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

## Part B: Course Detail

Teaching Period: Term1 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

Robert Jacobson

51.06.20

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: Use ratio, proportion and percent to solve problems Use trigonometry to determine lengths and angles Use basic indices to solve problems Use measurements to solve mensuration problems in two and three dimensions Substitute into and transpose simple equations and formulae Solve problems by plotting points Present and evaluate statistical information Identify connections between formulae and graphical representations Identify connections between formulae and graphical representations 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 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. 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. 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 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 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 7.1 Collect, organise and graphically represent statistical information 7.2 Interpret, analyse and describe statistical information. 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. 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

• work sheets
• group activities

Teaching Schedule

 wk. no. Dates Topics 1 9/2 10/2 Induction, Numeracy test, Bodmas, Directed nos., 2 16/2 17/2 Significant figures, rounding off Scientific notation 3 23/2 24/2 Test 1 Fractions & decimals 4 2/3 3/3 Indices 5 9/3 10/3 Ratio & proportion Percentage 6 16/3 17/3 Test 2 Metric conversions 7 23/3 24/3 Area Volume 8 30/3 31/3 Perimeter Contd. 9 6/4 7/4 Statistics Test 3 10 13/4 14/4 Revision Exam

Learning Resources

Prescribed Texts

References

Other Resources

Overview of Assessment

Assessment in this course will include:

• Class tests
• End of term 1 exam
• End of term 2 exam

Assessment Matrix

Other Information

Classroom lessons 18 x 4 hours 72 hours

Work on Group Activities 10 hours

Revision and preparation for worksheets 28 hours

TOTAL 110 hours

Course Overview: Access Course Overview