Authentic Problems: Pyramids in a Box


This unit for Year 6 is one of a set of ten units in the special topic “Mathematical Inquiry into Authentic Problems”. Each of these units is designed around the 4D Guided Inquiry Model, and highlights the importance of students providing mathematical evidence. The lessons adopt a carefully designed pedagogy to help students master content knowledge whilst learning about the process of inquiry. 

The inquiry is stimulated by a question about posting gifts: What is the best box to hold 2 different sized items that are packaged as pyramids?

This unit helps students build understanding of constructing and manipulating three-dimensional prisms and pyramids. They construct prisms and pyramids from nets, and iteratively refine the design of the packing box (of any shape) until it has a minimal amount of unused space. 

Read the Teachers' Guide (also included in the download) 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.