have created, and work through iterations to refine a box that has the least amount of left over space. Students will see the importance of collecting evidence, especially accurately labelled nets, and organising this evidence to show how they have packaged their two different sized pyramids.

Read the Teachers' Guide before using this resource.


Lesson 1: Discover

Students are introduced to the challenge of designing the best box to hold two different sized pyramids. The teacher reviews and extends prior knowledge of pyramids and prisms. Students manipulate, three dimensional objects and geometric construction materials to draw nets, making the connection between the shapes and positions of the faces on the object and in the net. They explore the different nets that can make one three-dimensional object.

Lesson 2: Devise

Students make a plan to answer the Inquiry question. They determine what ‘best’ means in this context, acknowledging that having a small amount of unused space in the box is a key consideration. Students draw nets and construct their two pyramids to be packaged, before sharing their initial ideas for constructing their best box.

Lesson 3: Develop

Students check and refine plans before implementing them to construct their box. They gather mathematical evidence as they work through iterations to reduce the amount of left over space in their box.

Lesson 4: Defend

Students prepare and present their justified solution to the inquiry question. They provide feedback on others’ presentations, focusing on the mathematical evidence used. Students reflect on the feedback given to determine what they did well and what they could do to improve their solution, models and presentation.

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