Sample work Mathematics Standard 1 Year 12: networks working on job sites
In this task, students analyse possible networks for travelling between job sites and locations and features of facilities at a water theme park. See how examples have been graded, including the intended outcomes and criteria for the assessment.
Nature of the task
Students create and analyse possible networks for travelling between job sites. They determine the shortest path to be taken by applying different strategies. They also use mathematical calculations to determine the locations and features of facilities at a water theme park.
Context
Students have engaged in learning for the subtopics, Networks and Paths and Right-Angled Triangles. They have participated in activities to develop knowledge of the concepts of networks and finding the minimum spanning tree, and skills to solve a variety of problems.
Outcomes assessed
MS1-12-3 interprets the results of measurements and calculations and makes judgements about their reasonableness
MS1-12-4 analyses simple two-dimensional and three-dimensional models to solve practical problems
MS1-12-8 applies network techniques to solve network problems
MS1-12-9 chooses and uses appropriate technology effectively and recognises appropriate times for such use
MS1-12-10 uses mathematical argument and reasoning to evaluate conclusions, communicating a position clearly to others
Assessment criteria
Students will be assessed on their ability to:
- solve problems based on a scenario
- select and use appropriate mathematical processes, technologies and language to investigate problems
- use reasoning to evaluate solutions and justify conclusions.
Graded student work samples
Ashley
Commentary
This response demonstrates an understanding of the language of networks and the ability to use simple network techniques to solve problems. The sequencing of steps in solving problems is clear, and diagrams have been constructed from the information provided. Although some calculations have been accurately completed, there is some confusion with regard to units (time vs distance; angles vs sides) that affected the results. An understanding of trigonometry is evident but it has not been always been accurately applied. Information in diagrammatic form has been used to assist in solving problems but has not been used consistently to make predictions and inferences or to draw conclusions. Reasoning has been applied but some arguments and conclusions lack depth. This response demonstrates characteristics of work typically produced by a student performing at the lower end of grade B at the end of the course.
Kim
Commentary
This response demonstrates sound understanding of the language of networks and limited accuracy in using problem-solving strategies. Some network techniques have been applied and simple trigonometry techniques have been used. Angles have been accurately rounded and there is some use of correct notation, but aspects of the task have been omitted. Distance has been interpreted as a time, and an angle has been interpreted as a length. Some higher order skill is evident in the application of Prim’s Algorithm but there are issues with scale calculations and the reasoning about the results is not accurate. This response demonstrates characteristics of work typically produced by a student performing at the lower end of grade C at the end of the course.
Ali
Commentary
This response demonstrates basic understanding of the language of networks but little understanding of how to construct a network. Some questions have been misinterpreted and diagrams have not been used as effectively as possible. The first step of working is not always correct, particularly with trigonometry, and there is a lack of mathematical argument. Two steps of working have been shown in response to some questions but simple network and trigonometric problems have not always been completed. Simple mathematical arguments have been given and diagrams have been drawn but the labelling is poor. Scale has been correctly calculated, and technology has been used to find a distance in kilometres. This response demonstrates characteristics of work typically produced by a student performing at grade D standard at the end of the course.
Morgan
Commentary
This response demonstrates limited understanding of the language and basic concepts of networks. Many questions have been omitted, and the diagrams are incomplete, very basic or have been incorrectly drawn. There is evidence of difficulty in accurately locating angles and sides. Some trigonometry questions have been correctly answered but the context of questions has not been effectively interpreted. This response demonstrates characteristics of work typically produced by a student performing at grade E standard at the end of the course.