Transcript 投影片 1 - HKEAA

New Senior Secondary
Mathematics Curriculum
Sharing of SBA Task Exemplars
(Draft)
HKEAA
September 2006
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Resources for Setting
Assessment Tasks (1)
Exemplars from
HKEAA & CDI
2008
15 tasks
2009
15 tasks
2011
10 tasks
2013
10 tasks
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NSS Math Curriculum
Sharing of SBA Task Exemplars
• First Exemplar:
Structures
• Second Exemplar:
Sweets in boxes
• Third Exemplar:
Performance of Broadband Internet Service
Providers
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First Exemplar: Structures
Part A
John uses some square tiles to pave the
walkway in his garden.
1. He uses six white tiles to form a 2 x 3
rectangle.
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2. He adds more and more tiles to the
original six tiles, forming the following
three patterns.
3. Students are required to count the number
of tiles in these patterns and investigate
the number of tiles in the nth pattern.
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Part B
Peter uses some cubes to make 3-D models.
1. He uses six cubes to form a 2 x 3 x 1
rectangular block.
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2. He adds more and more cubes to the
original six cubes, forming the following
three models.
3. Students are required to count the number
of cubes in these models and investigate
the number of cubes in the nth model.
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Teacher Guidelines
1. This task requires students to
a. observe number patterns in some structures;
b. make a conjecture through generalization;
c. test / justify the conjectures.
2. It is anticipated that in general, students can
complete the task in 2 hours. However, teachers
can exercise their professional judgment to adjust
the time allowed to cater for the needs of their
students.
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3. If necessary, teachers may give a brief description
of the task at the beginning, e.g. models made
with multilink cubes may be useful for
introducing Part B.
4. Teachers may feel free to modify the question to
cater for the needs of their students, e.g. using
other shapes or solids as the starting pattern.
5. Feedback should be provided to students after
marking the task, e.g. different approaches in
handling each part could be discussed.
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Second Exemplar:
Sweets in boxes
Parts A and B
• Investigate the existence of integral
solutions of some simple linear equations,
such as
2x+y=7
 2 x + 3 y = 13
 x + 2 y = 12
 2 x + 4 y = 26
3x+6y=5
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Parts C and D
• Donald broke open all large and small
packets and poured out all the sweets inside.
Students are required to find the numbers of
sweets originally contained in the packets.
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Part E
• Students, being managers of logistic
companies, are required to pack 108160
chocolates into 192 large size boxes and 80
small size boxes, subject to some extra
requirements.
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Part F
• Given that the linear equation
ax+by=c
has infinitely many integral solutions.
Students are required to investigate some
relations among a, b and c .
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Annex 1:
Diophantine Equations
• Diophantine equations are equations with two or
more variables whose values are restricted to
integers.
• E.g. x + y = 4 is a linear Diophantine equation
which has infinitely many integral solutions, such
as (-2,6), (-1,5), (0,4), (1,3), (2,2), …
• If x and y are restricted to positive integers only,
then the equation will only have three solutions,
namely (1,3), (2,2) and (3,1).
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Teacher Guidelines
1. This task requires students to
a. solve linear equations in two variables;
b. understand some basic knowledge about
Diophantine equations, choose a suitable
strategy to handle daily life problems, carry
out the plan and evaluate the solution
obtained.
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2. Annex 1 provides a simple introduction to
Diophantine equations and some techniques
in determining whether a Diophantine
equation has infinitely many integral
solutions or not. Teachers may present it to
students to study before the assessment
activity (either at home or in class), or
describe it briefly at the beginning of the
assessment activity.
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Third Exemplar: Broadband ISPs
Part A
• The downloading times of the same file
through ISP X and ISP Y are given. Students
are required to represent the given data by
suitable statistical measures and comment
which ISP performs better.
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Part B
• A researcher records the downloading times
of files of different sizes. Students are
required to explain which ISPs performs
better, state some limitations of the research
and suggest some possible improvements.
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Teacher Guidelines
1. This task requires students to
a. select and use appropriate statistics measures
to analyse data;
b. select and use appropriate charts to analyse
data;
c. interpret results;
d. point out limitations and suggest
improvements.
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2. If necessary, teachers may give a brief
description of the task at the beginning, e.g.
teachers may consider to explain technical terms
involving internet services such as ISP, file size
(MB) and downloading speed (Mbps) etc.
3. Teachers may feel free to modify the question to
cater for the needs of their students. For
example, students using different ISPs can be
grouped in pairs. Instead of providing the data
set, teachers may ask students to collect data for
this task at home and tabulate them as in the
tables given in Part A and Part B.
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Thank you !!
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