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 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 
Element: 
2. Use trigonometry to determine lengths and angles 
Performance Criteria: 
2.1 Use Pythagoras’ Theorem to determine an unknown side of a 
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 length and perimeters of rectangles, circles and 
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 
Element: 
7. Present and evaluate statistical information 
Performance Criteria: 
7.1 Collect, organise and graphically represent statistical 
Element: 
8. Identify connections between formulae and graphical representations 
Performance Criteria: 
8.1 Use graphical techniques to draw linear and simple nonlinear 
Element: 
9. Use algebraic techniques to analyse and solve problems 
Performance Criteria: 
9.1 Develop formulae to describe relationships between variables 
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, 
2  13/2 
Revision of number skills: Fractions & decimals 
3  20/2 
Ratio and proportion 
4  27/2 
Indices TEST 1. 
5  5/3 
Indices cont. 
6  12/3 
Metric conversions

7  19/3 
Area 
8  26/3 
Perimeter

9. 
2/4

Revision/Midsemester break 
Week number  Week beginning  Topics 
9
 9/4 
Midsemesterbreak/ 
10  16/4 

11  23/4 
Trigonometric ratios cont. Revision 
12
 30/4 
TEST 4./Simplifying algebraic expressions 
13
 7/5 
Solving word problems involving linear equations 
14

14/5 
TEST 5./Statistics 1.  Univariate data 
15
 21/5 
Linear relations/STATISTICS ASSIGNMENT 
16
 28/5 

17
 4/6 
Statistics 2 cont. Due date for submission of Statistics Assignment: Friday June 8th 
18 
11/6 
Revision 
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
 5 Class Tests (best 4 results of 5 tests) 40%
 Statistics assignment 15%
 Midsemester Test 15%
 Final Examination 30%
Assessment Matrix
Test 1.  Test 2.  Test 3.  Midsemester 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 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
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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