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

Part B: Course Detail

Teaching Period: Term2 2015

Course Code: MATH5341

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

School: 155T Vocational Health and Sciences

Campus: City Campus

Program: C4327 - Certificate IV in Tertiary Preparation

Course Contact: Nancy Varughese

Course Contact Phone: +61 3 9925 4713

Course Contact Email:

Name and Contact Details of All Other Relevant Staff

Alice Abraham

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


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


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


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


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


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


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
5.4Solve simple linear equations


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


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


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


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

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 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

date (mon) topics
L1=>Lesson 1, L2=>Lesson 2 Exercise
1 6 jul number skills

L2: Order of Operations & Directed Numbers, Begin Fractions

1.1, 1.2
2 13th Jul basic calculations L1: Fractions and Decimals, Rounding 2.1, 2.2, 2.3
      L2: Scientific Notation, Significant Figures 5.2, 2.4
3 20th Jul   L1: Calculations using Decimals 2.5
      L2: Ratio and Proportion 2.6
4 27th Jul Algebra And Linear Graphs L1: Percentages 2.7
      L2: Quiz 1 (20%)
(Numbers, fractions, decimals, percentages)
 5 3rd Aug    L1: Basic Algebra. Write equations and solve 3.6
      L2: Solving Linear Equations 3.4, 3.5
6 10th Aug   L1: Transposition & Substitution 3.1, 3.2, 3.3
      L2: Graphing Linear Relations
Workbook Assessment1 (15%)
7 17th Aug   L1: Determining Linear Relations 3.7
      L2: Types of Data. Collecting & Representing Data 4.1
8 24th Aug Statistics L1: Mean, Median, Mode, 5-Figure summary  
      L2: Bivariate, Lines of best fit 4.2
9 7th Sep   L1: Quiz 2 (20%)  
    Indices L2: Simplify Indices 5.1
10 14th Sep   L1: Simplify Indices 5.1
      L2: Assessed Project in Class (15%) (non-linear graphs)  
11 21 Sep Measurement L1: Metric Conversion  
      L2: Pythagoras Theorem  
12 28 Sep   L1: Perimeters of basic shapes and combined shapes 6.1
      L2: Areas of basic shapes and combined shapes 6.1
13 5 Oct   L1: Surface Area and Volume 6.2
      L2: Excursion  
14 12 Oct Geometry & Trigonometry L1 & L2: Trigonometric Ratios and Applications 6.4
15 19 Oct   L1 & L2: Applications of Trigonometry  
16 26 oct   L1 & L2: Revision  
17 2 nov   L1: Revision  
      L2: Open Book Test (30%)  

Learning Resources

Prescribed Texts

Solve Maths Problems Question Booklet, 2015 version 1.4


Any year 10 or 11 maths textbook.

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

- binder with plastic sleeves for storing Exercises and Worksheets

Overview of Assessment

Assessment in this course will include:
Worksheets (ungraded)
Exercises (ungraded)
Quizzes (graded)
Assignment (graded)
Tests (graded)

Assessment Tasks

2 Quizzes, 20% each = 40%

1 Workbook Assessment 15%

1 Assessed project 15%

Final Exam = 30%

Assessment Matrix

Other Information

Classroom lessons 17 x 4 hours = 72 hours

Tutorials 17 x 1 hour = 17 hours
Work outside class on Exercises, Worksheets etc = 6 hours
Assignment work = 5 hours
Revision and preparation for assessment tasks = 10 hours

TOTAL 110 hours

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 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 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