Four Cube Houses

Task 103 ... Years 2 - 8


This architect's puzzle is to build as many different houses as possible from four cubes given that the cubes must be placed face to face. Orientation on the 'block of land' determines whether two houses are the same. If a house could be rotated on the block to fit the shape of another house, then the two are the same.

This cameo has a From The Classroom section which includes a unique approach to a 'fishbowl' introduction to the problem and several examples of children's work from Marissa Cashmore, who has used this task as a whole class lesson for many years.



  • 4 wooden cubes
  • Laminated board to experiment with recording
  • Marking pen and erasing cloth
  • Recording sheet


  • mathematics in context
  • construction of 3D models
  • representing 3D objects in 2D (isometric & plan/elevation views)
  • scale diagrams
  • operations with money
  • basic number skills
Four Cube Houses


A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

There are 15 solutions:

An obvious mathematician's question is what happens for other cube houses? Students might then explore 1, 2, 3, and 5 cube houses. Perhaps a pattern will develop linking the number of solutions in each case.

Another direction for extension is to consider what it might cost to build each four cube house. Assign a cost to each square floor section, external wall section and roof section. They won't all be the same because each of these has different construction requirements. For example:

  • Floor - $10,000
  • Wall - $4,000
  • Roof - $6,000
If you want to go further than comparing the prices of the four cube houses, you could ask:
  • Using these prices try to design a million dollar home.

Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

To run this as a whole class lesson you will need lots of cubes. Linking cubes such as Multi-Link are less satisfactory than cubes that don't join because linking cubes permit students to include cantilever sections in the design - cubes that 'stick out' into the sky and would in real life need posts to support them. These are not allowed in the problem.

Once you have the equipment the problem is easy to state and easy to start. There is considerable support in the Maths300 lesson and some amazing Classroom Contributions. For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 118, Four Cube Houses.

Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Four Cube Houses task is an integral part of:

  • MWA Space & Logic Years 5 & 6

The Four Cube Houses lesson is an integral part of:

  • MWA Space & Logic Years 5 & 6
  • MWA Space & Logic Years 9 & 10
Four Cube Houses is also included as a task and a lesson in Points of View: Representing 3D Objects in 2D, a kit supporting the exploration of a Mixed Media teaching strategy.

From The Classroom

Milk Crates Houses

Marissa Cashmore, Macclesfield Primary School
Years 5/6


Marissa also provides consultant services through: Motivating All Learners To Succeed
Four Cube Houses is the perfect inquiry maths task. I have used this task over many years, with students in Years 3 to 6 and it is always a winner with them as well. Each time I deliver this lesson, I make slight alterations to suit the students, enabling and extending where needed.

The addition of the milk crates was a bit of an exploration. These were used as a whole class fish bowl where individual students built one house at a time with the crates.

Pairs then scaled it down and built it with 2cm wooden cubes at their own work space.


After three or four houses were 'found', the provocation How many four cube houses can we make in total? was given.


That introduced the need for recording and the opportunity to introduce and refine the skills related to using isometric dot paper to represent 3D objects in 2D.

A collection of houses makes a community so the next step was...

Oops. There's one, perhaps two, upside down according to the 4 Cube House Rules.

Now I am on the hunt for more milk crates ... I wonder how many crates I need to collect to build a large scale community?

Teaching Craft Suggestion

Green Line
Follow this link to Task Centre Home page.