Authentic Problems: 10 000 Centicubes


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What is the best container to hold 10 000 centicubes?

This unit integrates content in number and measurement to deepen students’ understanding and confidence working with larger numbers, and to help build an understanding that numbers are partitioned and combined flexibly. Students negotiate what 'best' means and explore ways to reach 10 000 centicubes without actually counting. They determine suitable bases and heights and represent their base with concrete materials and grid paper. To convince others that their container is best, students record their calculations, construct a 3D model of their container and explain the benefits of their container.

Read the Teachers' Guide before using this resource.


Lesson 1: Discover

The challenge is to make the best container to hold 10 000 centicubes. Students review mathematical vocabulary, and possible shapes, then predict the size of a suitable prism by looking at just one centicube as a guide. They use the idea of stacking layers of equal size to suggest some container dimensions arising from multiplicative partitioning of 10 000. They record using number sentences and pictures.

Lesson 2: Devise

Students discuss what is meant by “best” container for an educational supplier to use to package 10 000 centicubes. They work in small groups to create a plan to make a suitable container (including giving all dimensions) before presenting their ideas for feedback.

Lesson 3: Develop

Groups agree on their ‘best’ container to use and determine the dimensions for each face. Plans for the best containers are swapped to provide feedback on whether sufficient mathematical evidence has been recorded to enable the container to be constructed easily. The models of the containers are then constructed.

Lesson 4: Defend

Groups prepare and present their justified solution to the inquiry question. Students examine the reasoning of other groups, and use calculators and rules to validate the solutions. Later, they act on feedback on their own presentations. Groups compare their container with one constructed by another group and record the similarities and differences. As an extension, students consider what reasonable mathematical adjustments might be made to the container if neat packing of cubes is not assumed.

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