# Authentic Problems: 10 000 Centicubes

ACMNA073; ACMNA076; ACMMG290; ACMNA072; ACMMG084

This unit for Year 4 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 answers the question: What is the best container to hold 10 000 centicubes? The unit integrates content in number and measurement to deepen students’ understanding and confidence in working with larger numbers, especially for flexibly partitioning numbers into convenient components.  Students negotiate what 'best' means and explore ways to identify 10 000 centicubes without counting all. They determine suitable bases and heights, record their calculations, construct a 3D model and explain the benefits of their container.

### 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.

Last updated July 15 2019.