Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M4SP01
Numeracy Progression: Understanding geometric properties: P3
At this level, students should have a good understanding of the properties of common shapes. Build on students’ knowledge of shape by combining and cutting 2D shapes.
Tangrams provide opportunities to combine shapes into a pattern or to make composite shapes. Model how to describe the tangram arrangements using correct geometric language such as by flipping, sliding or rotating a shape.
There is an opportunity to connect learning about composite shapes and compare these by area using informal measurements such as squares (AC9M4M02). Also, fractions can be explored as students describe cutting of shapes and find equivalent representations of fractions (AC9M4N03).
Teaching and learning summary:
 Investigate composite shapes breaking down into 2D shapes.
 Describe and compare compound shapes using geometric language.
 Create and recreate composite shapes using tangrams.
 Compare areas of shapes by informal means.
Students:
 identify and classify different 2D shapes by their properties
 create composite shapes from verbal or written instructions
 identify common 2D shapes that are part of a composite shape by recreating it from these shapes
 find the area of composite shapes using informal measures such as squares.
Some students may:
 have difficulty recognising plane shapes in different orientations. Students who regularly encounter plane shapes in one specific orientation may have difficulty in classifying shapes correctly and recognising their properties when they look 'different'. For example, a square orientated on one of its vertices may be mistakenly identified as a diamond. Exploring shapes in different orientations (for example, in tangrams) may assist students in addressing this.
 be confused about properties of shapes. To encourage thinking about properties of shapes try using true/false statements. For example, statements may include:
 A square is half the size of a rectangle. (True)
 Every square is a rectangle. (True)
 Every rectangle is a square. (False)
 A square has 4 lines of symmetry (True)
 A rectangle has 4 lines of symmetry. (False)
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
 We are learning how to identify the properties of 2D shapes.
 We are learning about how to combine shapes to make a tangram animal.
Why are we learning about this?
 Tangrams help us develop important geometric skills such as spatial visualisation, which is often helpful in design.
What to do
 Look at this tangram. What animal does it look like? How many different shapes is it made from?
 Take a sheet of paper and draw, colour and cut out the shapes to create the same pattern.
 Now take the same shapes and rearrange them to make a tangram of a different object. Draw your tangram.
Success criteria
I can:
 name familiar 2D shapes
 create a tangram using a variety of shapes.
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Teaching strategies
A collection of evidencebased teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.

Worked examples
A worked example is not just a preworked question that is given to the students. There are several types of worked examples and ways of using them.
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Collaborative Learning
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.
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Concrete, Representational, Abstract (CRA)
The CRA model is a threephased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Tangrams: an interactive challenge
Teacher notes to guide students’ investigation of combining plane shapes into other arrangements.
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Mathigon: tangram
Use this virtual manipulative for students to practise spatial rotation and explore relationships between shapes.
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Tangrams 3: exploring halves
A video that guides students to apply their knowledge of fractions to explore and combine tangram shapes.
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Finding the area of compound shapes
Use this interactive to explore area of compound shapes.
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Shape overlays: picture
Students position two simple shapes to form an overlap, then cut out that new shape.
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reSolve: Geometry – Trapezium pieces
This lesson explores different shapes that can be formed by cutting a trapezium in two with one straight line.
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