Growing TrisquaresTask 238 ... Years 4  10SummaryThe crux of this problem is that 4 Trisquares can be joined to make a new, scaled up, Trisquare. This provides a 'template' for constructing the next size, and the next, and the next... The visual pattern can also be represented as a number pattern and this leads to graphing, equation work and scale factors.
This task is a partner to Task 237, Trisquares. Between them present the mathematics which also appears in Task 166, Sphinx and its Sphinx Album. Growing Trisquares is also related to Task 115, Dividing Shapes. This cameo has a From The Classroom which shows magnificent work from a Year 9 class at Wade High School who were so enthusiastic about the challenge that they cut out masses of paper Trisquares to complete an incredible set of posters. 
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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. 
The starting point for this investigation is the solution for Question 1. Everything else grows from this. At a mathematics workshop for students in Wagga Wagga, these children were very excited about combining their Trisquares to make a Size 4.
Perhaps Jenny saw this pattern, thought about Size 3 then guessed she might need 9 unit Trisquares and that's how her challenge on the card came about. Of course, if Size 3 can be made, then we must ask about Sizes 5, 6 and 7 and so on. Size 6 could be interesting. Perhaps it could be made from either four Size 3s or nine Size 2s? To round off the investigation, one might ask what would happen if a Trisquare became a Tricube. 
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. 
To convert this lesson to a whole class investigation you will need lots of Trisquares. You could save this drawing, import it into a word processor and make a master from which students cut their pieces... The photos in the From The Classroom section below probably say all that needs to be said about the whole class lesson possibilities of this task. At this stage, Growing Trisquares does not have a matching lesson on Maths300. However Lesson 25, Sphinx, is built around the same mathematics and includes a broad suite of examples from classrooms around the world. 
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. 
Growing Trisquares is not in any MWA kit. However it can be used to enrich the Pattern & Algebra kit at Years 5/6 and the Pattern & Algebra kit at Years 9/10. 
Wade High School
Year 9

This group of students were not known for their efforts in mathematics, but Task 115, Dividing Shapes, caught their imagination and led to this amazing work with 'home made' Trisquares. As the Trisquares grew so did the students understanding of number patterns, number pairs, graphing, perimeter and area. 