Tricube Constructions ATask 77 ... Years 4  8SummaryStudents are shown a looking down view of a 'building' they know is made from all four Tricubes. From this they are asked to construct the 'buildings' and draw them isometrically.Tricube Constructions A also appears on the Picture Puzzles Shape & Space A menu where the problem is presented using one screen, two learners, concrete materials and a challenge. In this context it is called Tricube Building A. 
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IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
To solve parts (d) and (e), it may be necessary to explore the idea that a two storey building is not necessarily two layers high all over. If so, ask the students to place a Tricube so it stands up as an Lshape. If they were standing on the ground outside this building they would say it was two storeys high, even though it is not so all over. With this in mind, the answers are:
Part A
To some extent this task card already expresses the iceberg. There are many ways to make a building from four Tricubes and Question 2 encourages students to find their own. However you could also ask students to draw the front and side views to go with each top view on the card and each of their own buildings. Further, given one 'building' on the card has more than one answer, perhaps there are others which also have more than one answer. 
Note: This investigation has been included in Maths At Home. In this form it has fresh context and purpose and, in some cases, additional resources. Maths At Home activity plans encourage independent investigation through guided 'homework', or, for the teacher, can be an outline of a class investigation.
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Whole Class InvestigationTasks 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. 
If you want the whole class to work on this investigation simultaneously, you will need a class set of Tricubes. These are no longer commercially available (see note), but making them in art or woodwork class could be a crossfaculty project. You can even get by using linking cubes. The only annoying part of that being that there will always be at least one lug sticking out of a surface somewhere. We strongly recommend you look at Tricube Constructions A on the Maths At Home site as you plan the whole class experience for this task. It turns the activity into a homework project which will allow you to use class time differently. If you can't supply sets of Tricubes to take home, even with the help of the craft teacher, the MAH notes provide simple instructions for learner and parent to make a set at home. The content of this form of the activity also includes more work on isometric drawing. Like every Maths At Home activity, it has a selfevaluation component built into the notes. Your homework project therefore offers opportunity to explore much of the required curriculum content in 3D space and a contribution to the assessment of the unit of work you are building. An alternative way to use this task is in a work station, probably with other spatial tasks, and rotate students through the station over a period of time. Keep a class scrap book at the work station in which each group records its new puzzle as suggested above. At this stage, Tricube Constructions A does not have a matching lesson on Maths300. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
Tricube Constructions A is not in any Maths With Attitude kit, however, it would work well as one of the ten tasks in a Mixed Media Unit based around the topic of Representing 3D Objects in 2D. Schools with Picture Puzzles would use one of more of these slide shows as the software component. 