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Bentwood Boxes

Design, build, measure and explain.

Unit project · Design & explain

Bentwood Boxes

How can three containers fit their items and nest within one another?

Plan the work

Your Part 1 worksheet asks for open rectangular-prism containers. A broader project description discusses trapezoid-shaped nesting boxes. Follow the version and requirements assigned in class; the mathematics below helps with either.

01 · Learn the context

Bentwood boxes are a continuing cultural practice among First Peoples of the Northwest Coast. Different Nations and artists have distinct histories and practices. The classroom project cites Math First Peoples, First Nations Schools Association (2020). Learn about the people and purposes of the objects; do not assume one design represents all Nations.

02 · Measure three items

Choose two small items and prepare the paper canoe specified in class. Record length, width and height with units. Decide how each item will be oriented and allow practical clearance and material thickness.

03 · Design the containers

Draw and label a net for each of three containers. The Part 1 worksheet specifies rectangular prisms with no lids. Label matching edges, dimensions and units. Check that each object fits its container and that each smaller box can fit inside the next one.

04 · Build and calculate

Construct models using the assigned materials. Show surface-area and volume calculations for each box using dimensions appropriate to the question. A lidless rectangular box uses its bottom and four walls for surface area. Capacity depends on internal measurements.

05 · Compare and explain

Compare each smaller box with the next larger one as directed. A volume ratio compares capacities; a surface-area ratio compares surface amounts. Neither ratio alone proves physical fit. Show dimensions, orientation, clearance and nesting, then explain your design choices and reflect on improvements.

Experiment with one container

Open box model

Select “No top” to match the Part 1 worksheet. The model uses a rectangular prism and ignores thickness and tabs; real capacity requires internal measurements.

LengthWidthHeight No top

Predict first, then change one dimension. Diagrams are schematic; results use the entered values. Rounded values are marked ≈.

An invented example

A lidless rectangular container has outside dimensions 5 cm × 4 cm × 3 cm. Ignore material thickness and tabs for this calculation.

Bottom = 5 × 4 = 20 cm².
Two long walls = 2(5 × 3) = 30 cm²; two short walls = 2(4 × 3) = 24 cm².
Open surface area = 74 cm². The corresponding idealized volume is 60 cm³.
To test nesting, compare each internal dimension with the smaller box’s outside dimensions in a workable orientation. A smaller volume by itself is insufficient.

Before submitting

Project checklist

Three item sketches, measured dimensions, and three labelled container nets.
Three models that hold the assigned items and nest, allowing clearance.
Surface-area and volume calculations, with units and a clear statement of which faces are included.
Comparisons and percentages use the quantities and reference boxes specified by your teacher.
Reasons for your design choices and a brief reflection on the process.

Your teacher provides deadlines, materials, assessment criteria and the version of the task you should follow.

Revisit a skill

← Surface Area & Volume