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

## Part B: Course Detail

Teaching Period: Term1 2012

Course Code: MATH5309

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

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C3209 - Certificate III in Science

Course Contact: Judith McCann

Course Contact Phone: 99258366

Course Contact Email: judith.mccann@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

There are no pre-requisites or co-requisites for this course.

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: VPAU073 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 length and perimeters of rectangles, 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 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 information 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
• demonstrate estimating skills to check calculations and reasonableness of outcomes
• use mathematical symbolism, charts, diagrams and graphs as appropriate to convey mathematical thinking and processing.
• use calculators, computers for word processing or spreadsheets as appropriate

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 solution of problems relevant  to each topic
• working independently or in groups to solve problems in exercise sheets
• working in groups to solve more challenging problems

Teaching Schedule

 Week number Week beginning Topics 1 6/2 Induction, Numeracy test, Revision of number skills:   Order of operations, Directed nos., 2 13/2 Revision of number skills: Fractions & decimals Rounding off and significant figures 3 20/2 Ratio and proportionPercentage 4 27/2 Indices TEST 1. 5 5/3 Indices cont.Scientific notation 6 12/3 Metric conversions TEST 2. 7 19/3 Area Volume 8 26/3 Perimeter TEST 3. 9. 2/4 Revision/Mid-semester break

 Week number Week beginning Topics 9 9/4 Mid-semesterbreak/                                     MIDSEMESTER TEST 10 16/4 Theorem of Pythagoras Trigonometric ratios 11 23/4 Trigonometric ratios cont. Revision 12 30/4 TEST 4./Simplifying algebraic expressionsSolving linear equations 13 7/5 Solving word problems involving linear equationsFormulae 14 14/5 TEST 5./Statistics 1. - Univariate data 15 21/5 Linear relations/STATISTICS ASSIGNMENT 16 28/5 Statistics 2 - Bivariate data 17 4/6 Statistics 2  cont. Due date for submission of Statistics Assignment: Friday June 8th 18 11/6 Revision  FINAL 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

Overview of Assessment

Assessment in this course will include:

• 5 Class Tests (best 4 results of 5 tests) 40%
• Statistics assignment 15%
• Mid-semester Test 15%
• Final Examination  30%

Assessment Matrix

 Test 1. Test 2. Test 3. Mid-semester Test Test 4. Test  5. Statistics Assignment Final  Examination Element 1 Use ratio, proportion and percent to solve problems. 1.1 Determine a ratio from information in a practical problem and express it in   simplestform                                                                                                                                             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. 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. 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 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 simple equations and formulae 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 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 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 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 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

Other Information

1. Classroom lessons 18 x 4 hours = 72 hours

Tutorials       18 x 1 hour = 18 hours

Work on Group Activities 10 hours

Revision and preparation for assessment tasks 10 hours

TOTAL 110 hours

2. 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, should refer to the assessment prcedures described on the C3209 Certificate III in Science webpage of myRMIT Studies(Blackboard)  Program Information/General information for new students.

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