Hong Kong Diploma of Secondary Education Examination
MATHEMATICS
Compulsory Part
SCHOOL-BASED ASSESSMENT
Sample Assessment Task
Transformation and Tessellation
Marking Guidelines
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保 留 版 權 2009
Hong Kong Examinations and Assessment Authority
All Rights Reserved 2009
1
Draft as of September 2009
Assessment Scale
The assessment scale for tasks on Problem-solving is shown in the following table.
Level of
performance
Very good
Good
Fair
Weak
•
Marks
Mathematical Knowledge and Problemsolving Skills
13–16
The student demonstrates a complete
understanding
of
the
underlying
mathematical knowledge and problemsolving 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.
9 – 12
The student demonstrates a substantial
understanding
of
the
underlying
mathematical knowledge and problemsolving 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.
5–8
The student demonstrates a basic
understanding
of
the
underlying
mathematical knowledge and problemsolving 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.
1–4
The student demonstrates a limited
understanding
of
the
underlying
mathematical knowledge and problemsolving 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.
Marks
4
3
2
1
Mathematical Communication
Skills
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.
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.
The student is able to
communicate basic ideas with
limited success in using
appropriate mathematical terms
and terminology.
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 and the marking guidelines for
assessing students with different abilities.
Transformation and Tessellation (E)
2
Draft as of September 2009
Marking Guidelines
Solution
Performance
Part A
Evidence: Parallelogram/ equal
sides/ size of ∠ A
(a)
D
C
Weak:
Not a parallelogram
Fair:
A parallelogram with
unequal sides
Good:
A rhombus with each
side 4 cm ± 0.1 cm
A
B
Very good:
A rhombus with
each side 4 cm ± 0.1 cm
and ∠ A = 60° ± 1°
(b)
Evidence: Anticlockwise/
orientation (of the vertices)/
preservation (of the shape)/
rotational angle
C
B
Weak:
Wrong orientation
Fair:
Correct orientation
with incorrect rotational angle
Good:
Correct orientation
and correct rotational angle with
the shape/size slightly altered
D
Very good:
Correct
orientation, correct rotational
angle and preserve the shape
and size
A
Transformation and Tessellation (E)
3
Draft as of September 2009
Marking Guidelines
Solution
Performance
(c)
Evidence: Gaps/ overlaps/
congruent figures
Weak:
With gaps/overlaps
and non-congruent figures
Fair:
With gaps/overlaps
and congruent figures
Good:
Without gaps and
overlaps, tessellate with 2
congruent rhombuses only
Very good:
Without gaps
and overlaps, tessellate with
more than 2 congruent
rhombuses
Part B
(a)
Evidence: rectangle/ semi-circle/
translation
Weak:
D
C
A rectangle only
Fair:
Correct positions of the
semi-circles with correct sizes
Good:
The semi-circles are
translated
Very good:
The semi-circles
are correctly translated
A
E
Transformation and Tessellation (E)
F
B
4
Draft as of September 2009
Marking Guidelines
Solution
Performance
(b)
Evidence: Gaps/ overlaps/
congruent figures
Weak:
With gaps/overlaps
and non-congruent figures
Fair:
With gaps/overlaps
and congruent figures
Good:
Without gaps and
overlaps, tessellate with 2
congruent figures only
Very good:
Without gaps
and overlaps, tessellate with
more than 2 congruent figures
Part C
Evidence: Semi-circle AEF/
Δ BFG / semi-circle BKC/
(a)
reflection/ rotation
M
A
Weak:
Correct construction
of the semi-circle AEF
D
E
Fair:
Correct construction
of the right angled Δ BFG or
the reflection of the arc BHC
F
Good:
Complete the rotation
of semi-circle AEF and
Δ BFG
G
Very good:
Complete the
rotations and the black eye with
appropriate proportion
H
C
B
K
Transformation and Tessellation (E)
5
Draft as of September 2009
Marking Guidelines
Solution
Performance
(b)
Evidence: Gaps/ overlaps/
congruent figures
Weak:
With gaps/overlaps
and non-congruent figures
Fair:
With gaps/overlaps
and congruent figures
Good:
Without gaps and
overlaps, tessellate with 2
congruent figures only
Very good:
Without gaps
and overlaps, tessellate with
more than 2 congruent figures
Part D
(a)
Instructions of drawing a circular arc and a line segment
Instructions of two different transformations
Evidence: Description of the
instructions/ Mathematical
language used/ Geometric
transformations/ Geometric
constructions
Weak:
Instructions that
could not be able to produce the
drawing
Fair:
Mathematical
language/geometric techniques
are used in the description of
the instructions
Good:
Transformations are
clear and complete
Very good:
Majority of the
instructions correct and
involves the use of correct
mathematical
language/geometric techniques
Transformation and Tessellation (E)
6
Draft as of September 2009
Marking Guidelines
Solution
(b)
Performance
Drawing a circular arc and a line segment
Using two different transformations
Evidence: Line segment/
circular arc/ transformations
Weak:
Two correct
constructions according to
his/her instructions
Fair:
Complete/correct
diagram according to his/her
instructions
Good:
The construction of
the diagram includes all the
requirements and most likely
the diagram can tessellate a
plane
Very good:
The
constructions are clear and
correct with construction lines.
The completed diagram should
look like an animal aesthetically
(c)
Evidence: Gaps/ overlaps/
congruent figures
Correct tessellation of 2 diagrams
Correct drawing of tessellation
Weak:
With gaps/overlaps
and non-congruent figures
Fair:
With gaps/overlaps
and congruent figures
Good:
Without gaps and
overlaps, tessellate with 2
congruent figures only
Very good:
Without gaps
and overlaps, tessellate with
more than 2 congruent figures
Transformation and Tessellation (E)
7