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

Part B: Course Detail

Teaching Period: Term2 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

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

  • class discussion
  • work sheets
  • group activities

 

 

 

 

 


Teaching Schedule

 Week number   Week beginning  Topics
 1  11/7
 Induction, Numeracy test,
Bodmas, Directed nos.,
 2  18/7
 Significant figures, rounding off
Scientific notation
 3  25/7

Fractions & decimals

Test 1

 4  1/8

 Indices
Indices cont. 
 5  8/8

 Ratio & proportion
Percentage

 6  15/8

 Metric conversions

Test 2.
 7  
22/8

Area

Surface area
Volume

 8  29/8

Perimeter

Perimeter cont. 
 9

 5/9
 

Revision

Test 3

Exam 

 

 Week number                   Week beginning  Topics

          

10                                                

                                            

                        12/9                                                  

Trigonometric ratios

Theorem of Pythagoras                                                                                                                                                                                                                                      

         

11

 

                           19/9

Trigonometric ratios cont. 

Revision

 

 

                           26/9  Mid - semester break

          

12

 

                           3/10

Simplifying algebraic expressions

Test 4./ Solving Linear equations

           

13

 

                           10/10

Solving word problems

Formulae

 

14

 

                           17/10

Statistics 1. - Univariate data

Test 5. / Statistics 1. cont.

 

15

 

                            24/10

Linear relations

Linear relations cont.

 

16

 

                           31/10

Statistics 2 - Bivariate data

Test 6. / Statistics 2 cont.

 

17

 

                             7/11

 Revision

Final exam


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

  • 6 Class Tests 50% 
  • End of term 1 Exam  25%
  • End of term 2 Final exam  25% 


Assessment Matrix

    Test 1. Test 2. Test 3. Exam Test 4. Test  5. Test  6. Final  Exam

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

Classroom lessons 18 x 4 hours = 72 hours

Tutorials       18 x 1 hour = 18 hours

Work on Group Activities 10 hours

Revision and preparation for worksheets 10 hours

TOTAL 110 hours

Course Overview: Access Course Overview