Back To Back Building

Task 60 ... Years 2 - 10


Student A makes a 3D object from a collection of linking cubes. Student B is sitting back to back with Student A and can't see what is made. Student B has the same colours as Student A and is challenged to recreate the original object by following to the oral instructions of the first student. The objective is to become increasingly precise in using mathematical language.


  • 12 interlocking cubes - 2 of each of six colours


  • spatial language
  • language of orientation - left, right, up, down etc.
  • language of transformation geometry - rotate, reflect, translate
  • spatial perception
Back To Back Building


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

There are no specific answers to this challenge. The focus is on improving the accuracy and efficiency of student language.

What did you get?
Students also experience transformations of objects in space which is informal groundwork for 3D geometry.

To extend the task beyond the language objective, encourage students to use numbers by choosing their first cube as the starting point and then giving instructions in terms of block 'steps' right/left (R/L), away/towards (A/T), up/down (U/D) (from your body). This is consistent with 3D co-ordinate geometry conventions and uniquely describes the position of each cube in space?

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.

This task is easy to convert to a whole class investigation. You just need a collection of cubes and a chart to record useful (and less-useful) language. The first stage is collect and sift student language. The next is to introduce appropriate mathematical terms. A further step is to introduce number related challenges based on an agreed system of axes such as those suggested above. Then challenges could be in the form:

The red block is your start. The blue block is at (0, -1, 0).
The ordered triple stands for placement along the (R/L, A/T, U/D) (or x, y, z) axes with the first of each pair being in the positive direction.

A way to 'see' this is to point using your left hand and:

  • point your thumb up
  • your middle finger to the right
  • your first finger away from you.
These are the three positive directions.

At this stage, Back To Back Building does not have a matching lesson on Maths300.

Teachers and students have adapted Poly Plug to the Back To Back Building idea. Visit Back to Back Building in Menu Maths Pack B.

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 Back To Back Building task is an integral part of:

  • MWA Space & Logic Years 3 & 4
  • MWA Space & Logic Years 7 & 8
This task is also included in the Task Centre Kit for Aboriginal Students and the Primary Library Kit.

Green Line
Follow this link to Task Centre Home page.