# Course Title: Use a range of techniques to solve mathematical problems

## Part B: Course Detail

Teaching Period: Term2 2018

Course Code: MATH7085

Course Title: Use a range of techniques to solve mathematical problems

School: 360T Education

Campus: Brunswick Campus

Program: C5383 - Diploma of Teacher Education Preparation

Course Contact: Soosan Kian

Course Contact Phone: +61 3 9925 9183

Course Contact Email: soosan.kian@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Armen Dickranian

Nominal Hours: 110

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

No Pre-requisites

Course Description

This unit focuses on developing the skills and knowledge to use a range of specialist techniques and concepts to solve mathematical problems.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: VU22074 Use a range of techniques to solve mathematical problems Element: 1 Use ratio, proportion and percent to solve problems Performance Criteria: 1.1 Determine a ratio from information in a practical problem and express it in simplest form 1.2 Divide a quantity into a given ratio 1.3 Convert between fractions, decimals and percent forms 1.4 Calculate a percentage increase or decrease of a quantity Element: 2 Use trigonometry to determine lengths and angles. Performance Criteria: 2.1 Use Pythagoras’ Theorem to determine an unknown side of a right angled triangle 2.2 Use Pythagoras’ Theorem and trigonometric ratios to find unknown side lengths and angles in triangles Element: 3 Use indices to solve problems Performance Criteria: 3.1 Evaluate  index form expressions 3.2 Simplify exponential expressions using the first two index laws 3.3 Convert between decimal numbers and numbers expressed in Standard Notation 3.4 Perform calculations with numbers expressed in Standard Notation, using a calculator Element: 4 Use measurements to solve mensuration problems in two and three dimensions. Performance Criteria: 4.1 Determine lengths and perimeters of rectangles, triangles, circles and simple combined shapes using appropriate and correct units 4.2 Determine areas of rectangles, triangles, circles and simple combined shapes using appropriate and correct units 4.3 Determine volumes of prisms and pyramids with rectangular, triangular and circular cross-sections and with simple combined shapes as cross sections using appropriate and correct units Element: 5 Substitute into and transpose equations and formulae. Performance Criteria: 5.1 Substitute given values into equations and formulae 5.2 Write equations to solve problems 5.3 Transpose formulae 5.4 Solve linear equations Element: 6 Solve problems by plotting points. Performance Criteria: 6.1 Plot given points and points determined from the general formula y = mx+c on the Cartesian plane 6.2 Determine the gradient of a straight line 6.3 Determine the equation of a straight line, where the equation has the general form y = mx+c, y = a and x = b 6.4 Use interpolation and extrapolation to make predictions from the line of best fit, noting limitations Element: 7 Present and evaluate statistical information. Performance Criteria: 7.1 Collect, organise and graphically represent statistical data 7.2 Interpret and analyse statistical information Element: 8 Identify connections between formulae and graphical representations. Performance Criteria: 8.1 Use graphical techniques to draw linear and non-linear graphs 8.2 Develop equations for given linear graphs, including lines of best fit Element: 9 Use algebraic techniques to analyse and solve problems. Performance Criteria: 9.1 Develop formulae to describe relationships between variables and substitute into formulae to find particular values 9.2 Use a range of techniques to solve a range of algebraic problems and perform algebraic manipulations

Learning Outcomes

The learning outcomes are to confirm ability to:

• apply a wide range of mathematical concepts and techniques to solve mathematical problems including:
• using ratio, proportion and percent
• using trigonometry to determine lengths and angles
• using basic indices
• using measurements to solve mensuration problems in two and three dimensions
• substituting into and transposing simple equations and formulae
• presenting and evaluating statistical information
• identifying connections between formulae and graphical representations
• using algebraic techniques to analyse and solve problems
• apply estimation to check calculations and reasonableness of problem solving outcomes
• use mathematical symbolism, charts, diagrams and graphs to convey mathematical thinking and processing.

Details of Learning Activities

This unit is part of the Diploma of Teacher Education Preparation program. The learning and assessment in the program is delivered through face to face teaching, Unsupervised Directed Study and participation in work placement. It is strongly advised you attend all sessions in order to engage in the required learning activities, ensuring the maximum opportunity to gain the competency. You are not required to attend to complete Unsupervised Directed Study, however you are expected to complete the work given and will at times be required to show evidence the work has been completed. Your Unsupervised Directed Study will be posted on Canvas.

The student learning experience will be facilitated through participation in a range of activities:

• Group discussion
• Assignments
• Practical demonstrations and direct observation of actual work and simulated work practice
• Oral presentations
• Individual and group projects - Completing the projects will include negotiated independent study time and practical work relevant to the unit of competency.

Teaching Schedule

This unit will be delivered weekly.
Please note: While your teacher will cover all the material in this schedule, the weekly order is subject to change depending on class needs and availability of speakers and resources. Should the teaching schedule change students will be advised via Canvas.
Library Orientation & an RMIT Online Systems Information Session will be scheduled during the first two weeks of your program. Information about student services, rights and responsibilities is available on the RMIT website https://www.rmit.edu.au/students

Teaching Schedule

 Week Elements 1 Orientation 2 Student and subject introductions Factors, Multiples & Prime numbers 1.1 3 Ratios in problems Quantities in given ratios 1.1 1.2 4 Conversions between fractions, decimals and percentages 1.3 5 Conversions (continued) Percentage increases and decreases 1.3 1.4 6 Introduction to Graphical representations (incl. scaling) 7.1 7 Graphical construction of data 7.1 8 Interpretation of statistics and graphs 7.2 9 Assessment 1– Proportions, Statistics and Graphs Test 1.1-1.4 7.1, 7.2 10 Plotting points (straight lines) on cartesian planes 6.1 11 Finding gradients of straight lines 6.2 12 Determining equations of straight lines 6.3 13 Lines of best fit (interpolation and extrapolation) 6.4 14 Non-linear graphs (exponential and quadratic) 8.1 15 Lines of best fit 8.2 16 Assessment 2- Straight line and Non-linear equations Test 6.1-6.4 8.1-8.2 17 Overview and reflection on using a range of techniques to solve mathematical problems

Learning Resources

Prescribed Texts

References

Other Resources

RMIT will provide you with resources and tools for learning in this course through handouts, our online systems and access to facilities and relevant software. You will also have access to the library resources. It is recommended that you bring:

• Display folder with plastic sleeves
• Highlighter pens
• Notebook or loose leaf paper
• USB (Memory stick)

Overview of Assessment

You must demonstrate the critical aspects of assessment and evidence required for the Unit in order to be deemed competent. Assessment methods have been designed to measure achievement of each competency in a flexible manner over a range of assessment tasks. You may be assessed by:
• Oral or written questioning
• oral presentations
• Assignments and projects
• Direct observation and demonstration in actual work practice
• Presentation of a portfolio of evidence which may comprise documents, and/or photographs and/or video and audio files
• Work-based activities
• Third-party feedback from a work supervisor/employer
Feedback will be provided throughout the semester in class and/or online discussions, through individual and group feedback on practical exercises and by individual consultation.

If you have a long term medical condition and/or disability it may be possible to negotiate to vary aspects of the learning or assessment methods. You can contact the program manager or the Equitable Learning Services if you would like to find out more.

The Student Charter www.rmit.edu.au/about/our-education/supporting-learning-and-teaching/student-charter/ summarises your responsibilities as an RMIT University student as well as the responsibilities of the university.

Your course assessment conforms to RMIT assessment principles, regulations, policies and procedures which can be found on the RMIT University website at: http://www1.rmit.edu.au/browse;ID=qwxbqbg739rl1

Assessment 1 – Proportions, Statistics and Graphs Test (Week 9)

Assessment 2 – Straight line and Non-linear equations Test (Week 16)

Assessment tasks in this unit are assessed using the following competency based results:
CA - Competency achieved
NYC - Not Yet Competent

All Assessment tasks should be submitted by the due date. If an extension is required please contact your teacher and/or Coordinator before the due date.
You must complete a submission cover sheet for every piece of submitted work.
All assessment tasks including electronically recorded student work will be kept by the University for student feedback and to meet government requirements.
Resubmissions:
If you are found to be Not Yet Competent in a Course Assessment Task you may be allowed one resubmission only. Your teacher will provide feedback regarding what you need to do to improve and will set a new deadline for the resubmission. The highest grade you will receive if your resubmission is successful is 'CA'

Assessment Matrix

The assessment matrix demonstrates alignment of assessment tasks with the relevant Unit of Competency and with the critical aspects of assessment for each unit. A copy of the assessment matrix is available for all students.

Other Information

Attendance - The major learning experience involves participating in face to face classes. It is strongly advised that you attend all sessions in order to engage in the required learning activities, ensuring the maximum opportunity to gain the competency.
Feedback - Monitoring academic progress is an important enabling and proactive strategy to assist you to achieve your learning potential. Students may be asked to attend interviews with relevant teachers and Program Coordinator to discuss academic progress.