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

## Part B: Course Detail

Teaching Period: Term2 2013

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

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 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 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 nonlinear 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 beginning Topic/Assessment Exercises 8/7 Induction and Numeracy Assessment Number Skills -Order of operations                            - Directed number Order of operations Exercise Directed number Exercise 15/7 Calculations involving fractions Fractions Exercise 1. 22/7 Word problems involving fractions Decimal places and significant figures Calculations involving decimals Fractions Exercise 2. Decimal places and significant figures Exercise Decimals Exercise 29/7 Ratio and proportionQUIZ 1. Ratio and proportion Exercise 1. Ratio and proportion Exercise 2. 5/8 Introduction to percentages Calculations involving percentages Introduction to algebra Percentages Exercise Basic Albegra Exercise 1. 12/8 Simplifying algebraic expressions Working with indices Basic Albegra Exercise 2. Basic Albegra Exercise 3. Indices Exercises 19/8 Scientific notation Solving linear equationsQUIZ 2. Scientific notation Exercise Linear Equations Exercise 0. Linear Equations Exercise 1. 26/8 RevisionMID-SEMESTER TEST 2/9 Solving linear equations Linear Equations Exercise 2. Linear Equations Exercise 3. 9/9 Working with formulae Formulae Exercise 1. Formulae Exercise 2. Formulae Exercise 3. 16/9 Metric conversion Calculating perimeter Calculating area Metric Conversion Exercise Perimeter Exercise 1. Perimeter Exercise 2. Area Exercise 1. Area Exercise 2. 23/9 MID-SEMESTER BREAK 30/9 Calculating volume Calculations involving the Theorem of PythagorasQUIZ 3. Volume Exercise Theorem of Pythagoras Exercise 1. Theorem of Pythagoras Exercise 1. 7/10 Introduction to trigonometric ratios Calculations involving trigonometric ratios Trigonometric Ratios Exercise 1 Trigonometric Ratios Exercise 2 14/10 Calculations involving trigonometric ratios Analysis of univariate dataQUIZ 4. Trigonometric Ratios Exercise 3. Statistics Exercise 1. Statistics Exercise 2. 21/10 Further analysis of univariate dataSTATISTICS ASSIGNMENT Introduction to linear relations  Working with linear relations Linear Relations Exercise 1. Linear Relations Exercise 2. Linear Relations Exercise 3. 28/10 Analysis of bivariate data Statistics Exercise 3. 4/11 RevisionFINAL EXAMINATION

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:

4 Quizzes(best 3 results of 4 quizzes) 20%
Statistics Assignment 15%
Mid-semester Test 25%
Final Test 40%

Assessment Matrix

Other Information

1. Breakdown of nominal hours:
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

2.Note: This course will contribute to your grade average result in the Certificate IV in Tertiary Preparation (Science) qualification. Please note that you must achieve a CREDIT average across the program to be granted a guaranteed pathway in the following programs.
Diploma of Nursing (subject to passing the VETASSESS)
Diploma of Laboratory Technology (Biotechnology)
Diploma of Technology (Pathology Testing)
Diploma of Conservation and Land Management
Diploma of Dental Technology.

Course Overview: Access Course Overview