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

## Part B: Course Detail

Teaching Period: Term1 2014

Course Code: MATH5341

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

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C4327 - Certificate IV in Tertiary Preparation

Course Contact: Nancy Varughese

Course Contact Phone: +61 3 9925 4713

Course Contact Email: nancy.varughese@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Teacher: David Thomas
email:
david.thomas@rmit.edu.au

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

None.

Course Description

The purpose of this unit is to provide learners with the knowledge and skills to use a range of specialist techniques and concepts to solve mathematical problems.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: VU21058 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 right-angled triangles Element: 3. Use basic indices to solve problems. Performance Criteria: 3.1 Evaluate simple index form expressions 3.2 Simplify simple 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 Section C: Unit Information 22219VIC Certificate III in Science and 22220VIC Certificate IV in Science © State of Victoria Version 1 2013 Page 36 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 Element: 5. Substitute into and transpose simple equations and formulae. Performance Criteria: 5.1 Substitute given values into simple equations and formulae 5.2 Write equations to solve simple problems 5.3 Transpose simple formulae 5.4 Solve simple 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 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, 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, analyse and describe statistical information Element: 8. Identify connections between formulae and graphical representations. Performance Criteria: 8.1 Use graphical techniques to draw linear and simple 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

At the completion of this course, the student must be able to:
apply a wide range of strategies 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
− solving problems by plotting points
− presenting and evaluating statistical information
− identifying connections between formulae and graphical representations
− using algebraic techniques to analyse and solve problems

Details of Learning Activities

Students are expected to participate actively in all learning activities that include:
- discussion of mathematical concepts relevant to each topic
- discussion of the mathematical routines and procedures for solving problems related to each topic
- working independently or in groups in solving problems on exercise and work sheets
- working in groups to solve more challenging problems requiring interpretation and evaluation of results

Teaching Schedule

 Week Week beginning Topics Exercises 1 10 Feb Induction Number Skills – Order of Operations Number Skills – Directed Numbers 1.1, 1.2 2 17 Feb Fractions 2.1a, 2.1b 3 24 Feb Decimal Places and Significant Figures Decimals 2.2, 2.3 4 3 March Ratio and Proportion Test 1: Number Skills and Fractions 2.4 5 10 March Percentages Indices 2.5, 3.1 6 17 March Scientific Notation Introductory Algebra and Simplifying Algebraic Expressions 3.2, 4.1 7 24 March Test 2: Fractions, Decimals, Percentages, Ratios, Indices and Scientific Notation Solving Linear Equations 4.2a 8 31 March Revision Mid-Semester Exam worksheets 9 7 April Solving Worded Linear Equations 4.2b 10 14 April Transposition and Substitution 4.3 11 28 April Statistics: Univariate Data 5.1a, 5.1b 12 5 May Statistics: Univariate Data Statistics: Bivariate Data 5.1c, 5.2 13 12 May Linear Relations 4.4a, 4.4b 14 19 May Test 3: Algebra, Univariate Data, Linear Relations. Metric Conversion and Perimeter Area 6.1 6.2a 15 26 May Volume & Pythagoras’ Theorem 6.2b, 6.3 16 2 June Trigonometric Ratios 6.4 17 9 June Revision & Final Exam worksheets

Learning Resources

Prescribed Texts

References

 Any Year 10 or Year 11 Mathematics textbook. MATHEMATICS for Biology/Pathology Technicians by Carly Marshall and Sue van Megen 0 7035 8505 0

Other Resources

Students are required to purchase:

- a scientific calculator for use in class and when completing assessment tasks

- lined exercise book in which to complete Exercises

- binder with plastic sleeves for storing Exercises and Worksheets

- writing materials

Overview of Assessment

Assessment in this course will include:

3 Tests, 10% each = 30%

Mid-Semester Exam = 20%

Statistics Assignment =15%

Final Exam = 35%

Assessment Matrix

Other Information

Classroom lessons 17 x 4 hours = 72 hours

Tutorials 17 x 1 hour = 17 hours
Work outside class on Exercises, Worksheets etc = 6 hours
Assignment work = 5 hours
Revision and preparation for assessment tasks = 10 hours

TOTAL 110 hours

Students who are absent on the day of an assessment task, whose performance in an assessment task has been severely affected by some unforeseen circumstance or who are unable to submit an assignment by the due date, need to apply for Special Consideration and apply within the allowed time frame

Extension of time for submission of assessable work- A student may apply for an extension of up to 7 days from the original due date. They must lodge the application form (available on the web http://mams.rmit.edu.au/seca86tti4g4z.pdf ) at least the day before the due date. The application is lodged with the School Admin Office on Level 6, Bdg 51. Students requiring longer extensions must apply for Special Consideration (form available on the Web). For missed assessments such as exams- you (& your doctor if you are sick) must fill out a special consideration form. This form must be lodged at the HUB or online with supporting evidence (eg medical certificate), prior to, or within, 48 hours of the scheduled time of examination.

Late work that is submitted without an application for an extension will not be corrected

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