Expected level of development
Australian Curriculum Mathematics V9: AC9M7SP04
Numeracy Progression: Understanding geometric properties: P4
At this level, students are introduced to the use of algorithms for sorting and classifying. They can use flowcharts to do this. Algorithmic thinking is a design process and flowcharts are used to show a sequence of steps and/or instructions and require decision-making by the user or the inputs.
It's important to highlight the hierarchy used in creating and designing these charts about quadrilaterals and polygons, as the levels in the hierarchical scheme illustrate how shapes and their properties are related to each other, for instance. In the design of creating these algorithms, students make connections at a deeper level.
Flowcharts may be constructed using paper and pen or digital applications such as smartdraw or diagrams.net. They may be tested by peers or used as an assessment or class activity.
Teaching and learning summary:
- Introduce flowcharts and how they work.
- Introduce the different components of a flowchart.
- Demonstrate how to construct a flowchart that sorts objects for a given attribute.
- Illustrate the hierarchical nature of flowchart design.
- Show that decision-making is part of the design in the sequence of steps and is therefore available to the user of the chart.
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Teaching strategies
A collection of evidence-based 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.
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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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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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Worked examples
A worked example is not just a pre-worked question that is given to the students. There are several types of worked examples and ways of using them.
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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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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.
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Level 7 Algorithms in Mathematics
A three-lesson sequence that explores the steps and decision-making processes involved in algorithms with multiple outcomes, focusing on topics such as shape classification, divisibility rules, and other mathematical facts.
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Celebrity quadrilaterals: algorithms
In this lesson students develop an understanding of how a decision tree algorithm works.
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Flowchart
Present this printable flowchart to students and ask them to design and create their own flowcharts to classify shapes. Ask questions: which variables work? Encourage refinement of the algorithm with your feedback.
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Assessment
By the end of Year 7, students can design and create algorithms to sort and classify shapes.
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Have fun with flowcharts
Ask students to create a set of instructions or flow chart to identify different polygons that exist in the real world. For example, present pictures of your school and have students use their instructions to classify plane shapes that can be identified in the pictures. Students may present their creations to the class on A3 paper.
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