HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION
MATHEMATICS
Compulsory Part
SCHOOL-BASED ASSESSMENT
Sample Assessment Task
How long is your shoelace?
Marking Guidelines
教育局 課程發展處 數學教育組
Mathematics Education Section, Curriculum Development Institute The Education Bureau of the HKSAR
Assessment Scale
The assessment scale for tasks on Problem-solving is shown in the following table.
Level of
performance Marks Mathematical Knowledge and Problem-solving Skills Marks Mathematical Communication Skills
Very good 13 – 16
The student demonstrates a complete understanding of the underlying mathematical knowledge and problem- solving skills which are relevant to the task, and is consistently competent and accurate in applying them in handling the task. Typically, the student is able to formulate a correct strategy, carry out the strategy and demonstrate a complete understanding of the significance and possible limitations of the results obtained.
4
The student communicates ideas in a clear, well organised and logically true manner through coherent written/verbal accounts, using appropriate and correct mathematical presentation to express, interpret and critically review the results obtained.
Good 9 – 12
The student demonstrates a substantial understanding of the underlying mathematical knowledge and problem-solving skills which are relevant to the task, and is generally competent and accurate in applying them in handling the task. Typically, the student is able to formulate a correct strategy and attempts to carry out the strategy for completing the task.
3
The student is able to communicate ideas properly through written/verbal accounts, using appropriate forms of mathematical presentation such as mathematical formulae or geometric facts.
Fair 5 – 8
The student demonstrates a basic understanding of the underlying mathematical knowledge and problem- solving skills which are relevant to the task, and is occasionally competent and accurate in applying them in handling the task. Typically, the student has a basic understanding of the task and is able to formulate a correct strategy for solving the task.
2
The student is able to communicate basic ideas with limited success in using appropriate mathematical terms and terminology.
Weak 1 – 4
The student demonstrates a limited understanding of the underlying mathematical knowledge and problem- solving skills which are relevant to the task, and is rarely competent and accurate in applying them in handling the task. Typically, the student has a bare understanding of the task and can only attempt to complete the simplest part of the task.
1
The student attempts to communicate ideas using some basic forms of mathematical presentation such as symbols, notations, diagrams, tables, graphs etc., but has little success in doing so.
The full mark of a SBA task on Problem-solving submitted should be scaled to 20 marks, of which 16 marks are awarded for the mathematical knowledge and problem-solving skills while 4 marks are awarded for the mathematical communication skills.
Teachers should base on the above assessment scale to design SBA tasks for assessing students with different abilities and to develop the marking guidelines.
Shoelace Marking Guidelines (E) 2
Marking Guidelines
Solution Performance
Part A
1. Two different lacing methods are given below as an example.
2. (a) 4! = 24 (b) 6! / 2 = 360
Shoelace Marking Guidelines (E)
Evidence:
Methods for lacing
Weak: Not able to give feasible lacing method
Fair: Able to provide one feasible lacing method
Good: Able to give 2 different and feasible lacing methods
Evidence:
The solution
Weak: Wrong working and answers
Fair: Correct working for one part
Good: Correct working and answer for one part
Very good: Correct working and answers for both parts
Marking Guidelines
Solution Performance
Part B
1. Shoelace length for Criss-cross Lacing:
=w+2l+10
√
w2+d2Shoelace length for Straight Lacing:
=2d+5w+2l+4
√
w2+(2d)2¿2d+5 w+2l+4
√
w2+4d2Shoelace length for Diagonal Straight Lacing:
=5w +2l+5
√
w2+d2+√
w2+(5d)2¿5w+2l+5
√
w2+d2+√
w2+25d22. For w = 5 cm , d = 1 cm and l = 3 cm , the shoelace length for (i) Criss-cross Lacing is approximately 62.0 cm
(ii) Straight Lacing is approximately 54.5 cm
(iii) Diagonal Straight Lacing is approximately 63.6 cm
Hence, the Diagonal Straight Lacing requires the longest shoelace.
Part C
1. Two examples of the feasible lacing methods are given below:
Cross Lacing Lattice Lacing
2. Shoelace length for Cross Lacing:
=w+2l+10
√
w2+d2Shoelace length for Lattice Lacing:
=4d+w +2l+6
√
w2+(3 d)2¿4 d+w+2l+6
√
w2+9d2Shoelace Marking Guidelines (E)
Evidence:
The solutions
Weak: Wrong working and answers
Fair: Only one answer in (1) and the corresponding working are correct
Good: Only two answers in (1) and the corresponding working are correct
Very good: All answers and working in (1) and (2) are correct
Evidence:
1. The method suggested 2. The shoelace length
Weak: The method suggested is not feasible
Fair: The method suggested is partly feasible
Good: The method suggested is feasible
Very good: The method suggested is feasible and the length of shoelace is correctly calculated
