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

## Part B: Course Detail

Teaching Period: Term1 2017

Course Code: MATH5341

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

School: 174T School of VE Engineering, Health & Science

Campus: City Campus

Program: C4386 - Certificate IV in Tertiary Preparation

Course Contact: Namrita Kaul

Course Contact Phone: +61 3 9925 4309

Course Contact Email: namrita.kaul@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Iain McKenzie

9925 4723

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 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 data 7.2 Interpret, analyse and describe statistical information Element: 8 Identify connections between formulae and graphical representations Performance Criteria: 8.1 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

Details of Learning Activities

- 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 Date (start) Topics Exercises 1 8th Feb Number Skills Order of Operations & Directed Numbers Fractions 1.1, 1.2 2 13th  Feb Basic Fractions and Decimals,  Significant Figures Scientific Notation 2.1, 2.2, 2.3, 2.4, 5.2 3 20th Feb Calculations Calculations using Decimals (calculator) Ratio and Proportion 2.5 2.6 4 27th Feb Percentages Quiz 1  (15%) (Numbers, fracs, decimals) Basic Algebra:  Substitute & Transpose 2.7   3.1, 3.3 5 6th March Algebra And Simplifying Algebraic Expressions Algebraic techniques to solve problems  Solving Linear Equations 3.2     3.4 6 13th March Linear Graphs Graphing Linear Relations Determining Linear Relations Workbook Assessment1 (15%) 3.5, 3.6, 3.7, 3.8, 3.9 7 20th March Applications of Linear Equations and graphs Lines of Best Fit 8 27th March Statistics Types of Data. Collecting & Representing Data Mean, Median, Mode, 5-Figure summary, Scatter Plot, Line of Best Fit 4.1 – 4.4   4.5 9 3rd April Indices Simplify Indices (2 Index Laws) Quiz 2  (15%) 5.1 10A 10th April Non-linear graphs Metric Conversion Simple Non-linear graphs and their equations 9.1 - 9.6 Mid Semester Break (Easter) 10B 17h April Non-linear graphs Group Task: Non-linear graphs Presentation    (10%) 11 24th April Pythagoras Theorem. Perimeters of basic shapes and combined shapes (correct units) 6.3 12 1st May Geometry & Trigonometry Areas of basic shapes and combined shapes (correct units) Volumes of prisms and pyramids and combined shapes. (Correct Units) 6.1   6.2 13 8th May Geometry & Trigonometric Ratios and Applications 6.4 14 15th May Trigonometry Revision of trigonometry 15 22nd May Workbook Assessment 2 (15%) Revision 16 29th May Revision Open Book Test   (30%)

Learning Resources

Prescribed Texts

References

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

Overview of Assessment

Assessment  in this course may include:
Worksheets
Quizzes
Assignments
Written Tests

 Task Topics covered Weighting Date Quiz 1 Numbers, Fractions, Decimals 15% Week 4 Workbook 1 Fractions, Decimals and Basic Algebra 15% Week 6 Quiz 2 Statistics and Linear Equations 15% Week 8 Group Task Non-Linear Graphs and Relations 10% Week 10 Workbook 2 Statistics, Indices, Geometry and Trigonometry 15% Week 15 Test Indices, Pythagoras,  Geometry & Trigonometry 30% Week 16

Assessment Matrix

Other Information

This course is graded in accordance with competency-based assessment, but which also utilises graded assessment

CHD Competent with High Distinction (80 – 100%)
CDI Competent with Distinction (70 – 79%)
CC Competent with Credit (60 – 69%)
CAG Competency Achieved – Graded (50 – 59%)
NYC Not Yet Competent
DNS Did Not Submit for assessment

All assessment types must be passed (tests and assignments). For example, if there are two tests you need to have an average of 50% to pass. You can’t make up marks from one type of assessment to another (e.g. pass the tests but fail the workbook component).
APPLICATION FOR EXTENSION OF TIME FOR SUBMISSION OF ASSESSABLE WORK- A student may apply for an extension of up to 7 days from the original due date. They must lodge the application form (available online http://www1.rmit.edu.au/students/assessment/extension) at least 24 hours before the due date. The application is lodged with the School Admin Office on Level 6, Bdg 51, or emailed to the Coordinator.
Late work that is submitted without an application for an extension will not be corrected.
Students requiring extensions longer than 7 days must apply for Special Consideration (see the ‘Help me’ link in blackboard, via myRMIT studies or http://www1.rmit.edu.au/students/specialconsideration) For missed assessments such as exams - you (& your doctor if you are sick) must fill out a special consideration form. This form must be lodged online with supporting evidence (e.g. medical certificate), prior to, or within, 48 hours of the scheduled time of examination.
If you miss an assessment task due to unavoidable circumstances, you need to follow the procedure of special consideration and apply within the allowed time frame.

Course Overview: Access Course Overview