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
Assessment Tasks
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