What is this sequence about?
This learning sequence aims to develop students’ spatial sense and geometric reasoning. Spatial sense is necessary for appreciating geometric form in art, nature and architecture, and for describing and analysing the world (Van De Walle, et. al., 2019). This sequence uses the real-world context of architecture and design to develop student understanding of location and position, transformation and symmetry, and visualisation.
This sequence provides opportunities for students to be young designers where they will solve problems, construct architectural structures, and create designs for their homes. Students will investigate the properties of two-dimensional shapes and three-dimensional objects, the interrelationships of shapes and the effects of changes to shapes. This sequence aims to equip students with the skills required to describe movement and arrangement of objects, apply geometric transformations, and explore with geometry to build their spatial reasoning and visualisation skills.
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Big understandings Geometry helps us represent the space in which we live to describe location, movement, and spatial relationships. Transformation and symmetry can be used to describe our world and to solve problems. |
The sequence has been written by teachers for teachers. It has been designed to provide students with rich, engaging learning experiences that address the Victorian Curriculum. The sequence consists of five flexible stages, including suggested learning intentions.
Overview of stages
1. Urban Designs
Suggested Learning Intentions
- To develop spatial awareness through thinking and reasoning about direction, distance, and location
3. Exterior Designs
Suggested Learning Intentions
- To investigate symmetry in shapes to create designs
5. Interpreting Designs
Suggested Learning Intentions
- To explore how visualisation and spatial reasoning can help us to solve problems
2. Architectural Designs
Suggested Learning Intentions
- To explore the connection between three-dimensional objects and their two-dimensional representations
4. Interior Designs
Suggested Learning Intentions
- To solve problems involving shapes, through the application of geometric transformation
Prior knowledge
Before you commence this sequence, students should be familiar with the properties of two-dimensional shapes and three-dimensional objects, the language of relative position and direction, compass bearing, types of angles and knowledge of symmetry in the environment.
You can find support for building students’ understanding of these concepts in the Mathematics Curriculum Companion. The Teaching Context and Teaching Ideas related to the content descriptions VCMMG142, VCMMG143, VCMMG146, VCMMG171, VCMMG173 and VCMMG174, may be particularly useful.
Teaching strategies
The Mathematics Curriculum Companion provides teachers with content knowledge, suggested teaching and learning ideas as well as links to other resources. Resources are organised by Mathematics strands and sub-strands and incorporate the proficiencies: Understanding, Fluency, Problem Solving and Reasoning. The Companion is an additional resource that you could refer to when you are planning how you might use the sequence in your school.
The sequence highlights opportunities to apply the High Impact Teaching Strategies (HITS), which are a component of the Victorian Teaching and Learning Model.
The sequence highlights the use of a variety of scaffolding practices to help support students in the learning process, in particular:
- collaborating
- modelling
- guiding
- probing
- orienting.
Vocabulary
Students should be able to understand and use the following concepts and terms by the end of the learning sequence:
| Scales | Distance |
| Legends | Compass directions |
| Coordinates | x-axis |
| Cartesian plane | y-axis |
| Grid reference | Symmetry |
| Quadrant | Transformations |
| Route | Translation |
| Direction | Reflection |
| Rotation | Vertical |
| Horizontal | Elevation |
You can find definitions of some of these terms in the Glossary for the Mathematics Curriculum.
It is recommended that the explicit teaching of vocabulary occur throughout this learning sequence. The Literacy in Mathematics section of the Literacy Teaching Toolkit provides several teaching strategies with worked examples demonstrating how teachers can use literacy to support student understanding of mathematical language. A further set of strategies demonstrate how to develop students' literacy skills to support their mathematical problem solving.
Assessment
Opportunities for formative and summative assessment are identified at different stages of the learning sequence. Look for the 'Assessment Opportunity' icon.
You may want to develop a rubric to assess students’ progress. A range of Formative Assessment resources are available from the Victorian Curriculum and Assessment Authority. This includes a Guide to Formative Assessment Rubrics, a series of modules to support you to develop your own formative assessment rubrics, and sample rubrics across six curriculum areas that demonstrate how you can put formative assessment rubrics into practice in the classroom.
In developing a rubric, you may wish to co-construct assessment criteria with your students. Each stage of the sequence provides sample success criteria for students working at Level 5.
The Victorian Curriculum and Assessment Authority has published annotated work samples that provide teachers with examples of student learning achievement at multiple levels for each strand of the Mathematics curriculum.
Victorian Curriculum connections
Level 4
This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 5, but also addresses the following content descriptions from Level 4:
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Content description |
Stage |
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Mathematics |
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Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (VCMMG170) |
Architectural designs Interpreting Designs |
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Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects (VCMMG171) |
Architectural Designs Exterior Designs Interior Designs Interpreting Designs |
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Use simple scales, legends and directions to interpret information contained in basic maps. (VCMMG172) |
Urban Designs |
The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum in Mathematics Level 4:
- Students create symmetrical simple and composite shapes and patterns, with and without digital technology
- Students interpret information contained in maps
A table showing curriculum content addressed across Levels 4 to 6 in this learning sequence is available in word and PDF formats.
Level 5
This sequence addresses content from the Victorian Curriculum in Mathematics and Critical and Creative Thinking. It is primarily designed for Level 5, and addresses the following content descriptions:
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Content description |
Stage |
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Mathematics |
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Connect three-dimensional objects with their nets and other two-dimensional representations (VCMMG198) |
Architectural Designs |
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Use a grid reference system to describe locations. Describe routes using landmarks and directional language (VCMMG199) |
Urban Designs |
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Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (VCMMG200) |
Exterior Designs Interior Designs |
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Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (VCMMG201) |
Interior Designs |
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Follow a mathematical algorithm involving branching and repetition (iteration) (VCMNA194) |
Urban Designs |
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Creative and Critical Thinking |
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Consider the importance of giving reasons and evidence and how the strength of these can be evaluated (VCCCTR025) |
Architectural Designs |
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Digital Technologies |
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Design, modify and follow simple algorithms represented diagrammatically and in English, involving sequences of steps, branching, and iteration (VCDTCD032) |
Urban Designs |
The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 5:
- Students connect three-dimensional objects with their two-dimensional representations
- Students describe transformations of two-dimensional shapes and identify line and rotational symmetry
A table showing curriculum content addressed across Levels 4 to 6 in this learning sequence is available in word and pdf formats.
Level 6
This sequence addresses content from the Victorian Curriculum in Mathematics. It is primarily designed for Level 5, but also addresses the following content descriptions from Level 6:
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Content description |
Stage |
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Mathematics |
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Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies (VCMMG229) |
Interior Designs Interpreting Designs |
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Creative and Critical Thinking |
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Consider the importance of giving reasons and evidence and how the strength of these can be evaluated (VCCCTR025) |
Architectural Designs |
The sequence can be used to assess student achievement in relation to the following Achievement Standards from the Victorian Curriculum: Mathematics Level 6:
- Students investigate simple combinations of transformations in the plane, with and without the use of digital technology
A table showing curriculum content addressed across Levels 4 to 6 in this learning sequence is available in word and pdf formats.
Learning Progressions
The Numeracy Learning Progressions support teachers to develop a comprehensive view of how numeracy develops over time. You can use the Numeracy Learning Progressions to:
- identify the numeracy capability of your students
- plan targeted teaching strategies, especially for students achieving above or below the age-equivalent expected level in the Victorian Curriculum: Mathematics
- provide targeted feedback to students about their learning within and across the progressions.
The sequence is related to the following progression:
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Learning Progression |
Level 4 |
Level 5 |
Level 6 |
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Properties of shapes and objects |
Symmetry |
N/A |
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Using formal maps and plans |
Interpreting maps and plans |
N/A |
Click on the Learning Progression to access more detailed descriptions of student learning.