Course Title: Use a range of techniques to solve mathematical problems
Part B: Course Detail
Teaching Period: Term2 2011
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 nonclassroom activities.
Prerequisites and Corequisites
There are no prerequisites or corequisites 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 
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 
Element: 
3. Use basic indices to solve problems 
Performance Criteria: 
3.1 Evaluate simple index form expressions 
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 
Element: 
5. Substitute into and transpose simple equations and formulae 
Performance Criteria: 
5.1 Substitute given values into simple equations and formulae 
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 
Element: 
7. Present and evaluate statistical information 
Performance Criteria: 
7.1 Collect, organise and graphically represent statistical data 
Element: 
8. Identify connections between formulae and graphical representations 
Performance Criteria: 
8.1 Use graphical techniques to draw linear and simple nonlinear graphs 
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 
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
 class discussion
 work sheets
 group activities
Teaching Schedule
Week number  Week beginning  Topics 
1  11/7  Induction, Numeracy test, Bodmas, Directed nos., 
2  18/7  Significant figures, rounding off Scientific notation 
3  25/7 
Fractions & decimals Test 1 
4  1/8 
Indices 
5  8/8 
Ratio & proportion 
6  15/8 
Metric conversions Test 2. 
7  22/8 
Area Surface area 
8  29/8 
Perimeter Perimeter cont. 
9 
5/9 
Revision Test 3 Exam 
Week number  Week beginning  Topics 
10
 12/9 
Trigonometric ratios Theorem of Pythagoras 
11
 19/9 
Trigonometric ratios cont. 
 26/9  Mid  semester break 
12
 3/10 
Simplifying algebraic expressions Test 4./ Solving Linear equations 
13
 10/10 
Solving word problems Formulae 
14

17/10 
Statistics 1.  Univariate data Test 5. / Statistics 1. cont. 
15
 24/10 
Linear relations Linear relations cont. 
16
 31/10 
Statistics 2  Bivariate data Test 6. / Statistics 2 cont. 
17
 7/11 
Revision Final exam 
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:
Worksheets (ungraded)
Exercises (ungraded)
Quizzes (ungraded)
Tests (graded)
Assignment (graded)
MIdsemester Test (graded)
Final Examination (graded)
Assessment Tasks
 6 Class Tests 50%
 End of term 1 Exam 25%
 End of term 2 Final exam 25%
Assessment Matrix
Test 1.  Test 2.  Test 3.  Exam  Test 4.  Test 5.  Test 6.  Final Exam  
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 rightangled 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 crosssections 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 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  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
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 worksheets 10 hours
TOTAL 110 hours
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