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

Part B: Course Detail

Teaching Period: Term2 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 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:

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
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


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 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 number  Week beginning Topics
 1 25/6 

Induction, Numeracy test,
Revision of number skills:   Order of operations, Directed nos.,

 2 2/7 No classes
 3 9/7

Revision of number skills: Fractions & decimals
Rounding off and significant figures
 

 4 16/7

Ratio and proportion
Percentage

 5 23/7 

Percentage cont.
Indices
TEST 1

 6 30/7

Indices cont.
Scientific notation

 7  6/8 

 Metric conversions
TEST 2.

 8 13/8

Perimeter calculations
Area calculations

9.

20/8
 

Volume calculations
TEST 3.

10.27/8Revision
Mid-semester Test

 

 Week number         Week beginning Topics

          

11.                          

                                 

 3/9                                

Theorem of Pythagoras
Trigonometric ratios                                                                                                        

12.

10/9

Trigonometric ratios cont.
Revision
                                                                                                                                            

 13.

 17/9Simplifying algebraic expressions
Solving linear equations
TEST 4.

 

14. 

24/9Mid-semester break

           

15. 

1/10

Solving word problems involving linear equations
Formulae

 

16. 

8/10


Statistics 1. - Univariate data
TEST 5.
 

 

17. 

 15/10

Linear relations
STATISTICS ASSIGNMENT

 

18. 

22/10


Statistics 2 - Bivariate data
 

 19. 

29/10

 
Statistics 2  cont.

Due date for submission of Statistics Assignment: Thursday November 8th
 

 

20.

 

5/11

 

Revision 
FINAL EXAMINATION 


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)
MId-semester Test (graded)
Final Examination (graded)


Assessment Tasks

  • 5 Class Tests (best 4 results of 5 tests) 20% 
  • Statistics assignment 15%
  • Mid-semester Test 25%
  • Final Examination  40% 


Assessment Matrix

  Test 1.Test 2.Test 3.Mid-semester TestTest 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 right-angled 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 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

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 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

 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 0.5 hour = 9 hours

Work outside class on Exercises   9 hours 

Assignment  work   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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