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1
THE UNITED REPUBLIC OF TANZANIA
MINISTRY OF EDUCATION AND VOCATIONAL TRAINING
BASIC MATHEMATICS SYLLABUS FOR ORDINARY SECONDARY EDUCATION
FORM I - IV
ii
TABLE OF CONTENTS
Introduction……………………...................................................................…….iv Aims and Objectives of Education in Tanzania…..............................................…iv Aims and Objectives of Secondary Education in Tanzania…................................v General Competences……………………………....................................……….v General Objectives …………………..........................................………………..vi Structure and Organization of the syllabus…......................................................…vi Form One………….......................................................................................…….1 Form Two……………….......................................................................................59 Form Three…………………….............................…………………….….……..97
Form Four……………..................................................................................……137
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© Ministry of Education and Vocational Training, 2005First Reprint 2010Second Reprint 2012Third Reprint 2017
ISBN – 978 – 9976 - 61 – 304 – 9
Designed and prepared by:Tanzania Institute of Education, P.O. Box 35094,Dar es Salaam,TANZANIA.Tel 022-2773005/2774420/2780891Fax No. 255-51-2774420E-mail: director. [email protected]
All rights reserved. No part of this publication may be reproduced, reported, stored in retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the permission of the copyright owner.
iv
1.0 Introduction
This Basic Mathematics syllabus is a revised version which has been prepared to replace that of 1996 which has phased out. The revision process focused on change in paradigm from that of content based to competence based curriculum. Moreover, the revision was inevitable due to the fact that the 1996 syllabus did not sufficiently consider the current social, cultural, global, technological, subject biases and cross cutting issues taking place worldwide but particularly in Tanzanian Society.In addition, the revision has also taken into consideration on the requirements for the Secondary Education Development Plan (SEDP). This syllabus has been introduced for implementation from January 2005.
2.0 Aims and Objectives of Education in TanzaniaThe general aims and objectives of education in Tanzania are to:(a) Guide and promote the development and improvement of the personalities of the
citizens of Tanzania, their human resources and effective utilization of those resources in bringing about individual and national development.
(b) Promote the acquisition and appreciation of the culture, customs and traditions of the people of Tanzania.
(c) Promote the acquisition and appropriate use of literacy, social, scientific, vocational, technological, professional and other forms of knowledge, skills and attitudes for the development and improvement of the condition of man and society.
(d) Develop and promote self-confidence and an inquiring mind, and understanding and respect for human dignity and human rights and readiness to work hard for self-advancement and national development.
(e) Enable and expand the scope of acquisition, improvement and upgrading of mental, practical, productive and other skills needed to meet the changing needs of industry and the economy.
(f) Enable every citizen to understand the fundamentals of the National Constitution as well as the enshrined human and civic rights, obligations and responsibilities,
(g) Promote the love and respect for work, self and wage employment and improved performance in the production and service sectors.
(h) Inculcate principles of the national ethic and integrity, national and international cooperation, peace and justice through the study, understanding and adherence to the provisions of the national constitution and other international basic charter.
(i) Enable a rational use, management and conservation of the environment.
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3.0 Aims and Objectives of Secondary Education in Tanzania
In Tanzania, secondary education refers to post primary formal education offered to the learners who successfully completed seven years of primary education and have met the requisite entry qualifications.
The aims and objectives of secondary education are to:(a) Consolidate and broaden the scope of baseline ideas, knowledge, skills and attitudes
acquired and developed at the primary educational level.(b) Enhance the development and appreciation of national unity, identity and ethic,
personal integrity, respect for human rights, cultural and moral values, customs, traditions and civic responsibilities and obligations.
(c) Promote the development of competency in linguistic ability and effective use of communication skills in Kiswahili and in at least one foreign language.
(d) Provide opportunities for the acquisition of knowledge, skills, attitudes and understanding in prescribed or selected fields of study.
(e) Prepare students for tertiary and higher education, vocational, technical and professional training.
(f) Inculcate a sense and ability for self-study, self-confidence and self-advancement in new frontiers of science and technology, academic and occupational knowledge and skills.
(g) Prepare the student to join the world of work.
4.0 General Competences
By the end of the four years course, the student should have the ability to:(a) Think critically and logically in interpreting and solving problems.(b) Use mathematical languages in explaining and clarifying mathematical ideas.(c) Apply mathematical knowledge and techniques in other fields.
5.0 General Objectives
By the end of the four years course, the student should be able to:(a) Promote the development and application of mathematical skills in solving practical
problems in daily life.(b) Apply mathematical concepts in interpreting situations at local and global levels.(c) Develop a foundation of mathematical knowledge, techniques and life skills for
studying mathematics and related subjects.
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6.0 Structure and Organization of the SyllabusThis Basic Mathematics syllabus has a slightly different structure compared to that of 1997. The following items were added for improvement: (a) General competences for the whole course.(b) Competences for each class, i.e Form One to Form Four. (c) Suggested areas for assessment.(d) Number of periods per sub-topic.(e) Column for sub-topics.
The structure of the syllabus is as follows:6.1 Class Level CompetencesCompetences are skills, knowledge and attitudes attained by the learners after the learning process. Competences have been stated for each class/level of Basic Mathematics course. The class level objectives are derived from the class level competences.
6.2 Class Level ObjectivesFor each competence intended to be achieved, one or more objectives haves been stated in order to achieve it. The general objectives for Form One to Form Four are stated in general terms to indicate the scope of content to be covered within each level. 6.3 TopicsThe topics have been derived from the class level competences and objectives. Some topics in the 1997 Basic Mathematics syllabus have been retained. Also some content from Cross-Cutting Issues (CCI), and the phased out bias subjects have been integrated. Topics have been arranged to attain a logical order starting from the simple to the most difficult ones. Both block and spiral arrangements of topics have been adopted.
6.4 Sub-TopicTopics have been divided into sub-topics. The subtopics have been arranged to attain a logical order.
6.5 Specific ObjectivesEach sub-topic has one or more specific objectives. These specific objectives are the expected outcomes in classroom instruction. They also reflect the process to attain competences within the cognitive, affective and psychomotor domains.
6.6 Teaching and Learning StrategiesThe Column of teaching and learning strategies indicates what the teacher and students are expected to be doing in the process of teaching and learning. Students are encouraged to work in small groups for maximum participatory and cooperative learning. The teacher shall assume the role of a facilitator to promote, guide and help students learning activities. The whole teaching and learning process should be a participatory and interactive, where
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the students learns by doing a series of logical activities.These suggested teaching and learning (T/L) strategies are not exhaustive. The teacher and students may use other learner centered strategy which suit the T/L environment.
6.7 Teaching and Learning ResourcesIn the teaching of Basic Mathematics a great variety of teaching – learning resources will be needed in quality and quantity. In case the commercial varieties of T/L resources are not available, the teacher should work with students to collect or improvise alternative resources available in the environment.
6.8 AssessmentFor every specific instructional objective, there is/are some suggested question(s) or areas for assessment. Formative and summative assessments should be geared towards mastery of the competences and skills developed within the course
6.9 Number of PeriodsNumber of periods is an estimated time to be used to teach a given topic/sub- topic. Each period is 40 minutes. The numbers of periods have been taken into account the time needed to adequately cover the sub-topic. Some topics need more time than others depending on the nature and weight of the topic. The teacher is advised to make maximum use of time allocated in classroom instruction. Lost instructional time should always be compensated for.
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DECLARATION
Ordinary level secondary education is a four years course which has been designed to prepare students for the Advanced Level or other tertiary education. A student will be recognized as a form four graduate when he/she successfully completes and pass secondary education examinations conducted by the National Examination Council of Tanzania.
This document is hereby declared as the Syllabus of Basic Mathematics for ordinary level secondary education course.
Commissioner for EducationMinistry of Education and Vocational Training
1
FORM ONE
CLASS LEVEL COMPETENCESThe student should have the ability to:
1. Distinguish different types of numbers.2. Estimate and compute numbers accurately .3. Convert units and fractions.4. Handle mathematical instruments in constructing and drawing geometrical figures.5. Solve problems on geometry, ratio, profit and loss, and simple interest.6. Graph and interpret linear equations.
CLASS LEVEL OBJECTIVESBy the end of Form One course the student should be able to:
1. Perform computations on numbers.2. Use approximations in solving simple problems.3. Convert and do computations on basic units.4. Construct and draw geometrical figures.5. Find the angles in geometrical figures.6. Solve linear equations in one or two unknowns.7. Find perimeters and areas of simple geometrical figures.8. Compute ratios, profit and loss and simple interest.9. Draw graphs of linear equations.10. Solve linear inequalities in one unknown .
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1.0
NU
MB
ERS
(I)
1.1
Bas
e te
n
n
umer
atio
nTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Iden
tify
the
plac
e va
lue
in e
ach
digi
t in
base
ten
num
erat
ion.
i) T
he te
ache
r to
guid
e st
uden
ts to
iden
tify
base
ten
num
erat
ion
with
the
ten
digi
ts.
ii) S
tude
nts i
n pa
irs to
w
rite
the
plac
e va
lue
of e
ach
digi
t in
any
give
n nu
mbe
r
i) N
umbe
r car
dsii)
Num
ber c
harts
iii
) Aba
cus
Is th
e st
uden
t ab
le to
iden
tify
the
plac
e va
lue
of a
num
ber
writ
ten
in b
ase
ten?
8
(b)
Rea
d nu
mbe
rs
in b
ase
ten
num
erat
ion
up
to o
ne b
illio
n
i) T
he te
ache
r to
guid
e st
uden
ts to
read
or
ally
num
bers
up
to
one
billi
onii)
Stu
dent
s in
grou
ps
to re
ad n
umbe
rs
give
n in
wor
ds a
nd
num
eral
s
i) N
umbe
r car
ds
ii) N
umbe
r cha
rts
iii) A
bacu
s
Is th
e st
uden
t ab
le to
read
nu
mbe
rs in
bas
e te
n nu
mer
atio
n up
to o
ne
billi
on?
(c)
Writ
e nu
mbe
rs
in b
ase
ten
num
erat
ion
up
to o
ne b
illio
n.
i) T
he te
ache
r to
guid
e st
uden
ts to
writ
e nu
mbe
rs u
p to
one
bi
llion
in n
umer
als
ii) S
tude
nts i
n pa
irs to
pr
actic
e on
writ
ing
num
eral
of n
umbe
rs
up to
one
bill
ions
gi
ven
wor
ds a
nd v
ise
vers
a.
Num
ber c
ards
Is t
he st
uden
t ab
le to
writ
e nu
mbe
rs in
bas
e te
n nu
mer
atio
n up
to o
ne
billi
on?
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NU
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ER
O
F PE
RIO
DS
(d)
App
ly n
umbe
rs
in d
aily
life
i) Th
e tea
cher
to gu
ide
stude
nts to
disc
uss t
he
role
of nu
mbe
rs in
daily
lif
e.ii)
Stu
dent
s to
high
light
com
mon
ap
plic
atio
ns o
f nu
mbe
rs in
dai
ly
life.
i) Ab
acus
ii) N
umbe
r car
dsIs
the
stud
ent
able
to a
pply
nu
mbe
rs in
dai
ly
life?
1.2
Nat
ural
and
Who
le N
umbe
rsTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Dis
tingu
ish
betw
een
natu
ral
and
who
le
num
bers
.
i) Th
e tea
cher
to
dem
onstr
ate na
tural
and
whole
num
bers
using
the
num
ber li
ne,
ii) S
tude
nts t
o pe
rfor
m
a ro
le p
lay
on
num
bers
i) Th
e num
ber li
ne
ii) N
umbe
r car
dsiii
) Num
ber c
harts
iv)
Col
ored
cha
lk
Is th
e st
uden
t ab
le to
di
stin
guis
h be
twee
n na
tura
l an
d w
hole
nu
mbe
rs?
6
(b) I
dent
ify e
ven,
od
d an
d pr
ime
num
bers
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e di
ffere
nce
betw
een
even
, odd
an
d pr
ime
num
bers
.ii)
Stu
dent
s in
pairs
to
iden
tify
even
, odd
an
d pr
ime
num
bers
fr
om o
ther
num
bers
.
Num
ber c
harts
Is th
e st
uden
t ab
le to
iden
tify
even
, odd
and
pr
ime
num
bers
?
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NU
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O
F PE
RIO
DS
(c) S
how
eve
n,
odd
and
prim
e nu
mbe
rs o
n nu
mbe
r lin
e.
(i) T
he te
ache
r to
guid
e st
uden
ts to
show
ev
en, o
dd a
nd
prim
e nu
mbe
rs o
n th
e nu
mbe
r lin
e.(ii
) St
uden
ts
indi
vidu
ally
to
prac
tice
on th
e id
entifi
catio
n of
ev
en, o
dd a
nd
prim
e nu
mbe
rs
usin
g a
num
ber
line.
i) Nu
mbe
r line
ii) E
rato
sthe
nes
siev
e
Is th
e st
uden
t ab
le to
show
ev
en, o
dd a
nd
prim
e nu
mbe
rs
on n
umbe
r lin
e?
(d)
Find
fact
ors o
f a
give
n nu
mbe
ri)
St
uden
ts in
pai
rs to
lis
t all
fact
ors o
f gi
ven
num
bers
.ii)
St
uden
ts
indi
vidu
ally
to fi
nd
the
fact
ors o
f giv
en
num
bers
usi
ng
a fa
ctor
tree
or
repe
ated
div
isio
n
Fact
or tr
eeIs
the
stud
ent
able
to fi
nd fa
c-to
rs o
f a g
iven
nu
mbe
r?
8
(e)
Use
fact
ors t
o fin
d th
e gr
eate
st
com
mon
fact
or
(GC
F) o
f nu
mbe
rs o
f tw
o or
mor
e nu
mbe
rs
i) Th
e tea
cher
to gu
ide
stude
nts to
iden
tify
com
mon
facto
rs of
two
or m
ore n
umbe
rs.
i) F
acto
r tre
e ii)
Fac
tor c
hart
Is th
e st
uden
t ab
le to
use
fa
ctor
s to
find
GC
F?
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TE
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ESS
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NU
MB
ER
OF
PER
IOD
S
ii) T
he te
ache
r to
guid
e st
uden
ts to
di
scus
s how
to
find
the
grea
test
co
mm
on fa
ctor
of
two
or m
ore
num
bers
.iii
) Stu
dent
s in
pairs
to
find
GC
F of
two
or m
ore
num
bers
us
ing
a se
t fac
tor/
divi
sors
or p
rime
fact
ors.
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ST
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EG
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TE
AC
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RN
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ESO
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ESS
ME
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NU
MB
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OF
PER
IOD
S
(f)
Use
fact
ors
or m
ultip
les
to fi
nd th
e lo
wes
t com
mon
m
ultip
le (L
CM
)
i) T
he te
ache
r to
guid
e
stud
ents
to id
entif
y co
mm
on m
ultip
les
of tw
o or
mor
e nu
mbe
rs.
ii) T
he te
ache
r to
guid
e a
disc
ussi
on o
n ho
w
to fi
nd th
e lo
wes
t co
mm
on m
ultip
les
(LC
M) o
f tw
o or
m
ore
num
bers
.iii
) St
uden
ts in
gro
ups
to fi
nd t
he L
CM
of
num
bers
usi
ng
mul
tiple
s and
prim
e fa
ctor
s.
i) Fa
ctors
tree
ii) N
umbe
r cha
rtsIs
the
stud
ent
able
to u
se fa
ctor
s or
mul
tiple
s to
find
LCM
?
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1.3
Inte
gers
The
stud
ents
shou
ld
be a
ble
to:
(a)
Iden
tify
inte
gers
i) Th
e te
ache
r to
guid
e di
scus
sion
on
real
lif
e ex
ampl
es w
hich
po
rtray
the
conc
epts
of
pos
itive
and
ne
gativ
e nu
mbe
rs
such
as d
ebts
and
cr
edits
, abo
ve a
nd
belo
w se
a le
vel a
nd
tem
pera
ture
s abo
ve
and
belo
w z
ero.
ii) T
he te
ache
r to
dem
onst
rate
to th
e st
uden
ts h
ow to
re
pres
ent i
nteg
ers
on th
e nu
mbe
r lin
e.iii
) St
uden
ts
indi
vidu
ally
to
prac
tice
on th
e re
pres
enta
tion
of in
tege
rs o
n a
num
ber l
ine.
i) M
anila
pap
er
ii) M
arke
r pen
sIs
the
stud
ent a
ble
iden
tify
inte
gers
?12
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NU
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OF
PER
IOD
S
(b) A
dd in
tege
rs.
i) Th
e te
ache
r to
dem
onst
rate
on
the
use
of th
e nu
mbe
r lin
e to
per
form
ad
ditio
n of
inte
gers
ii)
Stud
ents
in g
roup
s to
per
form
add
ition
of
inte
gers
usi
ng a
nu
mbe
r lin
e
Aba
cus
Is th
e st
uden
t abl
e to
add
inte
gers
?
(c) S
ubtra
ct in
tege
rs.
i) Th
e te
ache
r to
guid
e st
uden
ts to
use
th
e nu
mbe
r lin
e to
pe
rfor
m su
btra
ctio
n of
inte
gers
ii) S
tude
nts i
n pa
irs to
pe
rfor
m su
btra
ctio
n of
inte
gers
usi
ng a
nu
mbe
r lin
e.
i)
Man
ila P
aper
ii)
A
bacu
siii
) Mar
ker p
ens
iv)
Num
ber l
ine
Is th
e st
uden
t abl
e to
subt
ract
inte
gers
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S
(d)
Mul
tiply
inte
gers
.i)
The
teac
her t
o gu
ide
stud
ents
to p
erfo
rm
the
mul
tiplic
atio
n of
in
tege
rs.
ii)
Stud
ents
in
divi
dual
ly to
m
ultip
ly in
tege
rs
usin
g a
num
ber l
ine.
i) M
anila
pap
er
ii) M
arke
r pen
s iii
) Num
ber l
ine
Is th
e st
uden
t ab
le to
mul
tiply
in
tege
rs?
(e)
Div
ide
inte
gers
.i)
The
teac
her t
o gu
ide
a di
scus
sion
on
the
divi
sion
of i
nteg
ers.
ii) S
tude
nts i
n pa
irs to
pe
rfor
m d
ivis
ion
of
inte
gers
.
i)
Man
ila p
aper
ii)
M
arke
r pen
sIs
the
stud
ent a
ble
to d
ivid
e in
tege
rs?
(f)
Perf
orm
mix
ed
oper
atio
ns o
n in
tege
rs
i) Th
e te
ache
r to
dem
onst
rate
the
mul
tiplic
atio
n an
d di
visi
on o
f int
eger
s in
volv
ing
diffe
rent
si
gns a
nd th
e sa
me
sign
s usi
ng
BO
DM
AS
rule
.
i)
Man
ila p
aper
ii)
A
bacu
siii
) M
arke
r pen
s
Is th
e st
uden
t abl
e to
per
form
mix
ed
oper
atio
ns o
n in
tege
rs?
10
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
OF
PER
IOD
S
ii) S
tude
nts
indi
vidu
ally
to
per
form
m
ultip
licat
ion
and
divi
sion
of i
nteg
ers
with
diff
eren
t sig
ns.
2.0
FRA
CTI
ON
S2.
1 P
rope
r, Im
prop
er
and
Mix
ed
Num
bers
The
stud
ent s
houl
d be
abl
e to
:(a
) D
escr
ibe
a fr
actio
n.
i) Th
e te
ache
r to
use
fam
iliar
exa
mpl
es
to d
emon
stra
te
frac
tions
ii)
The
stud
ents
to
dis
cuss
oth
er
fam
iliar
exa
mpl
es
of fr
actio
ns.
i) Or
ange
s ii)
Pap
eriii
) Car
ds
Is th
e st
uden
t ab
le to
des
crib
e a
frac
tion?
8
(b) D
istin
guis
h pr
oper
, im
prop
er
frac
tions
and
m
ixed
num
bers
.
i) T
each
er to
gui
de
stud
ents
to c
ompa
re
and
cont
rast
nu
mer
ator
and
de
nom
inat
or,
diffe
rent
frac
tions
, so
as t
o di
stin
guis
h be
twee
n pr
oper
and
im
prop
er fr
actio
ns.
ii) S
tude
nts i
n pa
irs
to g
ener
ate
mix
ed
num
bers
from
im
prop
er fr
actio
ns.
i) Kn
ifeii)
Pai
r of s
ciss
ors
iii) C
uise
naire
rods
iv) M
anila
pap
er
v) R
azor
bla
de
Is th
e st
uden
t abl
e to
dis
tingu
ish
betw
een
prop
er,
impr
oper
and
m
ixed
num
bers
?
11
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IC
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TIV
ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
OF
PER
IOD
S
2.2
Com
paris
on
of F
ract
ions
The
stud
ent s
houl
d be
abl
e to
:(a
) Si
mpl
ify a
fr
actio
n to
its
low
est t
erm
s
i) T
he te
ache
r to
dem
onst
rate
to
stud
ents
how
to
sim
plify
frac
tions
to
low
est t
erm
s.ii)
St
uden
ts
indi
vidu
ally
to
sim
plify
frac
tions
to
the
low
est t
erm
s.
Num
ber o
f lin
eIs
the
stud
ent
able
to si
mpl
ify
frac
tions
to lo
wes
t te
rms?
10
(b)
Iden
tify
equi
vale
nt
frac
tions
i) T
he te
ache
r to
dem
onst
rate
ho
w to
gen
erat
e eq
uiva
lent
frac
tions
by
mul
tiply
ing
or d
ivid
ing
the
num
erat
or a
nd
deno
min
ator
by
the
sam
e nu
mbe
rii)
Stu
dent
s in
pairs
to
dem
onst
rate
eq
uiva
lent
frac
tions
i) Cu
isena
ire ro
dsii)
Man
ila p
aper
iii) O
rang
es
Is th
e st
uden
t ab
le to
iden
tify
equi
vale
nt
frac
tions
?
12
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IC
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TIV
ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
OF
PER
IOD
S
(c)
Arr
ange
fr
actio
ns in
or
der o
f siz
e
i) T
he te
ache
r to
guid
e di
scus
sion
on
how
to
use
LC
M to
co
mpa
re d
iffer
ent
frac
tions
ii) S
tude
nts i
n gr
oups
to
use
LC
M to
co
mpa
re fr
actio
ns
Cui
sena
ire ro
dsIs
the
stud
ent
able
to a
rran
ge
frac
tions
in o
rder
of
size
?
2.3
Ope
ratio
ns
on F
ract
ions
The
stud
ent s
houl
d be
abl
e to
:(a
) A
dd fr
actio
ns
i) Th
e te
ache
r to
guid
e st
uden
ts to
per
form
ad
ditio
n of
frac
tions
us
ing
real
obj
ects
.ii)
Stu
dent
s in
grou
ps to
pe
rfor
m a
dditi
on o
f fr
actio
ns.
i)
Ora
nges
ii)
Man
ilaiii
) Mar
ker p
ens
Is th
e st
uden
t abl
e to
add
frac
tions
?12
13
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IC
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TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Subt
ract
frac
tions
i) T
he te
ache
r to
guid
e st
uden
ts to
per
form
su
btra
ctio
n of
fr
actio
ns u
sing
real
ob
ject
s.ii)
Stu
dent
s in
pairs
to
perf
orm
subt
ract
ion
of fr
actio
ns u
sing
re
al o
bjec
ts.
i) M
anila
pap
er
ii) M
arke
r pen
iii
) Rea
l obj
ects
Is th
e st
uden
t ab
le to
subt
ract
fr
actio
ns?
14
TOPI
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IC
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TIV
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AC
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G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
OF
PER
IOD
S
(c)
Mul
tiply
fr
actio
nsi)
The
teac
her t
o gu
ide
stud
ents
to c
ondu
ct
mul
tiplic
atio
n of
fr
actio
ns u
sing
ill
ustra
tion.
ii)
Stud
ents
in
grou
ps to
con
duct
m
ultip
licat
ion
of
frac
tions
usi
ng
illus
tratio
n
i)
Man
ila p
aper
ii)
Mar
ker p
ens
iii)
Illus
tratio
n
Is th
e st
uden
t ab
le to
mul
tiply
fr
actio
ns?
(d)
Div
ide
frac
tions
i) T
he te
ache
r to
dem
onst
rate
th
e di
visi
on o
f fr
actio
ns.
ii) S
tude
nts i
n gr
oups
to
per
form
div
isio
n of
frac
tions
usi
ng
real
obj
ects
i) M
anila
pap
er
ii) M
arke
r pen
iii
) Ora
nges
Is th
e st
uden
t ab
le to
div
ide
frac
tions
?
15
TOPI
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TIV
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(e)
Perf
orm
mix
ed
oper
atio
ns o
n fr
actio
ns
i) Th
e te
ache
r to
guid
e st
uden
ts to
solv
e m
ixed
ope
ratio
ns o
n fr
actio
ns.
ii)
Stud
ents
in p
airs
to
per
form
mix
ed
oper
atio
ns o
n fr
actio
ns
i)
Man
ila p
aper
ii)
M
arke
r pen
iii)
Ora
nges
Is th
e st
uden
t ab
le to
per
form
m
ixed
ope
ratio
ns
of fr
actio
ns?
(f)
Solv
e w
ord
prob
lem
s in
volv
ing
frac
tions
.
i) Th
e te
ache
r to
form
ulat
e pr
actic
al
prob
lem
s inv
olvi
ng
frac
tions
and
gui
de
stud
ents
in so
lvin
g th
em sy
stem
atic
ally
.ii)
St
uden
ts in
gro
ups
to tr
ansl
ate
wor
d pr
oble
ms i
nto
equa
tions
and
solv
e th
em sy
stem
atic
ally
Man
ila p
aper
Is th
e st
uden
t ab
le to
solv
e w
ord
prob
lem
s in
volv
ing/
fr
actio
ns?
16
TOPI
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TIV
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AC
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G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
3.0
DEC
IMA
LS A
ND
PE
RC
ENTA
GES
3.1
Dec
imal
sTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Expl
ain
the
conc
ept o
f de
cim
als.
i) Th
e te
ache
r to
guid
e st
uden
ts to
ex
plai
n th
e co
ncep
t of
dec
imal
s thr
ough
br
ains
torm
ing.
ii) T
he st
uden
ts
indi
vidu
ally
to
rela
te d
ecim
als
and
frac
tions
with
de
nom
inat
or e
qual
to
10
i)
Shill
ings
ii)
C
ents
Is th
e st
uden
t ab
le to
exp
lain
th
e co
ncep
t of
deci
mal
?
4
(b) C
onve
rt fr
actio
ns
to te
rmin
atin
g an
d re
peat
ing
deci
mal
s and
vi
ce v
ersa
i) Th
e te
ache
r to
dem
onst
rate
th
e co
nver
sion
of
frac
tions
to
term
inat
ing
and
repe
atin
g de
cim
als
and
vice
ver
saii)
Stu
dent
s in
pairs
to
dem
onst
rate
th
e co
nver
sion
of
frac
tions
to
term
inat
ing
and
repe
atin
g de
cim
als
and
vice
ver
sa
i) S
hilli
ngs
ii) C
ents
Is th
e st
uden
t ab
le to
con
vert
frac
tions
to
term
inat
ing
and
repe
atin
g de
cim
al a
nd v
ice
vers
a?
17
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AC
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AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
3.2
Ope
ratio
ns o
n D
ecim
als
The
stud
ent s
houl
d be
abl
e to
:(a
) A
dd d
ecim
als
ii)
Stud
ents
in g
roup
s to
solv
e pr
oble
ms
invo
lvin
g ad
ditio
n of
dec
imal
s.
i)
Shill
ings
ii)
Cen
tsIs
the
stud
ent
able
to a
dd
deci
mal
s?
12
(b)
Subt
ract
dec
i-m
als
i) Th
e te
ache
r to
dem
onst
rate
the
plot
ting
of th
e de
cim
als o
n th
e nu
mbe
r lin
e.ii)
St
uden
ts in
pai
rs to
pr
actic
e th
e pl
ottin
g of
dec
imal
s on
the
num
ber l
ine
iii) S
tude
nts
indi
vidu
ally
to
subt
ract
dec
imal
s
i)
Cen
tsii)
Sh
illin
gsIs
the
stud
ent
able
to su
btra
ct
deci
mal
s?
(c)
Mul
tiply
de
cim
als
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e m
ultip
licat
ion
of d
ecim
als
horiz
onta
lly a
nd
verti
cally
ii)
Stud
ents
in g
roup
s to
mul
tiply
dec
imal
s
i)
Cen
tsii)
Sh
illin
gsIs
the
stud
ent
able
to m
ultip
ly
deci
mal
s?
18
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TIV
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AC
HIN
G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
Div
ide
deci
mal
si)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
the
divi
sion
of
deci
mal
s.ii)
St
uden
ts
indi
vidu
ally
to
dem
onst
rate
the
divi
sion
of d
ecim
als
i)
Shill
ings
ii)
Cen
tsIs
the
stud
ent
able
to d
ivid
e de
cim
als?
(e)
Perf
orm
mix
ed
oper
atio
ns w
ith
deci
mal
s
i) Th
e te
ache
r to
dem
onst
rate
the
subt
ract
ion
of
deci
mal
s ver
tical
ly
and
horiz
onta
lly.
ii)
Stud
ents
in p
airs
to
per
form
mix
ed
oper
atio
ns w
ith
frac
tions
.
i)
Shill
ings
ii)
C
ents
Is th
e st
uden
t ab
le to
per
form
m
ixed
ope
ratio
ns
with
dec
imal
s?
19
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TIV
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(f)
Solv
e w
ord
prob
lem
s in
volv
ing
deci
mal
s
i) T
he te
ache
r to
form
ulat
e pr
actic
al
prob
lem
s inv
olvi
ng
frac
tions
and
gui
de
stud
ents
in so
lvin
g th
em sy
stem
atic
ally
.ii)
Stu
dent
s in
grou
ps
to fo
rmul
ate
equa
tions
from
gi
ven
wor
d pr
oble
ms a
nd so
lve
them
.
i)
Shill
ings
ii)
C
ents
Is th
e st
uden
t ab
le to
sol
ve
wor
d pr
oble
ms
invo
lvin
g de
cim
als?
3.3
Perc
enta
ges
The
stud
ent s
houl
d be
abl
e to
:(a
) Ex
pres
s a
quan
tity
as a
pe
rcen
tage
i) T
he te
ache
r to
disc
uss w
ith
stud
ents
how
to
expr
ess a
qua
ntity
as
a p
erce
ntag
eii)
The
teac
her t
o sh
ow
stud
ents
how
to
writ
e pe
rcen
tage
s us
ing
the
sym
bol
(%)
iii)
Stud
ents
in g
roup
s to
` con
vert
give
n qu
antit
ies i
nto
perc
enta
ges.
i)
Shill
ings
ii)
C
ents
Is th
e st
uden
t ab
le to
exp
ress
qu
antit
ies a
s pe
rcen
tage
s?
8
20
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AC
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Con
vert
a fr
actio
n in
to
perc
enta
ge a
nd
vice
ver
sa
i) Th
e te
ache
r to
dem
onst
rate
the
conv
ersi
on o
f fr
actio
ns in
to
perc
enta
ges b
y m
ultip
lyin
g by
100
.ii)
Th
e te
ache
r to
guid
e st
uden
ts to
di
scus
s how
to
conv
ert p
erce
ntag
es
into
frac
tions
by
divi
ding
by
100.
iii)
Stud
ents
in p
airs
to
do
exer
cise
s on
conv
ertin
g fr
actio
ns
into
per
cent
ages
and
vi
ce v
ersa
.
Cha
rtsIs
the
stud
ent
able
to c
onve
rt fr
actio
ns in
to
perc
enta
ges a
nd
perc
enta
ges i
nto
frac
tions
?
(c)
Con
vert
a de
cim
al in
to
perc
enta
ge a
nd
vice
ver
sa
i) Th
e te
ache
r to
guid
e a
disc
ussi
on w
ith
stud
ents
how
to
conv
ert d
ecim
als
into
per
cent
ages
.
Cha
rtsIs
the
stud
ent
able
to c
onve
rt a
deci
mal
into
pe
rcen
tage
and
pe
rcen
tage
into
de
cim
al?
21
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) T
he te
ache
r to
guid
e st
uden
ts to
con
vert
perc
enta
ges i
nto
deci
mal
s(d
) A
pply
pe
rcen
tage
s in
daily
life
i) T
he te
ache
r to
guid
e st
uden
ts to
di
scus
s how
to
solv
e da
ily li
fe
prob
lem
s inv
olvi
ng
perc
enta
ges.
ii) S
tude
nts i
ndiv
idua
lly
i)
Pie
char
tsii)
R
esea
rch
repo
rts
Is th
e st
uden
t ab
le to
app
ly
perc
enta
ges i
n da
ily li
fe?
4.0
UN
ITS
4.1
Uni
ts o
f Len
gth
The
stud
ent s
houl
d be
abl
e to
:(a
) C
onve
rt on
e un
it of
leng
th to
an
othe
r
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e m
etric
syst
em
of le
ngth
and
thei
r pr
efixe
sii)
Stu
dent
s in
grou
ps
to e
stim
ate
and
mea
sure
diff
eren
t le
ngth
s in
thei
r su
rrou
ndin
gs.
i) Ta
pe m
easu
re,
rule,
ii) T
read
le w
heel
, ch
arts
of u
nits
of
leng
th
Is th
e st
uden
ts
able
to c
onve
rt on
e un
it of
le
ngth
to
anot
her?
4
22
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AC
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G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Perf
orm
co
mpu
tatio
ns o
n m
etric
uni
ts o
f le
ngth
.
i) T
he te
ache
r to
dem
onst
rate
the
com
puta
tion
and
conv
ersi
on o
f one
un
it in
to th
e ot
her.
ii) S
tude
nts i
n gr
oups
to
do
com
puta
tions
on
met
ric u
nits
of
leng
th u
sing
the
basi
c op
erat
ions
.
i) M
eter
rule
r ii)
Cha
rtsIs
the
stud
ent
able
to c
ompu
te
calc
ulat
ions
in
volv
ing
met
ric
unit
of le
ngth
s?
4.2
Uni
ts o
f Mas
sTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Con
vert
one
unit
of m
ass t
o an
othe
r
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e m
etric
syst
em
of m
ass a
nd th
eir
prefi
xes.
ii) T
he te
ache
r to
dem
onst
rate
the
conv
ersi
on o
f one
un
it to
the
othe
riii
) St
uden
ts in
gro
ups
to e
stim
ate
and
mea
sure
diff
eren
t w
eigh
ts in
thei
r su
rrou
ndin
g.
Dis
cuss
con
vers
ion
from
one
uni
t to
anot
her
i)
Wei
ghin
g sc
ale
ii)
Sprin
g ba
lanc
e iii
) St
anda
rd
wei
ghts
cha
rts
of u
nits
of
mas
s
Is th
e st
uden
t ab
le to
con
vert
one
unit
of m
ass
to a
noth
er?
4
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Perf
orm
co
mpu
tatio
n on
m
etric
uni
ts o
f m
ass
i) Th
e te
ache
r to
dem
onst
rate
the
com
puta
tions
on
met
ric u
nit o
f mas
sii)
St
uden
ts in
gro
ups
to d
o co
mpu
tatio
ns
on m
etric
uni
ts o
f m
ass u
sing
bas
ic
oper
atio
ns
Is th
e st
uden
t ab
le to
com
pute
ca
lcul
atio
n in
volv
ing
met
ric
units
of m
ass.?
4.3
Uni
ts o
f tim
eTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Con
vert
one
unit
of ti
me
to
anot
her
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
read
and
w
rite
time
usin
g a
12 h
our c
lock
ii)
Th
e te
ache
r to
dem
onst
rate
the
conv
ersi
on o
f one
un
it of
tim
e to
an
othe
riii
) St
uden
ts in
gro
ups
to d
o ex
erci
ses o
n co
nver
sion
of o
ne
unit
of ti
me
to th
e ot
her
i)
Clo
ckii)
C
lock
face
s iii
) Tim
e ta
bles
Is th
e st
uden
t ab
le to
con
vert
one
unit
of ti
me
to a
noth
er?
4
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AC
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Rea
d an
d co
nver
t un
it tim
e of
12
hour
clo
ck to
24
hour
clo
ck a
nd
vice
ver
sa
i) Th
e te
ache
r to
guid
e st
uden
t to
disc
uss
how
to re
ad a
nd
writ
e tim
e us
ing
a 24
hou
r clo
ck.
ii)
The
teac
her t
o gu
ide
stud
ents
to
disc
uss o
n ho
w to
co
nver
t tim
e fr
om
12 h
our c
lock
to a
24
-hou
r clo
ck a
nd
vice
ver
sa.
iii)
The
stud
ents
in
gro
ups t
o do
ex
erci
ses o
n ho
w to
re
ad ti
me
usin
g th
e 24
hou
rs c
lock
. iv
) Th
e st
uden
ts in
gr
oups
to c
onve
rt tim
es o
f 12
hour
cl
ock
to 2
4hou
r cl
ock
i)
24 h
our c
lock
ii)
12 h
our c
lock
Is th
e st
uden
t ab
le to
con
vert
time
in 1
2 ho
urs
to 2
4 ho
urs
cloc
k?
25
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
4.4
Uni
ts o
f Cap
acity
Stud
ent s
houl
d be
ab
le to
:(a
) St
ate
the
stan
dard
uni
t of
mea
surin
g ca
paci
ty
i) Th
e te
ache
r to
desc
ribe
the
mea
ning
of
capa
city
and
rela
te
it w
ith v
olum
e of
qu
antit
ies.
ii)
The
teac
her t
o gu
ide
a di
scus
sion
on
how
a li
tre is
re
late
d to
oth
er
units
of v
olum
e.iii
) St
uden
ts
indi
vidu
ally
to st
ate
the
unit
of c
apac
ity
and
conv
ert a
litre
in
to o
ther
uni
ts o
f vo
lum
es a
nd v
ice
vers
a.
i) Li
tre c
onta
iner
ii)
Bot
tles
Is th
e st
uden
t ab
le to
stat
e th
e st
anda
rd u
nit
of m
easu
ring
capa
city
?
4
(b) U
se th
e lit
re in
da
ily li
fei)
The
teac
her t
o gu
ide
stud
ents
to
bra
inst
orm
on
vario
us d
aily
life
si
tuat
ions
in w
hich
a
litre
is a
pplie
d to
m
easu
re c
apac
ity.
ii) S
tude
nts i
n gr
oups
to
solv
e pr
oble
ms
rela
ted
to u
nit o
f ca
paci
ty.
Con
tain
ers w
ith
capa
citie
s in
litre
sIs
the
stud
ent
able
to m
easu
re
in li
tres?
26
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
5.0
APP
RO
XIM
ATIO
NS
5.1
Rou
ndin
g of
f N
umbe
rsTh
e st
uden
ts sh
ould
be
abl
e to
:(a
) R
ound
off
who
le
num
bers
to g
iven
pl
ace
valu
es
i) Th
e te
ache
r to
show
st
uden
ts h
ow to
ro
und
off
num
bers
w
hen
the
digi
t to
the
right
is le
ss
than
5 a
nd w
hen
the
digi
t to
the
right
is
gre
ater
than
or
equa
l to
5.ii)
St
uden
ts in
pai
rs
to ro
und
off w
hole
nu
mbe
rs w
hen
the
digi
t to
the
right
s is
less
than
5 a
nd
whe
n it
is g
reat
er
than
or e
qual
to 5
.
i) N
umbe
r ii)
Cha
rtsIs
the
stud
ent
able
to ro
und
off
num
bers
to g
iven
pla
ce
valu
e?
4
(b) R
ound
off
deci
mal
s to
a gi
ven
num
ber o
f de
cim
al p
lace
s
i) Th
e te
ache
r to
guid
e st
uden
ts to
roun
d of
f dec
imal
s to
the
give
n n
umbe
r of
dec
imal
pla
ces
whe
n th
e di
git t
o th
e rig
ht a
re <
5
and
whe
n th
e
digi
ts t
o th
e rig
ht
are
>5.
ii) S
tude
nts
in g
roup
s to
roun
d of
f num
ber
of d
ecim
al p
lace
s
i)
Num
ber
patte
rns
ii)
Man
ila p
aper
iii) M
arke
t pen
s
Is th
e st
uden
t ab
le to
roun
d of
f a
num
ber t
o a
give
n nu
mbe
r of
deci
mal
pla
ces?
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ING
ST
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IES
TE
AC
HIN
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AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
5.2
Sig
nific
ant
Figu
res
The
stud
ent s
houl
d be
abl
e to
writ
e a
num
ber t
o a
give
n nu
mbe
r of s
igni
fican
t fig
ures
i) T
he te
ache
r to
guid
e a
disc
ussi
on o
n ho
w to
w
rite
nu
mbe
rs
with
dec
imal
s int
o si
gnifi
cant
figu
res.
ii) S
tude
nts
in
pa
irs
to w
rite
dow
n th
e di
ffere
nce
betw
een
deci
mal
pla
ces a
nd
sign
ifica
nt fi
gure
s
i)
Man
ila p
aper
ii)
Mar
ker p
ens
Is th
e st
uden
t ab
le to
writ
e nu
mbe
rs to
a
give
n n
umbe
r of
sign
ifica
nt
figur
es?
2
5.3
App
roxi
mat
ions
in
Cal
cula
tions
The
stud
ent s
houl
d be
abl
e to
per
form
ap
prox
imat
ion
ofal
l num
bers
in
calc
ulat
ion.
i) Th
e te
ache
r to
guid
e st
uden
ts to
do
app
roxi
mat
ions
to
the
num
bers
in
calc
ulat
ions
usi
ng
know
ledg
e of
roun
d of
f num
bers
.ii)
St
uden
ts in
gro
ups
to b
rain
stor
m
on d
aily
life
ci
rcum
stan
ces
in w
hich
ap
prox
imat
ions
of
num
bers
are
ap
plie
d.
i)
Num
ber c
harts
ii) M
anila
pap
eriii
) Mar
ket p
ens
Is th
e st
uden
t ab
le to
per
form
ap
prox
imat
ion
of n
umbe
rs in
ca
lcul
atio
n?
2
28
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ING
ST
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EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
6.0
GEO
MET
RY6.
1 Po
ints
and
Lin
esTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Expl
ain
the
conc
ept o
f a
poin
t.
i) Th
e te
ache
r to
guid
e st
uden
ts to
di
scus
s the
con
cept
of
a p
oint
by
usin
g ex
ampl
esii)
St
uden
ts in
pai
rs
to li
st v
ario
us
situ
atio
ns in
whi
ch
the
conc
ept o
f a
poin
t is u
sed
Mat
hem
atic
al S
etIs
the
stud
ent
able
to e
xpla
in
the
conc
ept o
f a
poin
t?
6
(b) E
xten
d th
e co
ncep
t of a
po
int t
o dr
aw a
lin
e
i) T
he te
ache
r to
dem
onst
rate
how
the
idea
of p
oint
s can
be
ext
ende
d to
get
a
stra
ight
line
.ii)
Stu
dent
s ind
ivid
ually
to
pra
ctic
e dr
awin
g an
d la
belin
g st
raig
ht
line
Cha
lk B
oard
rule
rIs
the
stud
ent
able
to d
raw
a
line
conn
ectin
g gi
ven
poin
ts?
(c)
Dis
tingu
ish
betw
een
a lin
e, a
lin
e se
gmen
t and
a
ray.
i) T
he te
ache
r to
show
th
e st
uden
ts h
ow to
dr
aw a
line
, a li
ne
segm
ent a
nd a
ray.
ii) S
tude
nts i
n gr
oups
to
nam
e a
line,
line
se
gmen
t and
a ra
y
i)
Man
ila p
aper
ii)
Mar
ker p
enIs
the
stud
ent
able
to
dist
ingu
ish
betw
een
a lin
e, a
lin
e se
gmen
t and
a
ray?
29
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
6.2
Ang
les
The
stud
ent s
houl
dbe
abl
e to
:(a
) D
raw
ang
les
ii) T
he te
ache
r to
show
th
e st
uden
ts h
ow to
na
me
an a
ngle
.iii
) The
teac
her t
o gu
ide
stud
ents
to d
raw
an
d na
me
diffe
rent
ty
pes o
f ang
les.
For
ex
ampl
e st
raig
ht
line,
righ
t ang
le,
acut
e, o
btus
e, a
nd
refle
x.iv
) Stu
dent
s in
pairs
to
dra
w a
ngle
s of
diffe
rent
size
s and
na
me
them
.
i) M
anila
pap
erii)
Mat
hem
atic
al
inst
rum
ent
Is th
e st
uden
t ab
le to
dra
w a
gi
ven
angl
e?
6
(b)
Mea
sure
ang
les
of d
iffer
ent
size
s usi
ng a
pr
otra
ctor
i)
The
teac
her t
o gu
ide
stud
ents
to
obse
rve
a pr
otra
ctor
an
d m
easu
ring
angl
es u
sing
pr
otra
ctor
.ii)
St
uden
ts to
pra
ctic
e m
easu
ring
diffe
rent
an
gles
usi
ng a
pr
otra
ctor
iii)
The
teac
her t
o de
mon
stra
te h
ow
to d
raw
an
angl
e us
ing
a pr
otra
ctor
i) M
athe
mat
ical
in
stru
men
tsii)
C
halk
boar
d ru
ler
iii) P
rotra
ctor
Is th
e st
uden
t ab
le to
mea
sure
an
gles
of
diffe
rent
size
s usi
ng a
pr
otra
ctor
?
30
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ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
in g
roup
s to
pra
ctic
e ho
w to
m
easu
re d
iffer
ent
angl
es u
sing
a
prot
ract
or.
(c)
Dra
w a
ngle
s us
ing
a pr
otra
ctor
i) T
he te
ache
r to
dem
onst
rate
how
to
draw
an
angl
e us
ing
a pr
otra
ctor
ii) S
tude
nts i
n gr
oups
to
dis
cuss
how
to
dra
w d
iffer
ent
angl
es u
sing
a
prot
ract
or
Prot
ract
or ru
ler
Is th
e st
uden
t ab
le to
dra
w
angl
es u
sing
a
prot
ract
or?
6.3
Con
stru
ctio
nsTh
e st
uden
t sho
uld
be a
ble
to:
(a) C
onst
ruct
a
perp
endi
cula
r bi
sect
or to
a li
ne
segm
ent.
i) Th
e te
ache
r to
dem
onst
rate
to
the
stud
ents
how
to
con
stru
ct a
pe
rpen
dicu
lar
bise
ctor
to a
line
se
gmen
t by
usin
g co
mpa
sses
ii)
Stud
ents
in g
roup
s to
pra
ctic
e ho
w
to c
onst
ruct
pe
rpen
dicu
lar
bise
ctor
s to
a lin
e se
gmen
t by
usin
g co
mpa
sses
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
con
stru
ct
a pe
rpen
dicu
lar
bise
ctor
to a
line
se
gmen
t?
12
31
TOPI
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CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Con
stru
ct a
n an
gle
of 6
0o us
ing
a pa
ir of
co
mpa
sses
.
i) Th
e te
ache
r to
dem
onst
rate
to th
e st
uden
ts h
ow to
co
nstru
ct a
n an
gle
of 6
0o by
usin
g co
mpa
sses
.ii)
St
uden
ts
indi
vidu
ally
to
cons
truct
ang
les
of 6
0o by
usin
g co
mpa
sses
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
con
stru
ct
an a
ngle
of 6
0o us
ing
a pa
ir of
co
mpa
sses
?
(c)
Bis
ect a
giv
en
angl
ei)
The
teac
her t
o ill
ustra
te to
the
stud
ents
how
to
bise
ct a
n an
gle
by
usin
g co
mpa
sses
ii)
The
teac
her t
o gu
ide
stud
ents
to
cons
truct
ang
les o
f 45
o, 3
0o , 50
o ,120
o , 13
5o by
com
bini
ng
cons
truct
ions
(iii)
Stud
ents
in
divi
dual
ly to
bi
sect
ang
les u
sing
co
mpa
sses
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
bis
ect a
gi
ven
angl
e?
32
TOPI
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CS
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IC
OB
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TIV
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AC
HIN
G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
Cop
y a
give
n an
gle
by
cons
truct
ion
i) T
he te
ache
r to
show
th
e st
uden
ts h
ow to
co
py a
giv
en a
ngle
by
con
stru
ctio
nii)
Stu
dent
s in
divi
dual
ly to
cop
y di
ffere
nt a
ngle
s by
cons
truct
ion
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
cop
y a
give
n an
gle
by
cons
truct
ion?
(e)
Con
stru
ct
para
llel l
ines
i) T
he te
ache
r to
dem
onst
rate
to th
e st
uden
ts h
ow to
co
nstru
ct p
aral
lel
lines
ii) T
he st
uden
ts in
pa
irs to
con
stru
ct
diffe
rent
par
alle
l lin
es.
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
con
stru
ct
para
llel l
ines
us
ing
com
pass
es
and
set s
quar
es?
33
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(f)
Iden
tify
diffe
rent
ty
pes o
f ang
les
form
ed b
y pa
ralle
l lin
es a
nd
a tra
nsve
rsal
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
di
ffere
nt ty
pes
of a
ngle
s for
med
by
par
alle
l lin
es
and
a tra
nsve
rsal
, in
clud
ing
corr
espo
ndin
g an
gles
, alte
rnat
e in
terio
r ang
les,
alte
rnat
e ex
terio
r an
gles
, ver
tical
ly
oppo
site
an
gles
, co
mpl
emen
tary
an
gles
and
su
pple
men
tary
an
gles
.ii)
St
uden
ts in
pa
irs to
find
the
size
s of d
iffer
ent
angl
es fo
rmed
by
para
llel l
ines
and
a
trans
vers
al.
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
iden
tify
rela
tions
hips
of
angl
es fo
rmed
by
par
alle
l lin
es a
nd a
tra
nsve
rsal
?
34
TOPI
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IC
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
6.4
Poly
gons
and
R
egio
nsTh
e st
uden
t sho
uld
be a
ble
to:
(a) D
escr
ibe
a po
lygo
n an
d a
regi
on
i) T
he te
ache
r to
guid
e th
e st
uden
ts to
dra
w
a po
lygo
n an
d its
pr
oper
ties (
side
s, ve
rtice
s, an
gles
)ii)
The
stud
ents
in
grou
p to
dis
cuss
di
ffere
nt p
olyg
ons
and
its p
rope
rties
.
i) M
athe
mat
ical
in
stru
men
tsii)
R
uler
Is th
e st
uden
t ab
le to
des
crib
e a
poly
gon
and
a re
gion
?
6
(b)
Con
stru
ct
diffe
rent
type
s of
trian
gles
i) Th
e te
ache
r to
show
ho
w to
dra
w a
nd
nam
e tri
angl
es a
nd
guid
e st
uden
ts to
di
scus
s on
the
side
s, ve
rtice
s and
ang
les.
ii) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
di
ffere
nt ty
pes o
f tri
angl
es a
nd th
eir
prop
ertie
s
i) M
athe
mat
ical
in
stru
men
tsii)
Rul
er
Is th
e st
uden
t ab
le to
con
stru
ct
diffe
rent
type
sof
tria
ngle
s?
35
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IC
OB
JEC
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nts i
n gr
oups
to
dra
w tr
iang
les
o di
ffere
nt g
iven
si
zes a
nd d
escr
ibe
the
type
s of
trian
gles
and
thei
r co
rres
pond
ing
prop
ertie
s?
(c) C
onst
ruct
di
ffere
nt
quad
rilat
eral
s
i) Th
e te
ache
r to
guid
e st
uden
ts to
dr
aw tr
iang
les u
sing
m
athe
mat
ical
sets
(g
iven
thre
e si
des,
one
side
and
two
angl
es, t
wo
side
s an
d th
e in
clud
ed
angl
e)ii)
Stu
dent
s in
grou
ps to
pra
ctic
e dr
awin
g di
ffere
nt
type
s of t
riang
les
give
n di
ffere
nt
mea
sure
men
ts
i) M
athe
mat
ical
in
stru
men
tii)
Geo
boar
diii
) R
ubbe
r ban
ds
Is th
e st
uden
t ab
le to
con
stru
ct
diffe
rent
type
s of
quad
rilat
eral
s?
36
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii)
The
teac
her t
o gu
ide
stud
ents
to
dis
cuss
how
to
con
stru
ct
rect
angl
es,
para
llelo
gram
s, sq
uare
, rho
mbi
and
tra
pezi
um.
(iv)
Stud
ents
in p
airs
to
con
stru
ct
rect
angl
es,
para
llelo
gram
s, sq
uare
s, rh
ombi
an
d tra
pezi
a.6.
5 C
ircle
sTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Dra
w a
circ
le
i) Th
e te
ache
r to
guid
e st
uden
ts to
iden
tify
circ
ular
obj
ects
in
the
surr
ound
ing.
ii) T
he te
ache
r to
dem
onst
rate
how
to
draw
a c
ircle
usi
ng
com
pass
esiii
) T
he te
ache
r to
guid
e st
uden
ts to
dr
aw c
ircle
s of
diffe
rent
size
s usi
ng
com
pass
e
i) G
eom
etric
al
inst
rum
ents
ii)
Man
ila p
aper
iii)
Rop
esiv
) G
eobo
ard
v)
Circ
ular
ob
ject
s
Is th
e st
uden
t ab
le to
dra
wa
circ
le w
hen
give
n ra
dius
or
diam
eter
s?
4
37
TOPI
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IC
OB
JEC
TIV
ES
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AC
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G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Des
crib
e di
ffere
nt p
arts
of
a ci
rcle
i) Th
e te
ache
r to
guid
e st
uden
ts
to d
iscu
ss th
e fo
llow
ing
term
s:
cent
re, d
iam
eter
, ra
dius
, cho
rd,
circ
umfe
renc
e, a
rc,
segm
ent,
sect
or.
ii)
Stud
ents
in
divi
dual
ly to
dr
aw a
circ
le a
nd
labe
l its
par
ts.
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
des
crib
e pa
rts o
f a c
ircle
?
7.0
ALG
EBR
A7.
1 A
lgeb
raic
O
pera
tions
The
stud
ent s
houl
d be
abl
e to
:(a
) U
se sy
mbo
ls to
fo
rm a
lgeb
raic
ex
pres
sion
s.
i) Th
e te
ache
r to
use
daily
life
exa
mpl
es
to sh
ow h
ow le
tters
ar
e us
ed to
repr
esen
t ob
ject
s.ii)
Th
e te
ache
r to
dem
onst
rate
to th
e st
uden
ts h
ow le
tters
ca
n be
use
d to
re
pres
ent n
umbe
rsiii
) Th
e te
ache
r to
show
stud
ents
how
to
form
alg
ebra
ic
expr
essi
ons u
sing
le
tters
.
Col
oure
d ch
alk
Is th
e st
uden
t ab
le to
use
sy
mbo
ls to
fo
rm a
lgeb
raic
ex
pres
sion
s?
4
38
TOPI
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IC
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TIV
ES
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AC
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G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
in
pairs
to fo
rm
diffe
rent
alg
ebra
ic
expr
essi
ons.
(b) S
impl
ify
alge
brai
c ex
pres
sion
s
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
add
and
su
btra
ct li
ke te
rms.
ii) S
tude
nts i
n pa
irs
to a
dd a
nd su
btra
ct
give
n al
gebr
aic
expr
essi
ons.
iii) T
he te
ache
r to
guid
e st
uden
ts
to d
iscu
ss o
n th
e m
ultip
licat
ion
and
divi
sion
of l
ike
and
unlik
e te
rms.
iv) S
tude
nts
indi
vidu
ally
to
prac
tice
on th
e m
ultip
licat
ion
and
divi
sion
of
like
and
unlik
e te
rms o
f alg
ebra
ic
expr
essi
ons.
Man
ila C
ards
Is th
e st
uden
t ab
le to
sim
plify
al
gebr
aic
expr
essi
ons?
39
TOPI
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OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
v) T
he te
ache
r to
guid
e st
uden
ts to
di
scus
s how
to
sim
plify
exp
ress
ions
in
volv
ing
brac
ket
and
frac
tions
.vi
) Stu
dent
s in
pairs
to
use
the
rule
of
BO
DM
AS
to
sim
plify
alg
ebra
ic
invo
lvin
g br
acke
ts.
7.2
Equa
tions
in o
ne
unkn
own
The
stud
ents
shou
ld
be a
ble
to
(a
) So
lve
an
eq
uatio
n in
on
e un
know
n
i) Th
e tea
cher
to
dem
onstr
ate to
the
stude
nts ho
w to
solve
an
equa
tion i
n one
un
know
n.ii)
The
stud
ents
in
grou
ps to
solv
e eq
uatio
ns in
one
un
know
n.
i) B
eam
balan
ce
ii) c
olou
red
chal
kIs
the
stud
ent
able
to so
lve
an
equa
tion
in o
ne
unkn
own
?
40
TOPI
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B-T
OPI
CS
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IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
OF
PER
IOD
S
(b)
For
m a
nd so
lve
an e
quat
ion
from
w
ord
prob
lem
s
i) Th
e te
ache
r to
guid
e th
e st
uden
ts to
fo
rmul
ate
equa
tions
in
volv
ing
one
unkn
own
from
wor
d pr
oble
ms .
ii)
Stud
ents
in g
roup
s to
form
ulat
e eq
uatio
ns fr
om
wor
d pr
oble
ms
invo
lvin
g on
e un
know
n an
d so
lve
them
. 7.
3 Eq
uatio
ns in
Tw
o U
nkno
wns
The
stud
ent s
houl
d be
abl
e to
:(a
) Sol
ve
sim
ulta
neou
s lin
ear e
quat
ions
i)
The
teac
her t
o gu
ide
stud
ents
to
gene
rate
pos
sibl
e so
lutio
ns (o
rder
ed
pairs
) of a
n eq
uatio
n in
two
unkn
owns
.ii)
Th
e te
ache
r to
dem
onst
rate
how
to
solv
e lin
ear
sim
ulta
neou
s eq
uatio
ns b
y el
imin
atio
n m
etho
d.
i)
Man
ila p
aper
ii)
M
arke
r pen
iii) C
olou
red
chal
k iv
) W
ork
shee
ts
Is th
e st
uden
t ab
le to
so
lve
linea
r si
mul
tane
ous
equa
tions
by
elim
inat
ion
and
subs
titut
ion
met
hod?
8
41
TOPI
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CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii)
The
stud
ents
in
pairs
to so
lve
diffe
rent
line
ar
sim
ulta
neou
s eq
uatio
ns b
y el
imin
atio
n m
etho
d.iv
) T
he te
ache
r to
dem
onst
rate
how
to
solv
e lin
ear
sim
ulta
neou
s eq
uatio
ns b
y th
e su
bstit
utio
n m
etho
d.v)
Th
e st
uden
ts
indi
vidu
ally
to
solv
e di
ffere
nt
linea
r sim
ulta
neou
s eq
uatio
ns b
y th
e su
bstit
utio
n m
etho
d.(b
) For
m li
near
si
mul
tane
ous
equa
tions
fr
om p
ract
ical
si
tuat
ions
i) T
he te
ache
r to
guid
e st
uden
ts to
form
lin
ear s
imul
tane
ous
equa
tions
from
wor
d pr
oble
ms
ii) T
he st
uden
ts to
solv
e lin
ear s
imul
tane
ous
equa
tions
from
wor
d pr
oble
ms.
Wor
kshe
etIs
the
stud
ent
able
to
form
line
ar
sim
ulta
neou
s eq
uatio
nsfr
om p
ract
ical
si
tuat
ions
?
42
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c) S
olve
line
ar
ineq
ualit
ies
from
pra
ctic
al
situ
atio
ns
i) St
uden
ts to
be
guid
ed b
y th
e te
ache
r to
solv
e lin
ear i
nequ
aliti
es
invo
lvin
g w
ord
prob
lem
sii)
Stu
dent
s to
solv
e lin
ear i
nequ
aliti
es
form
ulat
ed fr
om
prac
tical
situ
atio
ns
Wor
kshe
et
Is th
e st
uden
t ab
le to
so
lve
linea
r in
equa
litie
s in
volv
ing
wor
d pr
oble
ms?
7.4
Ineq
ualit
ies
The
stud
ent s
houl
d be
abl
e to
:(a
) Sol
ve li
near
in
equa
litie
s in
one
unkn
own.
i) Th
e te
ache
r to
guid
e th
e st
uden
ts
on h
ow to
use
the
sym
bols
>,<
, ≤
in m
athe
mat
ical
st
atem
ents
ii)
The
teac
her t
o de
mon
stra
te to
the
stud
ents
how
to
solv
e in
equa
litie
s in
volv
ing
one
unkn
own
with
out
chan
ging
the
sign
.
Col
oure
d ch
alk
Is th
e st
uden
t ab
le to
so
lve
linea
r in
equa
litie
s in
one
unkn
own?
6
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
43
iii)
Stud
ents
to so
lve
linea
r ine
qual
ities
w
hich
do
not
invo
lve
chan
ging
of
the
sign
iv)
The
teac
her t
o de
mon
stra
te to
th
e st
uden
ts to
so
lve
ineq
ualit
ies
invo
lvin
g ch
angi
ng
the
sign
(b) F
orm
line
ar
ineq
ualit
ies
from
pra
ctic
al
situ
atio
ns
i) Th
e te
ache
r to
guid
e st
uden
ts
grou
p di
scus
sion
on
how
to fo
rm li
near
in
equa
litie
s fro
m
wor
d pr
oble
ms
ii)
Stud
ents
to
form
ulat
e lin
ear
ineq
ualit
ies f
rom
pr
actic
al si
tuat
ions
i) M
anila
pap
er
ii) M
arke
t pen
sIs
the
stud
ent
able
tofo
rm li
near
in
equa
litie
s ?
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
44
(c)
Solv
e lin
ear
ineq
ualit
ies
from
pra
ctic
al
situ
atio
ns
i) St
uden
ts to
be
guid
ed b
y th
e te
ache
r to
solv
e lin
ear i
nequ
aliti
es
invo
lvin
g w
ord
prob
lem
sii)
St
uden
ts to
solv
e lin
ear i
nequ
aliti
es
form
ulat
ed fr
om
prac
tical
situ
atio
ns
Wor
kshe
etIs
the
stud
ent
able
toso
lve
linea
r in
equa
litie
s in
volv
ing
wor
d pr
oble
ms?
8.0
NU
MB
ERS
(II)
8.1
Rat
iona
l
Num
bers
The
stud
ent s
houl
d be
abl
e to
(a) D
efine
a ra
tiona
l nu
mbe
r
i)
The
teac
her t
o gu
ide
stud
ents
to
disc
uss r
atio
nal
num
bers
ii)
Stud
ents
in g
roup
s to
defi
ne ra
tiona
l nu
mbe
rs.
i) N
umbe
r lin
eii)
Man
ila p
aper
Is th
e st
uden
t ab
le to
defi
ne
a ra
tiona
l nu
mbe
r?
4
(b) P
erfo
rm th
e ba
sic
oper
atio
ns o
n ra
tiona
l num
bers
i)
The
teac
her t
o de
mon
stra
te to
st
uden
ts o
n ho
w to
pe
rfor
m th
e ba
sic
oper
atio
ns w
ith
ratio
nal n
umbe
rs.
ii)
Stud
ents
to fo
rm
grou
ps a
nd d
iscu
ss
on h
ow to
per
form
ad
ditio
n an
d su
btra
ctio
n w
ith
num
bers
.
Wor
kshe
ets
Is th
e st
uden
t ab
le to
per
form
th
e ba
sic
oper
atio
ns
on ra
tiona
l nu
mbe
rs ?
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
45
iii) T
he te
ache
r to
guid
e st
uden
ts to
mak
e co
nclu
sion
s on
the
pres
ente
d w
ork.
iv)
The
teac
her t
o de
mon
stra
te
mul
tiplic
atio
n an
d di
visi
on o
f rat
iona
l nu
mbe
rsv)
St
uden
ts in
gro
ups
to p
erfo
rm b
asic
op
erat
ions
on
ratio
nal n
umbe
rs.
8.2
Irra
tiona
l
Num
bers
The
stud
ents
shou
ld
be a
ble
to d
efine
irr
atio
nal n
umbe
rs
i) Th
e te
ache
r to
expl
ain
the
conc
ept
of ir
ratio
nal
num
bers
usi
ng
exam
ples
.ii)
Stu
dent
s in
divi
dual
ly
to o
utlin
e th
e di
ffere
nces
bet
wee
n ra
tiona
l and
irr
atio
nal n
umbe
rs.
Cha
rtsIs
the
stud
ent
able
to d
efine
a
irrat
iona
l nu
mbe
r?
2
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
46
8.3
Rea
l Num
bers
The
stud
ents
shou
ldbe
abl
e to
:(a
) Defi
ne re
al
num
bers
i)
The
teac
her t
o us
e th
e nu
mbe
r lin
e to
illu
stra
te th
e co
ncep
t of r
eal
num
bers
.ii)
Th
e te
ache
r to
expl
ain
to st
uden
ts
the
conc
ept o
f ab
solu
te v
alue
of
real
num
bers
usi
ng
prac
tical
exa
mpl
es.
iii)
Stud
ents
in g
roup
s to
solv
e pr
actic
al
prob
lem
s rel
ated
to
abso
lute
val
ue o
f a
real
num
ber.
i) M
anila
pap
erii)
Mar
ker p
eniii
) G
raph
pap
ers
Is th
e st
uden
tab
le to
defi
nere
al n
umbe
rs?
Is th
e st
uden
t ab
le to
solv
e pr
oble
ms
rela
ted
to
prac
tical
pr
oble
ms o
n re
al n
umbe
rs?
6
(b) F
ind
abso
lute
va
lue
of re
al
num
bers
i) T
he te
ache
r to
dem
onst
rate
the
abso
lute
val
ue o
f a
num
ber
ii) S
tude
nts
indi
vidu
ally
to fi
nd
the
abso
lute
val
ue o
f nu
mbe
rs.
Gra
ph p
aper
sIs
the
stud
ent
able
to fi
nd
abso
lute
va
lue
of re
al
num
bers
?
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
47
(c)
Solv
e re
late
d pr
actic
al
prob
lem
s
i) T
he te
ache
r to
guid
e st
uden
ts to
exp
lore
va
rious
act
iviti
es
in w
hich
abs
olut
e va
lue
of n
umbe
rs is
pr
actic
ed.
ii) S
tude
nts i
n pa
irs to
so
lve
prob
lem
s
Wor
kshe
ets
Is th
e st
uden
tab
le to
solv
e pr
oble
ms
rela
ted
to re
al
num
bers
?
9.0
RAT
IOS,
PR
OFI
T A
ND
LO
SS
9.1
Rat
ioTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Expr
ess a
ratio
in
its s
impl
est
form
i)
The
teac
her t
o gu
ide
stud
ents
to
dis
cuss
the
rela
tions
hip
betw
een
ratio
and
fr
actio
n.ii)
St
uden
ts in
gro
ups
to d
iscu
ss o
n ho
w
to e
xpre
ss a
ratio
in
sim
ples
t for
miii
) Th
e te
ache
r to
guid
e st
uden
ts
to m
ake
corr
ect
conc
lusi
ons
i)
Mon
eyii)
Rea
l obj
ectiv
esIs
the
stud
ent
able
to e
xpre
ss
a ra
tio in
the
sim
ples
t for
m?
4
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
48
(b)
Div
ide
a gi
ven
quan
tity
into
pr
opor
tiona
l pa
rts
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
on
how
to d
ivid
e a
give
n qu
antit
y in
to
its p
ropo
rtion
al
parts
ii) S
tude
nts i
n gr
oups
to
solv
e re
al li
fe
prob
lem
s rel
ated
to
ratio
s
i)
Mon
eyii)
Ph
ysic
al it
ems
Is th
e st
uden
tab
le d
ivid
e a
give
n qu
antit
y in
to
prop
ortio
nal
parts
?
9.2
Profi
ts a
nd L
oss
The
stud
ent s
houl
d be
abl
e to
:(a
) Fi
nd p
rofit
and
loss
i)
The
teac
her t
o gu
ide
stud
ents
to
dis
cuss
on
the
mea
ning
of p
rofit
an
d lo
ss.
ii) S
tude
nts i
n pa
irs
to d
eter
min
e pr
ofit
and
loss
.iii
) St
uden
ts in
pai
rs
to d
eter
min
e pr
ofit
and
loss
.
Mon
eyIs
the
stud
ent
able
to fi
nd
profi
t and
loss
?
4
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
49
(b)
Cal
cula
te
perc
enta
ge p
rofit
an
d pe
rcen
tage
lo
ss
i)
The
teac
her t
o de
mon
stra
te
how
to c
alcu
late
pe
rcen
tage
pro
fit o
r pe
rcen
tage
loss
.ii)
St
uden
ts to
solv
e pr
oble
ms r
elat
ed to
pe
rcen
tage
pro
fit
and
loss
.
Wor
kshe
ets
Is th
e st
uden
t ab
le to
cal
cula
te
perc
enta
ge
profi
t and
pe
rcen
tage
loss
?
9.3
Sim
ple
Inte
rest
The
stud
ent s
houl
d be
abl
e to
:(a
) C
alcu
late
si
mpl
e in
tere
st
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
on
the
form
ula
for c
alcu
latin
g
sim
ple
inte
rest
.
ii) S
tude
nts i
ndiv
idua
lly
to
use
the
form
ula
to
cal
cula
te si
mpl
e in
tere
st.
i) B
ank
Stat
emen
tsIs
the
stud
ent
able
to c
alcu
late
si
mpl
e in
tere
st?
4
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
50
(b)
Solv
e re
al li
fe
prob
lem
s rel
ated
to
sim
ple
inte
rest
i) T
he te
ache
r to
guid
e st
uden
ts to
solv
e re
al li
fe p
robl
ems
rela
ted
to si
mpl
e in
tere
st.
ii)
Stud
ents
in g
roup
s to
solv
e pr
oble
ms
on si
mpl
e in
tere
st
Wor
kshe
etIs
the
stud
ent
able
to so
lve
prob
lem
s re
late
d to
sim
ple
inte
rest
?
10.0
C
OO
RD
INAT
E G
EOM
ETRY
10.1
Coo
rdin
ates
of
a Po
int
The
stud
ent s
houl
d be
abl
e to
:(a
) R
ead
the
coor
dina
tes o
f a
poin
t
i)
The
teac
her t
o gu
ide
stud
ents
to
disc
uss h
ow to
dr
aw a
nd la
bel t
he
coor
dina
te a
xes.
ii)
The
teac
her t
o gu
ide
stud
ents
to
plot
a p
oint
in th
e x-
y pl
ane.
iii)
Stu
dent
s in
divi
dual
ly to
read
th
e co
ordi
nate
s of
give
n po
ints
.
i) G
raph
pap
ers
ii) G
eobo
ard
iii) R
ubbe
r ban
d
Is th
e st
uden
t ab
le to
read
the
coor
dina
tes o
f a
poin
t?
6
(b)
Plot
a p
oint
gi
ven
its
coor
dina
tes
i) Th
e te
ache
r to
guid
e st
uden
ts in
pl
ottin
g po
ints
of
give
n co
ordi
nate
sii)
Stu
dent
s in
grou
ps
to p
lot p
oint
s of t
he
give
n co
ordi
nate
i)
Geo
boar
dii)
G
raph
pap
er
iii) R
ubbe
r ban
d
Is th
e st
uden
t ab
le to
plo
t a
poin
t giv
en it
s co
ordi
nate
s ?
TOPI
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OPI
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SPE
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IC
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TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
51
(c) L
ocat
e a
poin
t on
the
coor
dina
te
plan
e.
i) T
he te
ache
r to
dem
onst
rate
the
loca
tion
of a
poi
nt
on th
e x-
y pl
ane.
ii)
Stud
ents
to lo
cate
po
ints
on
the
coor
dina
te p
lane
dr
awn
on th
e ch
alkb
oard
Gra
ph p
aper
Is th
e st
uden
t ab
le to
read
the
coor
dina
tes o
f a
give
n po
int?
10.2
Gra
dien
t (S
lope
) of a
Li
ne
The
stud
ent s
houl
dbe
abl
e to
cal
cula
te
the
grad
ient
of a
line
gi
ven
two
poin
ts
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e m
eani
ng o
f gr
adie
nt (s
lope
) of
a lin
e.ii)
The
teac
her t
o gu
ide
stud
ents
to
det
erm
ine
the
grad
ient
of a
line
gi
ven
two
poin
ts.
iii) S
tude
nts
indi
vidu
ally
to
calc
ulat
e th
e sl
ope
of a
line
giv
en tw
o po
ints
i)
Geo
boar
dii)
M
anila
pap
er
iii)
Gra
ph p
aper
iv
) R
ubbe
r ban
d
Is th
e st
uden
tab
le to
cal
cula
te
the
grad
ient
of
a lin
e gi
ven
any
two
poin
ts?
3
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10.3
Equ
atio
n of
a
line
Th
e st
uden
t sho
uld
be a
ble
to fi
nd th
e eq
uatio
n of
a li
ne
give
n th
e co
ordi
nate
s of
two
poin
ts o
n a
line.
i)
The
teac
her t
o gu
ide
stud
ents
to
use
the
defin
ition
of
gra
dien
t to
dete
rmin
e th
e eq
uatio
n of
a
line
in th
e fo
rm
whe
re
m is
gra
dien
t w
here
m is
gra
dien
t an
d c
is y
inte
rcep
t.ii)
St
uden
ts to
de
term
ine
an
equa
tion
of
line
in th
e fo
rm
i)
Man
ila p
aper
ii)
Gar
boar
diii
) Rub
ber b
and
iv)
Gra
ph p
aper
Is th
e st
uden
t ab
le to
find
the
equa
tion
of a
lin
e gi
ven
two
poin
ts?
3
10.4
Gra
phs
of L
inea
r eq
uatio
ns
The
stud
ent s
houl
d be
abl
e to
:(a
) Fo
rm th
e ta
ble
of v
alue
s
i)
The
teac
her t
o gu
ide
the
stud
ents
to
form
a ta
ble
of v
alue
s and
in
terc
epts
of
a gi
ven
linea
r eq
uatio
n.ii)
St
uden
ts
indi
vidu
ally
to fi
nd
the
tabl
e of
val
ues
of li
near
equ
atio
ns.
i)
Gra
ph p
aper
ii)
Gra
ph b
oard
Is th
e st
uden
t ab
le to
dra
w th
e gr
aph
of a
line
ar
equa
tion?
5
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(b) D
raw
the
grap
h of
a li
near
eq
uatio
n
i)
The
teac
her t
o de
mon
stra
te o
n ho
w to
dra
w th
e gr
aph
of li
near
eq
uatio
ns u
sing
a
tabl
e of
val
ues.
ii)
Stud
ents
in
divi
dual
ly to
use
th
e ta
ble
of v
alue
s to
dra
w th
e gr
aph
of li
near
equ
atio
ns
i) G
raph
pap
erii)
Gra
ph b
oard
Is th
e st
uden
t ab
le to
dra
w th
e gr
aph
of a
line
ar
equa
tion?
10.5
Sim
ulta
neou
s Eq
uatio
nsTh
e st
uden
t sho
uld
be a
ble
to so
lve
linea
r sim
ulta
neou
s eq
uatio
ns
grap
hica
lly.
i)
The
teac
her t
o gu
ide
stud
ents
to
plot
the
grap
h of
th
e lin
ear e
quat
ions
on
the
sam
e co
ordi
nate
pla
ne.
ii)
Stud
ents
to d
iscu
ss
in g
roup
s how
to
plot
gra
ph o
f the
lin
ear e
quat
ions
.iii
) Stu
dent
s in
pairs
to
solv
e lin
ear
sim
ulta
neou
s eq
uatio
ns
grap
hica
lly.
i)
Gra
ph p
aper
ii)
Col
oure
d ch
alk
Is th
e st
uden
tab
le to
so
lve
linea
r si
mul
tane
ous
equa
tion
grap
hica
lly?
2
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11.0
PE
RIM
ETER
S A
ND
A
REA
S
11.1
Per
imet
ers o
f Tr
iang
les a
nd
Qua
drila
tera
ls
The
stud
ent s
houl
dbe
abl
e to
find
th
e pe
rimet
ers
of tr
iang
les a
nd
quad
rilat
eral
s
i)
The
teac
her t
o gu
ide
stud
ents
to
disc
uss t
he m
eani
ng
of p
erim
eter
sii)
Th
e te
ache
r to
guid
e st
uden
ts
to d
iscu
ss h
ow
to d
eter
min
e pe
rimet
ers o
f tri
angl
es a
nd
quad
rilat
eral
s.iii
) St
uden
t to
perf
orm
a
grou
p w
ork
on
calc
ulat
ion
of
perim
eter
s of
trian
gles
and
qu
adril
ater
als
avai
labl
e in
the
surr
ound
ings
and
pr
esen
t in
a cl
ass
iv)
The
teac
her t
o gu
ide
stud
ents
to
mak
e co
nclu
sion
s on
the
grou
p w
ork
pres
enta
tions
.
i) Tr
iang
les
ii) Q
uadr
ilate
rals
iii
) Rop
eiv
) Tap
e m
easu
re
v) R
ule
Is th
e st
uden
tab
le to
find
the
perim
eter
s of
a tri
angl
es a
nd
quad
rilat
eral
s?
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11.2
Circ
umfe
renc
e of
a C
ircle
The
stud
ent s
houl
d be
abl
e to
:(a
) Es
timat
e th
e va
lue
of p
i, П
.
i) T
he te
ache
r to
guid
e st
uden
ts to
mea
sure
th
e ci
rcum
fere
nce
and
diam
eter
of
diffe
rent
circ
ular
ob
ject
s pra
ctic
ally
.ii)
The
teac
her t
o gu
ide
stud
ents
to
find
the
ratio
of
circ
umfe
renc
e,
usin
g th
e ob
tain
ed
mea
sure
men
t of
diam
eter
iii) T
he te
ache
r to
guid
e st
uden
ts to
com
pare
th
eir r
esul
ts to
de
duce
the
valu
e of
П.
i) C
ircul
ar o
bjec
tsii)
R
ope
iii) T
hrea
d iv
) R
uler
Is th
e st
uden
tab
le to
est
imat
e th
e va
lue
of p
i(П
)?
4
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(b) C
alcu
late
the
circ
umfe
renc
e of
a
circ
le.
i)
The
teac
her t
o de
mon
stra
te th
e ca
lcul
atio
n of
ci
rcum
fere
nce
of a
ci
rcle
.ii)
The
stud
ents
in
grou
ps to
cal
cula
te
the
circ
umfe
renc
e of
the
circ
le u
sing
a
form
ula
C =
П
d w
here
d is
a
diam
eter
of a
ci
rcle
and
C is
a
circ
umfe
renc
e
Wor
kshe
etIs
the
stud
ent
able
to
calc
ulat
e th
e ci
rcum
fere
nce
of a
circ
le?
11.3
Are
as o
f re
ctan
gles
and
tri
angl
es
The
stud
ent s
houl
d be
abl
e to
:(a
) Cal
cula
te th
e ar
ea
of a
rect
angl
e
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
on
how
to o
btai
n th
e fo
rmul
a fo
r the
ar
ea o
f rec
tang
le.
ii) S
tude
nts i
n pa
irs to
ca
lcul
ate
the
area
of
rect
angl
es
i) M
anila
pap
erii)
Mar
ker p
en
iii) G
eobo
ard
Is th
e st
uden
tab
le to
cal
cula
te
the
area
of a
re
ctan
gle?
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(b) C
alcu
late
the
area
of a
tria
ngle
i)
The
teac
her t
o gu
ide
stud
ents
to
disc
uss o
n ho
w to
re
duce
the
area
of
a tri
angl
e fr
om th
e ar
ea o
f a re
ctan
gle
ii)
Stud
ents
in
divi
dual
ly to
ca
lcul
ate
the
area
of
a tri
angl
e
i) M
anila
pap
erii)
Mar
ker p
enIs
the
stud
ent
able
to c
alcu
late
th
e ar
ea o
f a
trian
gle?
11.4
Are
as o
f tra
pezi
um a
nd
para
llelo
gram
The
stud
ent s
houl
d be
abl
e to
:(a
) C
alcu
late
are
a of
a
para
llelo
gram
i) T
he te
ache
r to
guid
e st
uden
ts to
find
th
e fo
rmul
a to
ca
lcul
atin
g th
e ar
ea
of p
aral
lelo
gram
ii) S
tude
nts
indi
vidu
ally
to
calc
ulat
e th
e ar
ea o
f pa
ralle
logr
am
i) M
anila
ii) M
arke
r pen
iii
) Geo
boar
d
Is th
e st
uden
tab
le to
cal
cula
te
the
area
of a
pa
ralle
logr
am?
4
(b) C
alcu
late
the
area
of a
trap
eziu
mi)
The
teac
her t
o gu
ide
stud
ents
to o
btai
n th
e fo
rmul
a fo
r ca
lcul
atin
g th
e ar
ea
of a
trap
eziu
m.
ii) S
tude
nts i
ndiv
idua
lly
to c
alcu
late
the
area
of a
trap
eziu
m
usin
g th
e fo
rmul
a
i) G
eobo
ard
ii) R
ubbe
r ban
dIs
the
stud
ent
able
to c
alcu
late
th
e ar
ea o
f a
trape
zium
?
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11.5
Are
a of
a c
ircle
The
stud
ent s
houl
d be
abl
e to
:C
alcu
late
the
area
of
a ci
rcle
i) T
he te
ache
r sho
uld
guid
e a
stud
ents
to
perf
orm
a p
ract
ical
ex
erci
se to
der
ive
the
form
ula
for
findi
ng th
e ar
ea (A
) of
a c
ircle
usi
ng A
=
П r2
ii)
Stud
ents
in g
roup
s to
cal
cula
te th
e ar
ea
of a
circ
le
Wor
kshe
ets
Is th
e st
uden
t ab
le to
cal
cula
te
the
area
of a
ci
rcle
?
2
FOR
M T
WO
59
CLASS LEVEL COMPENTENCES Student should have the ability to:
1. Find relationships among logarithms, exponents, radicals, right triangles and trigonometric ratios.
2. Use mathematical tables in computations.3. Verify laws and prove theorems.4. Do scale drawing and geometrical transformations.5. Factorize and solve problems.6. Organize and interpret data.7. Apply set operations in solving problems.
CLASS LEVEL OBJECTIVES By the end of Form Two course thestudentshouldbeable to:
1. Derive and apply the laws of exponents, radicals and logarithms in mathematical manipulations.
2. Do calculations using mathematical tables.3. Prove and apply congruency and similarity of figures.4. Represent reflections, rotations, translations and enlargement geometrically.5. Represent and interpret statistical data collected from real life situations such as
Road Safety, HIV/AIDS, environment and crimes.6. Perform operations on sets and apply sets to solve problems.
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1.0
EXPO
NEN
TS A
ND
R
AD
ICA
LS
1.1
Expo
nent
sTh
e st
uden
t sho
uld
be
able
to:
(a)
List
the
law
s of
expo
nent
s
i)
The
teac
her t
o di
spla
y th
e la
ws o
f exp
onen
ts
by a
wal
l cha
rtii)
Stu
dent
thro
ugh
thin
k pa
ir sh
are
to d
iscu
ss
law
s of e
xpon
ents
.
Wal
l cha
rtsIs
the
stud
ent
able
to st
ate
the
law
s of
expo
nent
s?
8
(b)
Ver
ify th
e la
ws o
f ex
pone
nts
i) Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
law
s of e
xpon
ents
ii) S
tude
nts i
n gr
oup
to d
educ
e la
ws o
f ex
pone
nts
i)
Mat
hem
atic
alta
bles
ii)
Num
ber c
harts
Is th
e st
uden
t ab
le to
ver
ify
the
law
s of
expo
nent
s?
(c)
App
ly la
ws o
f ex
pone
nts i
n co
mpu
tatio
ns
i)
The
teac
her t
o gu
ide
stud
ents
in a
pply
ing
the
law
s of e
xpon
ents
in
per
form
ing
rela
ted
com
puta
tions
.ii)
St
uden
ts in
gro
ups
to a
pply
law
s of
exp
onen
ts in
co
mpu
tatio
ns
Is th
e st
uden
t ab
le to
app
ly
the
law
s of
expo
nent
s in
perf
orm
ing
com
puta
tions
?
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1.2
Rad
ical
sTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Sim
plify
radi
cals
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
conc
ept o
f rad
ical
s us
ing
expo
nent
s.ii)
Th
e te
ache
r to
guid
e st
uden
ts to
find
the
squa
re ro
ots a
nd c
ube
root
s of n
umbe
rs b
y pr
ime
fact
oriz
atio
n m
etho
ds.
iii)
Stu
dent
s to
find
squa
re ro
ots a
nd c
ube
root
s of n
umbe
rs b
y pr
ime
fact
oriz
atio
n m
etho
d.
Man
ila p
aper
Is th
e st
uden
t ab
le to
sim
plify
ra
dica
ls?
12
(b)
Perf
orm
bas
ic
oper
atio
ns o
n ra
dica
ls
i) T
he te
ache
r to
dem
onst
rate
how
to
add
, sub
tract
, m
ultip
ly a
nd d
ivid
e ra
dica
ls.
ii) S
tude
nts t
o so
lve
prob
lem
s rel
ated
to
ope
ratio
ns o
n ra
dica
ls.
i)
Cub
e ro
ot ta
bles
ii) S
quar
e ro
ot
tabl
esiii
) M
ultip
licat
ion
tabl
es
Is th
e st
uden
t ab
le to
add
su
btra
ct,
mul
tiply
and
di
vide
radi
cals
?
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ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Rat
iona
lize
the
deno
min
ator
i) T
he te
ache
r to
guid
e st
uden
ts to
ratio
naliz
e th
e de
nom
inat
or a
nd
use
this
met
hod
to
sim
plify
radi
cals
to
sim
ples
t for
mii)
St
uden
ts in
gro
ups
to ra
tiona
lize
the
deno
min
ator
and
pr
esen
t the
ir w
ork
in
clas
s
i)
Man
ila p
aper
ii)
Mul
tiplic
atio
n ta
bles
Is th
e st
uden
t ab
le to
ra
tiona
lize
a gi
ven
deno
min
ator
?
(d)
Rea
d sq
uare
root
s an
d cu
be ro
ots
of n
umbe
rs fr
om
mat
hem
atic
al
tabl
es
i)
The
teac
her t
o gu
ide
stud
ents
to re
ad th
e sq
uare
root
s and
cub
e ro
ots o
f num
bers
us
ing
mat
hem
atic
al
tabl
es a
nd c
alcu
lato
rsii)
St
uden
ts to
solv
e pr
oble
ms i
nvol
ving
re
adin
g of
squa
re
a
nd c
ube
root
s of
num
bers
from
tabl
es
i)
Cal
cula
tors
ii)
Mat
hem
atic
al
tabl
es
Is th
e st
uden
tab
le to
de
term
ine
the
squa
re ro
ot a
nd
cube
root
of
num
bers
1.3
Tran
spos
ition
of
For
mul
aTh
e st
uden
t to
beab
le to
:(a
) M
ake
one
lette
r th
e su
bjec
t of t
he
form
ula
i) T
he te
ache
r to
dem
onst
rate
on
how
to
rear
rang
e th
e le
tters
to m
ake
one
lette
r sub
ject
of t
he
form
ula.
Mat
hem
atic
al
form
ula
Is th
e st
uden
t ab
le to
mak
e on
e le
tter t
he su
bjec
t of
the
form
ula?
5
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii)
Stud
ents
to d
o ch
alkb
oard
wor
k on
re
arra
ngin
g le
tters
to
mak
e on
e le
tter t
he
subj
ect.
iii) S
tude
nts i
ndiv
idua
lly
to re
arra
nge
lette
rs
and
mak
e on
e th
e su
bjec
t.(b
) Tr
ansp
ose
a fo
rmul
ae w
ith
squa
re ro
ots a
nd
pow
ers
i) T
he te
ache
r to
guid
e st
uden
t to
disc
uss
on tr
ansp
ositi
on o
f fo
rmul
ae w
ith ro
ots
and
pow
ers
ii) S
tude
nts t
o tra
nspo
se
form
ulae
with
root
an
d po
wer
s
Mat
hem
atic
alfo
rmul
aeIs
the
stud
ent
able
to tr
ansp
ose
form
ulae
with
le
tters
invo
lvin
g ro
ots a
nd
pow
ers?
2.0
ALG
EBR
A2.
1 B
inar
yO
pera
tions
The
stud
ents
shou
ldbe
abl
e to
: (a
) D
escr
ibe
the
bina
ry
oper
atio
ns.
The
teac
her a
nd st
uden
tto
dis
cuss
the
bina
ry
oper
atio
ns.
i) M
athe
mat
ical
fo
rmul
aeii)
C
olou
red
chal
ks
Is th
e st
uden
t ab
le d
escr
ibe
the
bina
ry
oper
atio
ns?
5
(b) P
erfo
rm b
inar
y op
erat
ions
i)
The
teac
her t
o gu
ide
stud
ents
to p
erfo
rm
bina
ry o
pera
tions
.ii)
St
uden
ts to
do
grou
p
w
ork
on b
inar
y
op
erat
ions
and
pre
sent
in th
e cl
ass
i)
Col
oure
d ch
alks
ii)
Man
ila p
aper
siii
) M
arke
r pen
s
Is th
e st
uden
t ab
le p
erfo
rm
bina
ry
oper
atio
ns
invo
lvin
g ex
pres
sion
?
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
2.2
Bra
cket
sin
Com
puta
tion
The
stud
ent s
houl
dbe
abl
e to
:(a
) Pe
rfor
m b
asic
op
erat
ions
in
volv
ing
brac
kets
i)
The
teac
her t
o gu
ide
stud
ents
to
disc
uss t
he ru
les
gove
rnin
g ba
sic
oper
atio
ns a
pplie
d to
alg
ebra
kno
wn
as
“BO
DM
AS”
ii)
Stud
ents
to d
iscu
ss
in g
roup
s how
to
appl
y B
OD
MA
S in
co
mpu
tatio
n
i)
Col
oure
d ch
alks
ii)
Man
ila p
aper
siii
) M
arke
t pen
s
Is th
e st
uden
t ab
le to
per
form
op
erat
ions
in
volv
ing
brac
kets
?
5
(b)
Sim
plify
alg
ebra
ic
expr
essi
on
invo
lvin
g th
e ba
sic
oper
atio
ns a
nd
brac
kets
i)
The
teac
her t
o gu
ide
stud
ents
to
sim
plify
the
alge
brai
c ex
pres
sion
s.ii)
St
uden
ts to
sim
plify
al
gebr
aic
expr
essi
ons
i)
Col
oure
d ch
alks
ii)
Man
ila p
aper
siii
) M
arke
r pen
s
Is th
e st
uden
ts
able
to si
mpl
ify
alge
brai
c ex
pres
sion
in
volv
ing
the
basi
c op
erat
ions
an
d br
acke
ts ?
2.3
Qua
drat
ic
Ex
pres
sion
sTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Form
a q
uadr
atic
ex
pres
sion
from
tw
o lin
ear f
acto
rs.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
how
to m
ultip
ly
two
linea
r fac
tors
to
form
a q
uadr
atic
ex
pres
sion
.ii)
St
uden
ts to
dis
cuss
in
gro
ups h
ow to
ex
pand
ing
linea
r fa
ctor
s.
i)
Man
ila sh
eet
ii)
Mar
ker p
ens
Is t
he st
uden
t ab
le to
form
qu
adra
tic
expr
essi
ons
give
n tw
o lin
ear
fact
ors?
5
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Writ
e th
e ge
nera
l fo
rm o
f a q
uadr
atic
ex
pres
sion
i) T
he te
ache
r to
expl
ain
the
gene
ral f
orm
of a
qu
adra
tic e
xpre
ssio
n
whe
re a
, b, c
are
real
nu
mbe
rs a
nd a
≠ 0
ii)
Stud
ents
to re
-arr
ange
qu
adra
tic e
xpre
ssio
ns
in th
e ge
nera
l for
m
i)
Col
oure
d ch
alks
ii)
Man
ila p
aper
s iii
) M
arke
r pen
s
Is th
e st
uden
tab
le to
writ
e th
e ge
nera
l for
m
of a
qua
drat
ic
expr
essi
on?
2.4
Fact
oriz
atio
nTh
e st
uden
t sho
uld
be a
ble
to:
(a) F
acto
rize
linea
r ex
pres
sion
s.
i)
The
teac
her t
o gu
ide
stud
ents
on
how
to
fact
oriz
e lin
ear
expr
essi
ons.
ii)
Stud
ent t
o fa
ctor
ize
linea
r exp
ress
ions
.
Is th
e st
uden
tab
le to
fact
oriz
e lin
ear
expr
essi
ons?
6
(b)
Fact
oriz
e qu
adra
tic
expr
essi
ons
i) T
he te
ache
r to
dem
onst
rate
on
how
to
fact
oriz
e th
e qu
adra
tic
expr
essi
ons u
sing
the
follo
win
g m
etho
ds:
- ins
pect
ion
- Spl
ittin
g th
e m
iddl
e te
rm- D
iffer
ence
of t
wo
squa
res
- per
fect
squa
res
i)
Mul
tiplic
atio
n ch
arts
ii)
Fact
or tr
eeiii
) C
olou
red
chal
ks
iv)
Illus
tratio
ns o
n di
ffere
nce
of
two
squa
res a
nd
perf
ect s
quar
es
Is th
e st
uden
t ab
le to
fact
oriz
e qu
adra
tic
expr
essi
on?
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts t
o w
ork
in g
roup
s on
the
four
tech
niqu
es o
f fa
ctor
izat
ion
and
pres
ent i
n cl
ass.
3.0
QU
AD
RAT
IC
EQU
ATIO
NS
3.1
Sol
ving
eq
uatio
nsTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Det
erm
ine
the
solu
tion
of a
qu
adra
tic e
quat
ion
by fa
ctor
izat
ion.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
the
theo
rem
of t
he
fact
ors o
f zer
o.ii)
Th
e te
ache
r to
guid
e st
uden
ts to
det
erm
ine
the
solu
tion
of a
qu
adra
tic e
quat
ion
usin
g th
e th
eore
m o
f th
e fa
ctor
s of z
ero.
iii)
Stud
ents
to fi
nd
solu
tion
of q
uadr
atic
eq
uatio
ns u
sing
the
theo
rem
of t
he fa
ctor
s of
zer
o.
i)
Man
ila p
aper
sii)
M
arke
r pen
siii
) Col
oure
d ch
alks
Is th
e st
uden
t ab
le to
de
term
ine
the
solu
tion
of
a qu
adra
tic
equa
tion
by
fact
oriz
atio
n m
etho
d?
8
(b) F
ind
the
solu
tion
of a
qua
drat
ic
equa
tion
by
com
plet
ing
the
squa
re
i) T
he te
ache
r to
dem
onst
rate
on
how
to
find
the
solu
tion
of
quad
ratic
equ
atio
ns
by c
ompl
etin
g th
e sq
uare
.
i) M
anila
pap
ers
ii) M
arke
r pen
siii
) Col
oure
d ch
alks
Is th
e st
uden
t ab
le to
find
th
e so
lutio
n of
qua
drat
ic
equa
tions
by
com
plet
ing
the
squa
re?
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts t
o w
ork
in g
roup
s to
solv
e qu
adra
tic e
quat
ions
by
com
plet
ing
the
squa
re.
iii) S
tude
nts t
o do
in
divi
dual
wor
k on
so
lvin
g qu
adra
tic
equa
tions
by
com
plet
ing
the
squa
re.
3.2
Gen
eral
so
lutio
n of
a
Qua
drat
ic
Equa
tion
The
stud
ent s
houl
dbe
abl
e to
:(a
) D
eriv
e th
e qu
adra
tic fo
rmul
a
The
teac
her t
o gu
ide
stud
ents
to d
eriv
e th
e qu
adra
tic fo
rmul
a us
ing
the
met
hod
of c
ompl
etin
g th
e sq
uare
Col
oure
d ch
alks
Is th
e st
uden
t ab
le to
der
ive
the
quad
ratic
fo
rmul
a?
5
(b)
Solv
e qu
adra
tic
equa
tions
usi
ng
quad
ratic
form
ula
i) T
he te
ache
r to
guid
e st
uden
ts o
n ho
w to
ap
ply
the
quad
ratic
fo
rmul
a to
solv
e pr
oble
ms
ii) S
tude
nts t
o so
lve
quad
ratic
equ
atio
ns
usin
g th
e fo
rmul
a
Col
oure
d ch
alks
Is th
e st
uden
t ab
le to
use
th
e qu
adra
tic
form
ula
to
solv
e qu
adra
tic
equa
tions
?
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
4.0
LOG
RIT
HM
S4.
1 St
anda
rd
Form
The
stud
ent s
houl
dbe
abl
e to
:(a
) W
rite
num
bers
in
stan
dard
form
.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
on th
e im
porta
nce
of
writ
ing
a nu
mbe
r in
stan
dard
not
atio
n.ii)
Th
e te
ache
r to
dem
onst
rate
how
to
writ
e nu
mbe
rs
in st
anda
rd fo
rm,
whe
re A
=10o
1≤
A<1
0.iii
) Stu
dent
s to
writ
e nu
mbe
rs in
stan
dard
fo
rm.
i)
Man
ila p
aper
sii)
C
olou
red
chal
ks
iii)
Man
ila p
ens
Is th
e st
uden
tab
le to
writ
e nu
mbe
rs in
st
anda
rd fo
rm?
5
(b)
Perf
orm
co
mpu
tatio
ns
whi
ch in
volv
e m
ultip
licat
ion
and
divi
sion
of
num
bers
exp
ress
ed
in st
anda
rd fo
rm.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
the
mul
tiplic
atio
n an
d di
visi
on o
f num
bers
ex
pres
sed
in st
anda
rd
form
.ii)
Stu
dent
s to
do
ques
tions
invo
lvin
g m
ultip
licat
ion
and
divi
sion
of n
umbe
rs
i)
Man
ila p
aper
sii)
C
olou
red
chal
ks
iii) M
arke
r pen
s
Is th
e st
uden
t ab
le to
per
form
co
mpu
tatio
ns
whi
ch in
volv
e m
ultip
licat
ion
and
divi
sion
of
num
bers
whe
n ex
pres
sed
in
stan
dard
form
?
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TE
AC
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EA
RN
ING
R
ESO
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S
ASS
ESS
ME
NT
NU
MB
ER
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RIO
DS
4.2
Law
s of
Loga
rithm
sTh
e st
uden
ts sh
ould
be a
ble
to:
(a)
Stat
e th
e la
ws o
f lo
garit
hms
Teac
her t
o gu
ide
stud
ents
on
how
to d
eriv
e th
e la
ws o
f log
arith
ms
Cha
rts o
f lo
garit
hmic
Law
Is th
e st
uden
t ab
le to
stat
e th
e la
ws o
f lo
garit
hms?
12
(b)
Ver
ify th
e la
ws o
f lo
garit
hms u
sing
th
e kn
owle
dge
of
expo
nent
s.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
rela
tions
hip
betw
een
expo
nent
s and
lo
garit
hms.
ii) S
tude
nts t
o so
lve
ques
tions
rela
ted
to
chan
ging
exp
onen
ts
to lo
garit
hms a
nd v
ice
vers
a.
Cha
rts o
f lo
garit
hmic
Law
s
Is th
e st
uden
tab
le to
ver
ify
the
law
s of
loga
rithm
s usi
ng
the
know
ledg
e of
exp
onen
ts?
(c)
Use
the
law
s of
loga
rithm
s to
sim
plify
lo
garit
hmic
ex
pres
sion
s
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
law
s of l
ogar
ithm
sii)
The
teac
her t
o de
mon
stra
te th
e us
e of
la
ws o
f log
arith
ms i
n co
mpu
tatio
ns.
iii) S
tude
nts t
o w
ork
in g
roup
s on
sim
plifi
catio
n of
loga
rithm
ic
expr
essi
ons a
nd
pres
ent i
n th
e cl
ass.
Cha
rts o
f law
s of
Loga
rithm
sIs
the
stud
ent
able
to u
se
the
law
s of
loga
rithm
to
sim
plify
lo
garit
hmic
ex
pres
sion
s co
rrec
tly?
70
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OB
JEC
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AC
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AN
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
Solv
e lo
garit
hmic
eq
uatio
ni)
The
teac
her t
o de
mon
stra
te o
n ho
w
to so
lve
loga
rithm
ic
equa
tions
.ii)
Stu
dent
s to
wor
k in
gr
oups
on
prob
lem
s in
volv
ing
loga
rithm
ic
equa
tions
and
con
duct
pe
er p
rese
ntat
ions
.
Cha
rts o
f lo
garit
hmic
law
s
Is th
e st
uden
tab
le to
solv
e lo
garit
hmic
eq
uatio
n?
(e)
App
ly la
ws o
f lo
garit
hms t
o fin
d pr
oduc
ts,
quot
ient
s, ro
ots
and
pow
ers o
f nu
mbe
rs.
i)
The
teac
her t
o gu
ide
stud
ents
to so
lve
prob
lem
s inv
olvi
ng
law
s of l
ogar
ithm
s.ii)
St
uden
t in
grou
ps to
so
lve
prob
lem
s on
law
s of l
ogar
ithm
s.
Cha
rts o
flo
garit
hmic
law
sIs
the
stud
ent
able
to a
pply
la
ws o
f lo
garit
hms t
o fin
d pr
oduc
ts,
quot
ient
, roo
ts
and
pow
ers o
f nu
mbe
rs?
4.3
Tabl
es o
f Lo
garit
hms
The
stud
ent s
houl
dbe
abl
e to
:(a
) R
ead
the
loga
rithm
ic ta
ble
i) T
he te
ache
r to
use
exam
ples
to e
xpla
in
the
two
parts
of
loga
rithm
: Man
tissa
an
d ch
arac
teris
tics.
ii) T
he te
ache
r to
guid
e st
uden
ts to
read
the
loga
rithm
ic ta
bles
for
give
n nu
mbe
rs.
iii)
Stud
ents
to re
ad
loga
rithm
s of
num
bers
.
Tabl
es o
f log
arith
ms
Is th
e st
uden
tab
le to
read
the
loga
rithm
ic
tabl
e co
rrec
tly?
Is th
e st
uden
t ab
le to
use
ta
bles
of
antil
ogar
ithm
s ?
8
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
The
teac
her t
o gu
ide
stud
ents
to re
ad th
e an
tilog
arith
m ta
bles
.v)
.Stu
dent
s to
use
antil
ogar
ithm
tabl
es to
re
ad n
umbe
rs w
hose
lo
garit
hms a
re g
iven
.(b
) App
ly lo
garit
hmic
ta
bles
to fi
nd
prod
ucts
and
qu
otie
nts o
f nu
mbe
rs.
i)
The
teac
her t
o gu
ide
stud
ents
to u
se ta
bles
of
loga
rithm
s, to
ob
tain
pro
duct
s and
qu
otie
nts o
f num
bers
.ii)
St
uden
ts to
do
com
puta
tions
on
mul
tiplic
atio
n an
d di
visi
on o
f num
bers
us
ing
loga
rithm
ta
bles
.
Loga
rithm
ic ta
bles
Is th
e st
uden
tab
le to
use
lo
garit
hmic
ta
bles
to fi
nd
prod
ucts
and
qu
otie
nts o
f nu
mbe
rs?
(c)
App
ly lo
garit
hmic
ta
bles
to fi
nd ro
ots
and
pow
ers o
f nu
mbe
rs.
i)
The
teac
her t
o sh
ow
the
stud
ents
how
to
use
loga
rithm
ic ta
bles
to
find
root
s and
po
wer
s of n
umbe
rs.
ii)
Stud
ents
in g
roup
s to
do
calc
ulat
ions
in
volv
ing
root
s an
d po
wer
s usi
ng
loga
rithm
ic ta
bles
.
Loga
rithm
ic ta
bles
Is th
e st
uden
t ab
le to
app
ly
loga
rithm
ic
tabl
es to
find
ro
ots a
nd p
ower
s of
num
bers
?
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AN
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
5.0
CO
NG
RU
ENC
E5.
1 C
ongr
uenc
e of
Tria
ngle
sTh
e st
uden
t sho
uld
be a
ble
to(a
) D
eter
min
e th
e co
nditi
ons f
or
cong
ruen
ce o
f tri
angl
es.
i) T
he te
ache
r to
expl
ain
the
mea
ning
of
cong
ruen
ce u
sing
pr
actic
al a
ctiv
ities
.ii)
Th
e te
ache
r to
lead
st
uden
ts to
exp
lore
th
e pr
oper
ties o
f co
ngru
ent fi
gure
s us
ing
prac
tical
ac
tiviti
es.
iii)
Stud
ents
to st
ate
and
writ
e th
e pr
oper
ties o
f co
ngru
ent t
riang
les.
i) M
anila
pap
ers
ii) G
eom
etric
fig
ures
iii) P
aper
cut
tings
iv)
Phot
ogra
phs
v)
Mat
hem
atic
al
sets
vi)
Mar
ker p
ens
vii)
Geo
boar
ds
Is th
e st
uden
t ab
le to
de
term
ine
the
cond
ition
s for
co
ngru
ence
of
trian
gles
?
8
(b)
Pro
ve c
ongr
uenc
e of
tria
ngle
.Th
e te
ache
r to
guid
est
uden
ts to
dis
cuss
the
cond
ition
s for
pro
of o
f co
ngru
ence
of t
riang
les:
A
ngle
Ang
le S
ide
(AA
S);
Side
, Sid
e, S
ide(
SSS)
; Si
de A
ngle
Sid
e(SA
S)an
d R
ight
ang
leH
ypot
enus
e Si
de (R
HS)
i) M
anila
pap
ers
ii) G
eom
etric
fig
ures
iii)
Pape
r cut
tings
iv
) Ph
otog
raph
sv)
M
athe
mat
ical
se
tsvi
) M
arke
r pen
s
Is th
e st
uden
tab
le to
pro
ve
cong
ruen
ce o
f tri
angl
es?
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IC
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JEC
TIV
ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
App
ly th
eore
ms
on c
ongr
uenc
e of
tri
angl
es to
solv
e re
late
d pr
oble
ms.
i)
The
teac
her t
o gu
ide
stud
ents
to
solv
e pr
oble
ms
usin
g th
e co
nditi
ons
for c
ongr
uenc
e of
tri
angl
esii)
St
uden
ts to
solv
e pr
oble
ms o
n co
ngru
ence
of
trian
gles
in g
roup
s an
d pr
esen
t the
ir w
ork
in c
lass
.
i) M
anila
pap
ers
ii) G
eom
etric
fig
ures
iii) P
aper
cut
tings
iv
) Pho
togr
aphs
v)
Mat
hem
atic
al
sets
vi)
Mar
ker p
ens
vii)
Geo
boar
ds
Is th
e st
uden
tab
le to
app
ly
cong
ruen
ce
theo
rem
s of
trian
gles
to
solv
e re
late
d pr
oble
ms?
12
6.0
SIM
ILA
RIT
Y6.
1 Si
mila
r
Fi
gure
sTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Iden
tify
sim
ilar
poly
gons
.
i) T
he te
ache
r to
guid
e st
uden
ts to
exp
lore
th
e pr
oper
ties o
f si
mila
r figu
res u
sing
ha
nds o
n ac
tiviti
es
such
as p
aper
cut
ting
refle
ctio
n in
a p
lane
m
irror
ii) S
tude
nts t
o ex
plor
e an
d w
rite
prop
ertie
s of
sim
ilar p
olyg
ons
i)
Sim
ilar o
bjec
ts,
ii)
Mirr
or, fi
gure
siii
) G
eobo
ards
iv)
Pape
r cut
tings
, v)
S
imila
r pic
ture
s vi
) M
athe
mat
ical
sets
,vi
i) G
raph
pap
ers
Is th
e st
uden
tab
le to
iden
tify
sim
ilar
poly
gons
?
8
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IC
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AC
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G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Prov
e si
mila
rity
theo
rem
s usi
ng
trian
gles
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
cond
ition
s for
si
mila
rity
of tr
iang
les
(SSS
, AA
A, S
AS
and
RH
S).
ii)
Stud
ents
to e
xplo
re
and
writ
e th
e co
nditi
ons f
or si
mila
r tri
angl
es.
i)
Man
ila p
aper
sii)
M
arke
r pen
sIs
the
stud
ent
able
to p
rove
si
mila
rity
theo
rem
s usi
ng
trian
gles
?
(c)
Solv
e pr
oble
ms
usin
g si
mila
rity
theo
rem
s of
trian
gles
.
i)
The
teac
her t
o de
mon
stra
te o
n ho
w
to so
lve
prob
lem
s in
volv
ing
sim
ilarit
y of
tria
ngle
s usi
ng
sim
ilarit
y th
eore
ms.
ii) S
tude
nts t
o so
lve
prob
lem
s usi
ng
sim
ilarit
y th
eore
ms.
Is th
e st
uden
tab
le to
solv
e pr
oble
ms u
sing
si
mila
rity
theo
rem
s of
trian
gles
?
7.0
GEO
MET
RIC
AL
TRA
NSF
OR
MA
-TI
ON
S
7.1
Refl
ectio
nTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Des
crib
e th
e ch
arac
teris
tics o
f a
refle
ctio
n in
a
plan
e
i)
The
teac
her t
o gu
ide
stud
ents
to in
vest
igat
e ch
arac
teris
tics o
f re
flect
ion
in a
pla
ne
by fo
ldin
g an
d cu
tting
s.ii)
St
uden
ts to
in
vest
igat
e an
d w
rite
the
prop
ertie
s of
refle
ctio
n.
i)
Plan
e m
irror
s,ii)
Geo
boar
ds,
Man
ila sh
eets
iii)
Gam
es, G
raph
s pa
pers
and
id
entic
al p
ictu
res
iv)
Rub
ber b
ands
Is th
e st
uden
t ab
le to
de
scrib
e th
e ch
arac
teris
tics o
f a
refle
ctio
n in
a
plan
e?
4
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G
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
7.2
Rot
atio
nsTh
e st
uden
ts sh
ould
be a
ble
to:
(a)
Des
crib
e ch
arac
teris
tics o
f a
rota
tion
on a
pla
ne.
i)
The
teac
her t
o gu
ide
stud
ents
to in
vest
igat
e th
e ch
arac
teris
tics o
f a
rota
ted
obje
ct o
n a
plan
e.ii)
Stu
dent
s to
stat
e an
d w
rite
the
prop
ertie
s of
rota
tion
in a
pla
ne.
i)
Gra
ph p
aper
s,ii)
G
eobo
ards
, iii
) Pa
per c
uttin
gs,
iv) M
athe
mat
ical
se
ts
Is th
e st
uden
tab
le to
des
crib
e ch
arac
teris
tics
of a
rota
tion
on
a pl
ane?
4
(b)
Rep
rese
nt d
iffer
ent
rota
tion
on a
pla
ne
by d
raw
ings
.
i) T
he te
ache
r to
guid
e st
uden
ts to
dra
w
rota
tions
of p
oint
s, lin
es a
nd p
olyg
ons
usin
g m
athe
mat
ical
se
tsii)
Stu
dent
s to
draw
ro
tatio
ns o
f poi
nts,
lines
an
poly
gons
in a
pl
ane.
iii) T
he te
ache
r to
guid
e
stud
ents
to b
rain
stor
m
on h
ow to
loca
te th
e
cen
tre o
f rot
atio
n by
con
stru
ctio
n
Mat
hem
atic
al se
tIs
the
stud
ent
able
to re
pres
ent
diffe
rent
ro
tatio
ns in
a
plan
e by
dr
awin
gs?
76
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv) S
tude
nts t
o so
lve
ques
tions
invo
lvin
g lo
catin
g th
e ce
ntre
of
rota
tion
v) S
tude
nts i
n gr
oups
to
app
ly ro
tatio
n pr
oper
ties t
o so
lve
rela
ted
prob
lem
s.7.
3 Tr
ansl
atio
nTh
e st
uden
t sho
uld
be a
ble
to re
pres
ent
trans
latio
n by
dr
awin
gs.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
tra
nsla
tion
by sl
idin
g re
al o
bjec
ts, l
ines
and
fig
ures
on
a pl
ane
with
out t
urni
ng th
em.
ii)
Stud
ents
to st
ate
and
writ
e pr
oper
ties o
f tra
nsla
tion.
i)
Mat
hem
atic
al
set,
ii)
Gra
ph p
aper
s iii
) G
eobo
ard
iv)
Rub
ber b
ands
Is th
e st
uden
tab
le to
stat
e pr
oper
ties o
f tra
nsla
tions
?
4
7.4
Enla
rgem
ent
The
stud
ent s
houl
dbe
abl
e to
:(a
) D
evel
op a
scal
e of
en
larg
emen
t.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss th
e re
latio
nshi
p be
twee
n si
mila
ritie
s and
hen
ce
deve
lop
scal
e of
en
larg
emen
t.ii)
Stu
dent
s to
solv
e pr
oble
ms r
elat
ed to
de
velo
ping
scal
e fa
ctor
i)
Mat
hem
atic
al
set
ii)
Diff
eren
t fig
ures
/obj
ects
iii) P
hoto
grap
hs
Is th
e st
uden
tab
le to
dev
elop
sc
ale
of
enla
rgem
ent?
12
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AC
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G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) I
dent
ify e
nlar
ged
figur
es.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
iden
tify
enla
rged
figu
res
ii) S
tude
nts t
o br
ains
torm
and
writ
e th
e pr
oper
ties o
f en
larg
emen
t
i)
Gra
ph p
aper
ii)
Pict
ure
cutti
ngs
iii)
Pape
r cut
tings
Is th
e st
uden
t ab
le to
iden
tify
enla
rged
fig
ures
?
(c)
Con
stru
ct
enla
rgem
ent o
f a
give
n fig
ures
.
i) T
he te
ache
r to
dem
onst
rate
how
to
cons
truct
enl
arge
men
t of
a g
iven
figu
reii)
Stu
dent
s to
do
chal
kboa
rd w
ork
on
cons
truct
ing
enla
rged
fig
ures
.iii
) The
teac
her t
o gu
ide
stud
ents
to lo
cate
the
cent
re o
f enl
arge
men
t by
con
stru
ctio
n.iv
) St
uden
ts to
solv
e pr
oble
ms r
elat
ed to
lo
catin
g th
e ce
ntre
of
enla
rgem
ent
i)
Mat
hem
atic
al
sets
ii)
Gra
ph p
aper
s iii
) G
eobo
ard
iv)
Rub
ber b
ands
Is th
e st
uden
tsab
le to
con
stru
ct
enla
rgem
ent o
f a
give
n fig
ures
?
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d) D
raw
figu
res t
o sc
ale.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
dra
w fi
gure
s us
ing
a gi
ven
scal
e.ii)
St
uden
ts to
dra
w
diffe
rent
figu
res t
o sc
ale.
i)
Mat
hem
atic
al
sets
ii)
Map
s
Is th
e st
uden
tsab
le to
dra
wfig
ures
to sc
ale?
(e)
Fin
d ac
tual
di
stan
ces
repr
esen
ted
by a
sc
ale
draw
ings
.
i)
The
teac
her t
o gu
ide
stud
ent t
o di
scus
s how
to
cal
cula
te a
ctua
l di
stan
ces r
epre
sent
ed
by a
scal
e dr
awin
gs.
ii)
Stud
ents
to a
pply
th
e pr
oper
ties o
f en
larg
emen
t to
solv
e re
late
d pr
oble
ms
Mat
hem
atic
al se
tsIs
the
stud
ent
able
to fi
nd
actu
aldi
stan
ces
repr
esen
ted
by a
sc
ale
draw
ings
?
7.5.
C
ombi
ned
Tran
sfor
mat
ions
The
stud
ent s
houl
dbe
abl
e to
:(a
) D
raw
com
bine
d tra
nsfo
rmat
ions
i)
The
teac
her t
o gu
ide
stud
ent t
o dr
aw c
ombi
ned
trans
form
atio
ns.
ii)
Stud
ents
to
draw
com
bine
d tra
nsfo
rmat
ions
in a
pl
ane
Mat
hem
atic
al se
tsIs
the
stud
ent
able
to d
raw
co
mbi
ned
trans
form
atio
ns?
4
79
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AC
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Solv
e si
mpl
e pr
oble
ms o
n co
mbi
ned
trans
form
atio
ns
i) T
he te
ache
r to
guid
e st
uden
ts in
gro
ups
to so
lve
prob
lem
s on
com
bine
d tra
nsfo
rmat
ion.
ii) S
tude
nts t
o so
lve
prob
lem
s on
com
bine
d tra
nsfo
rmat
ions
in a
pl
ane
by c
onst
ruct
ion.
Is th
e st
uden
t ab
le to
solv
e si
mpl
e pr
oble
ms
on c
ombi
ned
trans
form
atio
ns?
8.0
PYTH
AG
OR
AS
TH
EOR
EM
8.1
Proo
f of
Pyth
agor
as
Th
eore
m
The
stud
ents
shou
ldbe
abl
e to
pro
ve th
ePy
thag
oras
theo
rem
.
i)
The
teac
her t
o g
uide
st
uden
ts to
inve
stig
ate
the
illus
tratio
n of
Py
thag
oras
theo
rem
.ii)
The
teac
her t
o gu
ide
stud
ents
to p
rove
the
Pyth
agor
as th
eore
m.
iii) S
tude
nts t
o so
lve
prob
lem
s rel
ated
to
right
ang
led
trian
gles
.iv
) Stu
dent
s to
solv
e pr
oble
ms r
elat
ed to
rig
ht a
ngle
d tri
angl
es
i)
Geo
boar
dii)
Sq
uare
cut
tings
iii
) R
ight
ang
led
trian
gles
iv) S
quar
e ro
ot
tabl
esv)
Sq
uare
tabl
es
Is th
e st
uden
tab
le to
pro
ve
the
Pyth
agor
as
theo
rem
?
4
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ING
ST
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EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
8.2
App
licat
ion
of P
ytha
gora
s th
eore
m
The
stud
ent s
houl
d be
abl
e to
app
ly th
e Py
thag
oras
theo
rem
to
solv
e da
ily li
fe
prob
lem
s.
i) T
he te
ache
r to
g
uide
stud
ents
to
d
iscu
ss h
ow to
solv
e
rea
l life
pro
blem
s
usi
ng P
ytha
gora
s
theo
rem
. ii)
Stu
dent
s to
solv
e re
al
life
prob
lem
s usi
ng
Pyth
agor
as th
eore
m.
i)
Man
ila p
aper
ii)
Mar
ker p
ens
Is th
e st
uden
t ab
le to
app
ly
the
Pyth
agor
as
theo
rem
to
solv
e da
ily li
fe
prob
lem
s?
4
9.0
TRIG
ON
OM
ETRY
9.1
Trig
onom
etric
ra
tios
The
stud
ent s
houl
d be
abl
e to
defi
ne si
ne,
cosi
ne a
nd ta
ngen
t of
an a
ngle
usi
ng a
rig
ht-a
ngle
d tri
angl
e.
i) T
he te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
on
indi
rect
met
hods
of
find
ing
dist
ance
s e.
g. w
idth
of r
iver
and
he
ight
of a
tree
.ii)
The
teac
her t
o gu
ide
stud
ents
to d
raw
si
mila
r rig
ht a
ngle
d tri
angl
es g
iven
an
angl
e an
d a
side
iii
) Stu
dent
s to
mea
sure
th
e si
des o
f the
tri
angl
es d
raw
n a
nd
com
pare
the
ratio
of
side
s to
esta
blis
h tri
gono
met
ric ra
tios
(sin
e, c
osin
e an
d ta
ngen
t).
i)
Gra
ph p
aper
ii) M
athe
mat
ical
se
tsiii
) C
linom
eter
siv
) Ta
pe m
easu
re
v)
Rop
evi
) Tr
eadl
e w
heel
vi
i) Tr
igon
omet
ric
tabl
es
Is th
e st
uden
tab
le to
defi
ne
trigo
nom
etric
ra
tios?
6
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
to c
ompu
te
sine
s, co
sine
s and
ta
ngen
ts o
f rig
hts
angl
ed tr
iang
les
with
out t
able
s.9.
2 Tr
igon
omet
ric
Rat
ios o
f Sp
ecia
l A
ngle
s
The
stud
ent s
houl
dbe
abl
e to
:(a
) D
eter
min
e th
e si
ne,
cosi
ne a
nd ta
ngen
t of
30o ,
45o a
nd
60o w
ithou
t usi
ng
Trig
onom
etric
ta
bles
.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e us
e of
the
right
-ang
led
trian
gle
and
the
Pyth
agor
as
theo
rem
to d
eter
min
e si
ne, c
osin
e an
d ta
ngen
t for
30o ,4
5o an
d 60
o w
ithou
t usi
ng
trigo
nom
etric
tabl
esii)
Stu
dent
s to
find
the
sin,
cos
and
tan
for
30o ,
45o a
nd 6
0o w
ithou
t usi
ng ta
ble.
Mat
hem
atic
al se
tIs
the
stud
ent
able
to
dete
rmin
e th
e si
ne, c
osin
e an
d ta
ngen
t of
30o ,
45o a
nd 6
0o w
ithou
t usi
ng
trigo
nom
etric
ta
bles
?
6
(b) S
olve
sim
ple
trigo
nom
etric
pr
oble
ms r
elat
ed to
sp
ecia
l ang
les.
i)
The
teac
her t
o gu
ide
stud
ents
to d
o ca
lcul
atio
ns in
volv
ing
spec
ial a
ngle
ratio
s.ii)
St
uden
ts in
gro
ups
to d
o ca
lcul
atio
ns
invo
lvin
g si
ne, c
osin
e an
d ta
ngen
t for
30o ,
45o a
nd 6
0o .
Trig
onom
etric
tabl
esIs
the
stud
ent
able
to p
erfo
rm
calc
ulat
ions
re
late
d to
spec
ial
angl
es?
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AC
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AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
9.3
Trig
onom
etric
Tab
les
The
stud
ents
shou
ld b
e ab
le to
: (a
) Rea
d th
e tri
gono
met
ric ra
tios
from
tabl
es.
i) T
he te
ache
r to
guid
e th
e st
uden
t to
read
si
ne, c
osin
e an
d ta
ngen
t for
ang
les
betw
een
0o and
90o .
ii) S
tude
nts t
o re
ad si
ne,
cosi
ne a
nd ta
ngen
ts
betw
een
0o and
90o
iii) T
he te
ache
r to
guid
e st
uden
t to
disc
uss h
ow
to u
se ta
bles
to fi
nd
the
angl
e re
pres
entin
g a
give
n tri
gono
met
ric
ratio
.iv
) Stu
dent
s to
solv
e pr
oble
ms r
elat
ed to
fin
ding
ang
les o
f gi
ven
trigo
nom
etric
ra
tios.
Trig
onom
etric
tabl
esIs
the
stud
ent
able
to re
ad th
e tri
gono
met
ric
ratio
s usi
ng
trigo
nom
etric
ta
bles
?
5
(b)
Solv
e pr
oble
ms
invo
lvin
g tri
gono
met
ric
ratio
s usi
ng
trigo
nom
etric
ta
bles
i)
The
teac
her t
o de
mon
stra
te h
ow to
us
e tri
gono
met
ric
tabl
es to
solv
e re
late
d pr
oble
ms.
ii) S
tude
nts i
n gr
oups
to
do e
xerc
ises
invo
lvin
g tri
gono
met
ric ra
tios
Trig
onom
etric
tabl
esIs
the
stud
ent
able
to u
se
trigo
nom
etric
ta
bles
to so
lve
daily
life
pr
oble
ms?
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
9.4
Ang
les o
f El
evat
ion
and
Dep
ress
ion
The
stud
ent s
houl
d be
ab
le to
: (a
) Mea
sure
ang
les
of e
leva
tion
and
angl
es o
f de
pres
sion
i) T
he te
ache
r to
expl
ain
angl
es o
f ele
vatio
n an
d de
pres
sion
usi
ng
prac
tical
exa
mpl
es.
ii) T
he te
ache
r to
guid
e st
uden
ts to
mea
sure
an
gles
of e
leva
tions
an
d de
pres
sion
s usi
ng
clin
omet
ers.
i) T
rigon
omet
ric
tabl
esii)
C
linom
eter
siii
) R
ope
iv)
Trea
dle
whe
el
Is th
e st
uden
t ab
le to
mea
sure
an
gles
of
elev
atio
n an
d de
pres
sion
s?
6
(b) S
olve
pro
blem
s in
volv
ing
angl
es
of e
leva
tion
and
angl
es o
f de
pres
sion
.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
how
to fi
nd a
ngle
s of
ele
vatio
n an
d de
pres
sion
of d
ista
nt
obje
cts e
.g. h
eigh
t of
tree
s, to
wer
s and
bu
ildin
g.ii)
Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
cal
cula
te
the
heig
ht g
iven
th
e di
stan
ce to
the
obje
ct a
nd th
e an
gle
of e
leva
tion
or
depr
essi
on.
i) C
linom
eter
sii)
Mat
hem
atic
al
sets
iii)
Gra
ph p
aper
s iv
) Tr
igon
omet
ric
tabl
esv)
Ta
pe m
easu
re
vi)
Trun
dle
whe
el
vii)
Rop
e
Is th
e st
uden
t ab
le to
solv
e pr
oble
ms
invo
lvin
g an
gle
of e
leva
tion
and
depr
essi
on?
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RN
ING
ST
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EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nts t
o so
lve
prob
lem
s usi
ng
trigo
nom
etric
ratio
s an
d tri
gono
met
ric
tabl
es.
iv)
Stud
ents
to so
lve
prob
lem
s in
grou
ps
usin
g sc
ale
draw
ing
and
pres
ent t
heir
wor
k in
cla
ss.
10.0
SET
S10
.1 D
escr
iptio
n of
a se
tTh
e st
uden
t sho
uld
be a
ble
to(a
) D
efine
a se
t.
i) T
he te
ache
r to
use
obje
cts i
n th
e su
rrou
ndin
g to
ex
plai
n th
e co
ncep
t of
a se
t.ii)
Stu
dent
s to
brai
nsto
rm
on v
ario
us se
ts in
th
eir s
urro
undi
ng
i)
Rea
l obj
ects
ii)
Pict
ures
Is th
e st
uden
t ab
le to
defi
ne
set?
10
(b)
List
the
mem
bers
of
a se
t.i)
The
teac
her t
o sh
ow
stud
ents
set n
otat
ion.
ii)
The
teac
her t
o sh
ow
how
to u
se th
e se
t no
tatio
n.ii)
Stu
dent
s to
give
so
me
exam
ples
of
a se
t fro
m th
eir
surr
ound
ing
and
writ
e th
em u
sing
set
nota
tion.
i)
Play
ing
card
sii)
Te
ams o
f pl
ayer
s iii
) R
eal n
umbe
rsiv
) A
nim
als
Is th
e st
uden
t ab
le to
nam
e an
d lis
t the
mem
bers
of
a g
iven
set?
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ING
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EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Nam
e a
set.
i) T
he te
ache
r to
show
st
uden
ts h
ow to
nam
e se
ts.
ii) S
tude
nts t
o do
ex
erci
ses o
n na
min
g di
ffere
nt se
ts.
i)
Car
dii)
M
anila
shee
tIs
the
stud
ent
able
to n
ame
a se
t pro
perly
?
(d)
Des
crib
e se
ts
by li
stin
g an
d by
stat
ing
the
mem
bers
.
i) T
he te
ache
r to
dem
onst
rate
how
to
des
crib
e se
ts b
y w
ords
, lis
ting
and
form
ula,
ii) S
tude
nts t
o so
lve
ques
tions
invo
lvin
g se
t des
crip
tion
by
wor
ds, l
istin
g an
d fo
rmul
a.
Is th
e st
uden
t ab
le to
des
crib
e se
ts b
y lis
ting,
st
atin
g or
usi
ng
form
ula?
10.2
Typ
es o
f Se
tsTh
e st
uden
ts sh
ould
be
able
to:
(a)
Defi
ne a
uni
vers
al
set a
nd a
n em
pty
set.
i) T
he te
ache
r to
guid
e st
uden
t to
esta
blis
h th
e co
ncep
t of u
nive
rsal
se
t and
em
pty
set.
ii) S
tude
nts t
o so
lve
prob
lem
s rel
ated
to
em
pty
set a
nd
univ
ersa
l set
i)
Play
ing
card
sii)
Te
ams o
f pl
ayer
s iii
) R
eal n
umbe
rsiv
) D
inne
r set
s
Is th
e st
uden
t ab
le to
defi
ne
univ
ersa
l set
s an
d an
em
pty
set?
6
86
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Dis
tingu
ish
betw
een
finite
and
in
finite
sets
.
i) T
he te
ache
r to
guid
e st
uden
ts to
com
pare
fin
ite a
nd in
finite
sets
.ii)
Stu
dent
s to
com
pare
fin
ite a
nd in
finite
sets
i)
Play
ing
card
sii)
Te
ams o
f pl
ayer
siii
) R
eal n
umbe
rsiv
) D
inne
r set
Is th
e st
uden
tab
le to
di
stin
guis
h be
twee
n fin
ite
and
infin
ite se
ts?
(c)
Dis
tingu
ish
betw
een
equi
vale
nt a
nd
equa
l set
s
i) T
he te
ache
r to
guid
e st
uden
ts to
com
pare
se
ts in
ord
er to
de
term
ine
equi
vale
nt
and
equa
l set
s.ii)
Stu
dent
s to
com
pare
eq
uiva
lent
and
equ
al
sets
.
i)
Play
ing
card
sii)
Te
ams o
f pl
ayer
s iii
) R
eal n
umbe
rsiv
) D
inne
r set
Is th
e st
uden
t ab
le to
di
stin
guis
h be
twee
n eq
uiva
lent
and
eq
ual s
ets?
10.3
Sub
sets
The
stud
ent s
houl
d be
ab
le to
: (a
) Defi
ne a
subs
et.
i) T
he te
ache
r to
guid
e st
uden
ts to
use
ex
ampl
es to
form
su
bset
sii)
The
teac
her t
o gu
ide
stud
ents
to d
efine
a
subs
et.
iii) S
tude
nts t
o gi
ve
exam
ples
of s
ubse
ts in
th
eir s
urro
undi
ng
i)
Play
ing
card
sii)
Te
ams
iii)
Rea
l num
bers
iv)
Din
ner s
et
Is th
e st
uden
t ab
le to
defi
ne a
su
bset
?
10
87
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Lis
t sub
sets
of a
gi
ven
set
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w su
bset
s of a
set
can
be li
sted
.ii)
Stu
dent
s in
grou
ps to
do
exe
rcis
es o
n lis
ting
subs
ets o
f giv
en se
ts.
i)
Play
ing
card
sii)
T
eam
siii
) R
eal n
umbe
rs
iv)
Din
ner s
et
Is th
e st
uden
t ab
le to
list
su
bset
s of a
gi
ven
set?
(c)
Dis
tingu
ish
betw
een
prop
er
and
impr
oper
su
bset
s.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
the
mea
ning
of p
rope
r an
d im
prop
er su
bset
s us
ing
the
liste
d su
bset
s and
the
use
of
the
sym
bols
ii)
Stud
ents
to
do e
xerc
ises
to
diffe
rent
iate
pro
per
and
impr
oper
subs
ets.
i) P
layi
ng c
ards
ii) T
eam
s of p
laye
rsiii
) R
eal n
umbe
rsiv
) D
inne
r set
Is th
e st
uden
t ab
le to
di
stin
guis
h be
twee
n pr
oper
an
d im
prop
er
subs
ets?
(d)
Cal
cula
te th
e nu
mbe
r of s
ubse
ts
in a
set.
i) T
he te
ache
r to
lead
st
uden
ts to
dis
cuss
ho
w to
est
ablis
h th
e nu
mbe
r of s
ubse
ts o
f a
set w
ith n
mem
bers
as
2n .
ii) S
tude
nts t
o ap
ply
the
fo
rmul
a 2n t
o ca
lcul
ate
the
num
ber o
f sub
sets
fo
r a se
t with
n
elem
ents
.
i) P
layi
ng c
ards
ii) T
eam
s of p
laye
rs
iii)
Rea
l num
bers
iv
) D
inne
r set
Is th
e st
uden
t ab
le to
cal
cula
te
the
num
ber o
f su
bset
s in
a se
t?
88
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
10.4
Ope
ratio
ns
with
Set
sTh
e st
uden
ts sh
ould
be a
ble
to:
(a)
Fin
d un
ion
of tw
o se
ts.
i) T
he te
ache
r to
guid
e st
uden
ts to
use
real
lif
e ex
ampl
es to
di
scus
s the
uni
on o
f tw
o se
ts a
nd th
e us
e of
th
e sy
mbo
l .
ii) T
he te
ache
r to
guid
e st
uden
ts to
use
re
al li
fe e
xam
ples
to
dis
cuss
the
inte
rsec
tion
of tw
o se
ts a
nd th
e us
e of
the
sym
bol
.iii
) Stu
dent
s to
do
exer
cise
s inv
olvi
ng
the
unio
n an
d in
ters
ectio
n of
two
sets
.iv
) The
teac
her t
o gu
ide
stud
ents
to p
lay
gam
es o
n un
ion
and
inte
rsec
tion
of se
ts.
i)
Team
sii)
G
ames
iii
) O
bjec
tsiv
) P
layi
ng c
ards
v)
T
eam
s of
vi)
Pla
yers
vi
i) G
ames
vi
ii) O
bjec
tsix
) P
layi
ng c
ards
Is th
e st
uden
t ab
le to
find
un
ion
and
inte
rsec
tion
of
sets
?
6
b)
Fin
d th
e co
mpl
imen
t of a
se
t.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
find
the
com
plim
ent o
f a se
t gi
ven
a un
iver
sal s
et.
i)
Venn
dia
gram
ii)
Rea
l obj
ects
iii
) Fl
ip c
harts
iv
) C
olou
red
chal
ks
Is th
e st
uden
t ab
le to
find
the
com
plim
ent o
f a
set?
89
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts t
o do
ex
erci
ses i
nvol
ving
th
e co
mpl
imen
t of s
ets
(c)
Fin
d th
e nu
mbe
r of
ele
men
ts in
th
e un
ion
and
inte
rsec
tion
of tw
o se
ts.
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ul
nΑ∪Β
()=nΑ ()+n
Β () −nΑ∩Β
()
ii) S
tude
nts i
ndiv
idua
lly
to a
pply
the
form
ula
to so
lve
rela
ted
prob
lem
s
Is th
e st
uden
tab
le to
find
th
e nu
mbe
r of
elem
ents
in
the
unio
n an
d in
ters
ectio
nof
sets
?
10.5
Ven
n
D
iagr
ams
The
stud
ent s
houl
dbe
abl
e to
:(a
) R
epre
sent
a se
t by
usi
ng V
enn
diag
ram
s.
i) T
he te
ache
r to
illus
trate
ho
w to
repr
esen
t set
s us
ing
Venn
dia
gram
s.ii)
Stu
dent
s to
repr
esen
t se
ts b
y Ve
nn
diag
ram
s.
i) V
enn
diag
ram
sii)
Rea
l obj
ects
iii) C
olou
red
chal
ks
Is th
e st
uden
t ab
le to
repr
esen
t se
ts b
y us
ing
Venn
dia
gram
s?
8
(b)
Sol
ve p
robl
ems
on a
set b
y us
ing
Venn
dia
gram
s.
i) T
he te
ache
r to
guid
e st
uden
ts to
use
Ven
n di
agra
ms i
n so
lvin
g si
mpl
e pr
oble
ms
invo
lvin
g op
erat
ions
w
ith tw
o se
ts.
ii) S
tude
nts t
o so
lve
prob
lem
s inv
olvi
ng a
t m
ost t
wo
sets
usi
ng
Venn
dia
gram
.
i)
Venn
dia
gram
sii)
Te
ams o
f pl
ayer
s
Is th
e st
uden
t ab
le to
solv
e th
e pr
oble
ms o
n se
ts
by u
sing
Ven
n di
agra
ms?
90
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Inte
rpre
t in
form
atio
n fr
om
Venn
dia
gram
s.
i) S
tude
nts t
o so
lve
wor
d pr
oble
ms i
nvol
ving
op
erat
ions
on
sets
, co
mpl
imen
t of s
ets
and
Venn
dia
gram
s.ii)
The
teac
her t
o gu
ide
stud
ents
to e
xtra
ct
info
rmat
ion
from
Ve
nn d
iagr
ams.
i) V
enn
diag
ram
sii)
Col
oure
d ch
alks
iii) M
anila
pap
er
iv) M
arke
r pen
s
Is th
e st
uden
t ab
le to
inte
rpre
t in
form
atio
n fr
om V
enn
diag
ram
s?
11.0
ST
ATIS
TIC
S11
.1 P
icto
gram
sTh
e st
uden
t sho
uld
be
able
to:
(a) D
ispl
ay in
form
atio
n by
pic
togr
ams.
i)
The
teac
her t
o gu
ide
stud
ents
to c
olle
ct
data
e.g
. cla
ssro
om,
atte
ndan
ce, s
tude
nts,
ages
, hei
ghts
and
w
eigh
t, sc
hool
en
rolm
ent,
size
of
stud
ents
, fav
orite
dr
inks
, wai
st
mea
sure
men
ts.
ii) S
tude
nts t
o co
llect
raw
da
taiii
) The
teac
her t
o di
scus
s w
ith st
uden
ts h
ow
to re
pres
ent d
ata
by
pict
ogra
ms
iii)
Stud
ents
to re
pres
ent
data
by
usin
g pi
ctog
ram
s.
i) G
raph
pap
erii)
Mat
hem
atic
al se
t iii
) Obj
ects
iv) G
eobo
ard
v) R
ubbe
r ban
ds
Is th
e st
uden
tab
le to
dis
play
in
form
atio
n by
pi
ctog
ram
s?
4
91
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Inte
rpre
t pi
ctog
ram
si)
The
teac
her t
o di
scus
s with
stud
ents
ho
w to
inte
rpre
t pi
ctog
ram
s inv
olvi
ng
real
situ
atio
n in
thei
r su
rrou
ndin
gs.
ii) S
tude
nts i
n gr
oups
to
do e
xerc
ises
invo
lvin
g in
terp
reta
tion
of
pict
ogra
ms
i) T
ape
mea
sure
ii) W
eigh
ing
scal
es
iii) C
lass
jour
nals
iv) E
nrol
men
tv)
Reg
iste
r
Is th
e st
uden
t ab
le to
ext
ract
in
form
atio
n fr
om a
pi
ctog
ram
s?
11.2
Bar
Cha
rtsTh
e st
uden
t sho
uld
be a
ble
to:
(a)
Dra
w h
oriz
onta
l an
d ve
rtica
l bar
ch
arts
.
i) T
he te
ache
r to
show
st
uden
ts h
ow to
dra
w
bar c
harts
usi
ng
data
such
as a
cla
ss
atte
ndan
ce H
IV/A
IDS
deat
h ra
tes,
cash
cro
ps
and
scho
ol e
nrol
men
ts.
ii) S
tude
nts t
o dr
aw b
ar
char
ts u
sing
col
lect
ed
data
i)
Gra
ph p
aper
sii)
M
athe
mat
ical
in
stru
men
ts
Is th
e st
uden
tab
le to
dra
w
horiz
onta
l and
ve
rtica
l bar
ch
arts
?
4
(b) I
nter
pret
bar
cha
rts.
i) T
he te
ache
r to
guid
e a
disc
ussi
on o
n ho
w
to e
xtra
ct in
form
atio
n fr
om b
ar c
harts
.ii)
S
tude
nts i
n gr
oups
to
do
man
y ex
erci
ses
on in
terp
reta
tion
of
bar c
harts
and
con
duct
pe
er p
rese
ntat
ions
.
i) G
raph
pap
erii)
Mat
hem
atic
al
inst
rum
ents
iii
) Geo
boar
div
) R
ubbe
r ban
ds
Is th
e st
uden
t ab
le to
ext
ract
in
form
atio
n fr
om b
ar c
harts
?
92
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
11.3
Lin
e G
raph
sTh
e st
uden
ts sh
ould
be a
ble
to:
(a)
Rep
rese
nt d
ata
usin
g lin
e gr
aphs
i) T
he te
ache
r to
show
st
uden
ts h
ow to
dra
w
line
grap
hs u
sing
dat
a fr
om d
iffer
ent s
ourc
es.
ii) S
tude
nts t
o dr
aw
line
grap
hs u
sing
co
ntin
uous
dat
a su
ch
as te
mpe
ratu
res a
nd
heig
hts.
i)
Gra
ph p
aper
sii)
G
raph
boa
rdiii
) G
eobo
ard
iv)
Extra
cts f
rom
ne
wsp
aper
s.v)
R
ubbe
r ban
ds
Is th
e st
uden
tab
le to
repr
esen
t da
ta u
sing
line
gr
aphs
?
4
(b)
Inte
rpre
t lin
e gr
aphs
.i)
Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
inte
rpre
t dat
a fr
om th
e lin
e gr
aphs
.ii)
Stu
dent
s to
inte
rpre
t in
form
atio
n fr
om li
ne
grap
hs
Line
gra
phs
Is th
e st
uden
t ab
le to
inte
rpre
t da
ta fr
om
line
grap
hs
corr
ectly
?
11.4
Pie
Cha
rtTh
e st
uden
t sho
uld
be a
ble
to(a
) D
ispl
ay d
ata
usin
g pi
e ch
arts
.
i) T
he te
ache
r to
guid
e st
uden
ts to
cal
cula
te
angl
es o
f eac
h se
ctor
in
a p
ie c
hart
ii) T
he te
ache
r to
dem
onst
rate
how
to
draw
a p
ie c
hart
usin
g a
pair
of c
ompa
sses
an
d a
prot
ract
or.
i) C
olou
red
chal
ksii)
Rul
eriii
) Pro
tract
or
iv) A
pai
r of
com
pass
esv)
Col
oure
d pe
ncils
Is th
e st
uden
t ab
le to
dis
play
da
ta u
sing
pie
- ch
arts
?
4
93
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nts t
o pr
actic
e re
pres
entin
g da
ta o
r in
form
atio
n on
a p
ie
char
t
(b) I
nter
pret
pie
cha
rts.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
inte
rpre
t dat
a fr
om th
e pi
e ch
arts
.ii)
Stu
dent
s to
inte
rpre
t in
form
atio
n fr
om p
ie
char
ts
Pie
char
tsIs
the
stud
ent
able
to in
terp
ret
data
from
pie
ch
art c
orre
ctly
?
11.5
Fre
quen
cy
Dis
tribu
tion
Tabl
es
The
stud
ent s
houl
d be
ab
le to
:(a
) M
ake
freq
uenc
y di
strib
utio
n ta
bles
fr
om ra
w d
ata.
i) T
he te
ache
r to
show
stud
ents
how
to
repr
esen
t dat
a/
info
rmat
ion
usin
g fr
eque
ncy
dist
ribut
ion
tabl
es w
ith si
ngle
va
lues
and
with
gr
oupe
d va
lues
.ii)
Stu
dent
s to
prac
tice
on h
ow to
repr
esen
t da
ta u
sing
freq
uenc
y di
strib
utio
n ta
bles
Col
lect
ed d
ata
Is th
e st
uden
t ab
le to
mak
e a
freq
uenc
y di
strib
utio
n ta
ble
from
raw
dat
a?
4
94
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IC
OB
JEC
TIV
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Inte
rpre
t fre
quen
cy
dist
ribut
ion
tabl
es.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
inte
rpre
t fr
eque
ncy
dist
ribut
ion
tabl
es.
ii) S
tude
nts t
o do
ex
erci
ses i
nvol
ving
in
terp
reta
tion
of
freq
uenc
y di
strib
utio
n ta
bles
Col
lect
ed d
ata
Is th
e st
uden
t ab
le to
inte
rpre
t fr
eque
ncy
dist
ribut
ion
tabl
es?
11.6
Fr
eque
ncy
Poly
gons
The
stud
ent s
houl
dbe
abl
e to
:(a
) D
raw
freq
uenc
y po
lygo
ns fr
om
freq
uenc
y di
strib
utio
n ta
bles
.
i) T
he te
ache
r to
dem
onst
rate
how
to
dra
w fr
eque
ncy
poly
gons
usi
ng
freq
uenc
y di
strib
utio
n ta
bles
.ii)
Stu
dent
s to
prac
tice
draw
ing
freq
uenc
y po
lygo
ns to
repr
esen
t da
ta.
i)
Gra
ph p
aper
ii)
Mat
hem
atic
al
set
iii) C
olle
cted
dat
a
Is th
e st
uden
t ab
le to
repr
esen
t da
ta u
sing
fr
eque
ncy
poly
gons
?
4
(b)
Inte
rpre
t fre
quen
cy
poly
gons
i) T
he te
ache
r to
guid
e
stud
ents
to
in
terp
ret
freq
uenc
y po
lygo
ns.
ii) S
tude
nts
in
gr
oups
to
do
exer
cise
s on
inte
rpre
ting
freq
uenc
y po
lygo
ns
Freq
uenc
y po
lygo
nsIs
the
stud
ent
able
to in
terp
ret
freq
uenc
y po
lygo
ns
corr
ectly
?
95
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
11.7
His
togr
ams
The
stud
ents
shou
ldbe
abl
e to
:(a
) D
raw
his
togr
ams
from
freq
uenc
y di
strib
utio
n ta
ble.
i) T
he te
ache
r to
guid
e st
uden
ts to
dra
w
hist
ogra
ms u
sing
set
of d
ata
and
freq
uenc
y di
strib
utio
n ta
bles
.ii)
Stu
dent
s to
draw
ing
hist
ogra
ms u
sing
da
ta a
nd fr
eque
ncy
dist
ribut
ion
tabl
es
i)
Geo
boar
dii)
G
raph
pap
eriii
) C
olle
cted
dat
aiv
) M
athe
mat
ical
se
tv)
R
ubbe
r ban
ds
Is th
e st
uden
t ab
le to
dra
w
hist
ogra
ms f
rom
a
set o
f dat
a an
d a
freq
uenc
y di
strib
utio
n ta
ble?
4
(b)
Inte
rpre
t hi
stog
ram
si)
The
teac
her t
o gu
ide
stud
ents
to re
duce
in
form
atio
n fr
om
hist
ogra
ms.
ii) S
tude
nts t
o do
ex
erci
ses o
n in
terp
reta
tion
of
hist
ogra
ms
His
togr
ams
Is th
e st
uden
t ab
leto
ext
ract
cor
rect
in
form
atio
n fr
om
hist
ogra
ms?
11.8
Cum
ulat
ive
Freq
uenc
y C
urve
s
The
stud
ent s
houl
d be
able
to:
(a)
Dra
w c
umul
ativ
e fr
eque
ncy
curv
e fr
om a
cum
ulat
ive
freq
uenc
y di
strib
utio
n ta
ble.
i) T
he te
ache
r to
dem
onst
rate
how
to
cons
truct
cum
ulat
ive
f
requ
ency
dis
tribu
tion
tabl
es fr
om fr
eque
ncy
dist
ribut
ion
tabl
es.
ii) T
he te
ache
r to
guid
e st
uden
ts to
dra
w a
cu
mul
ativ
e fr
eque
ncy
curv
e by
usi
ng a
cu
mul
ativ
e fr
eque
ncy
dist
ribut
ion
tabl
e.
i)
Gra
ph p
aper
ii)
Mat
hem
atic
alIs
the
stud
ent
able
to d
raw
cu
mul
ativ
e fr
eque
ncy
curv
e fr
om a
fr
eque
ncy
tabl
e?
4
96
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nts t
o do
ex
erci
ses i
nvol
ving
dr
awin
g cu
mul
ativ
e fr
eque
ncy
curv
es(b
) In
terp
ret a
cu
mul
ativ
e fr
eque
ncy
curv
e.
i) T
he te
ache
r to
guid
e st
uden
ts to
ded
uce
info
rmat
ion
from
cu
mul
ativ
e fr
eque
ncy
dist
ribut
ion
tabl
e an
d a
cum
ulat
ive
freq
uenc
y cu
rve.
ii) S
tude
nts i
n gr
oup
to
inte
rpre
t cum
ulat
ive
freq
uenc
y di
strib
utio
n ta
bles
and
cum
ulat
ive
freq
uenc
y cu
rves
i)
Gra
ph p
aper
ii)
Gra
phs f
rom
pa
pers
and
jo
urna
ls
Is th
e st
uden
t ab
le to
inte
rpre
t a
cum
ulat
ive
freq
uenc
y cu
rve?
97
FORM THREE
CLASS LEVEL COMPETENCESStudent should have the ability to:
1. Use Mathematical knowledge, skills and concepts in solving real life related problems.
2. Analyse and interpret statistical data.3. Generate sequences and series.4. Prove circle theorems.5. Prepare simple trading account.6. Draw graphs.
CLASS LEVEL OBJECTIVESBy the end of Form Three course the student should be able to:
1. Apply the knowledge on rates and variation in real life situations2. Locate places on the earth’s surface and find the distance between any two places.3. Represent data statistically and draw conclusions from numerical statistical
information (mean, mode and medium).4. Apply computations on sequences and series to discover mathematical patterns
and solve problems on compound interest.5. Draw graphs of relations and functions and identify their properties6. Prove and apply circle theorems7. Solve real life problems involving double entry and trial balance.
98
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
1.0
REL
ATIO
NS
1.1
Rel
atio
nsTh
e st
uden
ts sh
ould
be
able
to:
(a)
Find
rela
tions
be
twee
n tw
o se
ts.
i) T
he te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
on
var
ious
rela
tions
in
volv
ing
two
grou
ps
in re
al li
fe si
tuat
ions
.ii)
The
teac
her t
o pr
epar
e gu
ide
lines
for a
role
pl
ay.
iii)
Stud
ents
to p
erfo
rm
a ro
le p
lay
in o
rder
to
defin
e th
e re
latio
ns.
i) C
olou
red
chal
ksii)
Rea
l obj
ects
Is th
e st
uden
t abl
e to
find
rela
tions
be
twee
n tw
o se
ts?
8
(b)
Find
rela
tions
be
twee
n m
embe
rs
in a
set.
i) Th
e te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
on
var
ious
rela
tions
be
twee
n m
embe
rs o
f tw
o se
ts in
real
life
si
tuat
ion.
ii) T
he te
ache
r to
dem
onst
rate
how
to
use
a re
latio
n no
tatio
n to
repr
esen
t a re
latio
n.
iii)
Stud
ents
to p
ract
ice
on h
ow to
repr
esen
t a
rela
tion
usin
g re
latio
ns
nota
tion
iv) S
tude
nts t
o pe
rfor
m
role
pla
y in
ord
er to
de
fine
mem
bers
of t
wo
sets
i) C
olou
red
chal
ksii)
M
anila
pap
eriii
) M
arke
r pen
siv
) R
eal o
bjec
ts
i) Is
the
stud
ent
able
to fi
nd
rela
tions
be
twee
n m
embe
rs in
a
set?
ii) Is
the
stud
ent
able
to w
rite
rela
tions
usi
ng
nota
tions
?
99
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OPI
CS
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IC
OB
JEC
TIV
ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Dem
onst
rate
re
latio
ns p
icto
rially
i) T
he te
ache
r to
dem
onst
rate
how
to
draw
arr
ows t
o re
late
m
embe
rs o
f set
s in
a re
latio
n.ii)
St
uden
ts to
illu
stra
te
rela
tions
by
pict
oria
l pr
esen
tatio
ns.
i)
Col
oure
d ch
alks
ii)
M
anila
pap
eriii
) Mar
ker p
ens
Is th
e st
uden
t ab
le d
emon
stra
te
rela
tions
pi
ctor
ially
?
1.2
Gra
ph o
f a
Rel
atio
nTh
e st
uden
t sho
uld
be
able
to d
raw
a g
raph
of
a re
latio
n re
pres
ente
d by
a li
near
ineq
ualit
y.
i) T
he te
ache
r to
guid
e st
uden
ts th
roug
h qu
estio
ns a
nd a
nsw
ers
to p
lot a
gra
ph o
f a
rela
tion
in th
e co
ordi
nate
syst
em.
ii) S
tude
nts i
n gr
oups
to
dra
w a
gra
ph o
f a
linea
r ine
qual
ityiii
) Stu
dent
s ind
ivid
ually
to
dra
w g
raph
s of
linea
r ine
qual
ities
.
i) G
raph
-pap
ers
ii) M
athe
mat
ical
in
stru
men
tsiii
) Squ
ared
pap
ers
iv) G
raph
s boa
rdv)
Geo
boar
dvi
) Rub
ber b
ands
Is th
e st
uden
t abl
e to
dra
w th
e gr
aph
of a
rela
tion?
6
1.3
Dom
ain
and
Ran
ge o
f a
Rel
atio
n
The
stud
ent s
houl
d be
ab
le to
:(a
) St
ate
the
dom
ain
of
a re
latio
n.
i) T
he te
ache
r to
guid
e st
uden
ts to
show
the
dom
ain
of a
rela
tion
by u
sing
pic
toria
l re
pres
enta
tion.
ii) S
tude
nts t
o sh
ow a
nd
stat
e th
e do
mai
n fr
om
grap
hs a
nd p
icto
rial
repr
esen
tatio
n.
i) C
olou
red
chal
ksii)
G
raph
pap
ers
iii)
Gra
ph b
oard
iv)
Geo
boar
dv)
Sq
uare
d pa
per
vi)
Rub
ber b
ands
Is th
e st
uden
t abl
e to
stat
e th
e do
mai
n of
a re
latio
n?
6
100
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nts t
o do
ex
erci
ses r
elat
ed to
do
mai
n of
rela
tion
(b)
Stat
e th
e ra
nge
of a
re
latio
n.i)
The
teac
her t
o gu
ide
stud
ents
to
show
the
rang
e of
a re
latio
n fr
om
grap
hs a
nd p
icto
rial
repr
esen
tatio
n.ii)
Stu
dent
s ind
ivid
ually
to
find
and
stat
e th
e ra
nge
of a
rela
tion
from
pic
toria
l re
pres
enta
tions
and
gr
aphs
.iii
) Stu
dent
s to
solv
e pr
oble
ms r
elat
ed to
ra
nge
of a
rela
tion.
i)
Gra
phs
ii) I
llust
ratio
ns o
f re
latio
nsiii
) Rub
ber b
ands
iv) M
anila
pap
er
v) M
arke
r pen
s.
Is th
e st
uden
t abl
e to
stat
e th
e ra
nge
of a
rela
tion?
1.4
Inve
rse
of a
R
elat
ion
The
stud
ent s
houl
d be
ab
le to
:(a
) Ex
plai
n th
e in
vers
e of
a re
latio
n.
i) T
he te
ache
r thr
ough
qu
estio
ns a
nd a
nsw
ers
to g
uide
a d
iscu
ssio
n on
the
inve
rse
of a
re
latio
n an
d th
e us
e of
th
e in
vers
e no
tatio
nii)
Stu
dent
s ind
ivid
ually
to
exp
lain
the
inve
rse
of re
latio
ns u
sing
the
inve
rse
nota
tion
i)
Gra
ph p
aper
ii)
Illus
tratio
ns o
f re
latio
nsiii
) Sq
uare
d pa
per
iv)
Geo
boar
dv)
R
ubbe
r ban
ds
Is th
e st
uden
t ab
le to
exp
lain
th
e in
vers
e of
a
rela
tion?
10
101
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Show
the
inve
rse
of a
rela
tion
pict
oria
lly.
i) Th
e te
ache
r to
show
st
uden
ts th
e in
vers
e of
a re
latio
n by
usi
ng
pict
ures
.ii)
Stu
dent
s in
grou
ps to
pr
actic
e on
show
ing
the
inve
rse
of a
rela
tion
pict
oria
lly
i) C
olou
red
chal
ks
ii) I
llust
ratio
n of
re
latio
nsiii
) Man
ila p
aper
iv
) M
arke
r pen
s
Is th
e st
uden
t ab
le to
show
th
e in
vers
e of
a re
latio
n pi
ctor
ially
?
(c)
Find
the
inve
rse
of
a re
latio
n.i)
The
teac
her t
o gu
ide
the
stud
ents
in fi
ndin
g th
e in
vers
e of
a
rela
tion.
ii)
Stud
ents
indi
vidu
ally
to
solv
e pr
oble
ms
whi
ch in
volv
e th
e in
vers
e of
rela
tion
in
real
life
situ
atio
ns.
i) C
olou
red
chal
ks
ii) I
llust
ratio
ns o
f re
latio
nsiii
) Man
ila p
aper
iv)
Mar
ker p
ens
Is th
e st
uden
t abl
e to
find
the
inve
rse
of a
rela
tion?
(d)
Dra
w a
gra
ph o
f th
e in
vers
e of
a
rela
tion.
i) T
he te
ache
r to
dem
onst
rate
how
to
draw
the
grap
h of
the
inve
rse
of a
rela
tion
ii) S
tude
nts i
n gr
oups
to
draw
the
inve
rse
of a
re
latio
niii
) Stu
dent
s ind
ivid
ually
to
dra
w g
raph
s of t
he
inve
rse
of re
latio
ns
i) G
raph
pap
er
ii) G
raph
boa
rdiii
) Mat
hem
atic
al
inst
rum
ent
iv) C
olou
red
chal
kv)
Geo
boar
dvi
) Squ
ared
pap
er
Is th
e st
uden
t abl
e to
dra
w th
e gr
aph
of th
e in
vers
e of
a
rela
tion?
102
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
2.0
FUN
CTI
ON
S2.
1 R
epre
sent
atio
n of
a fu
nctio
nTh
e st
uden
t sho
uld
be
able
to:
(a)
Expl
ain
the
conc
ept
of a
func
tion.
i) T
he te
ache
r to
guid
e st
uden
ts th
roug
h qu
estio
ns a
nd a
nsw
ers
to d
iscu
ss th
e co
ncep
t of
a fu
nctio
n.ii)
The
teac
her t
o de
mon
stra
te h
ow to
us
e fu
nctio
n no
tatio
n to
repr
esen
t a fu
nctio
n.
iii) S
tude
nts i
ndiv
idua
lly
to so
lve
prob
lem
s re
late
d to
the
conc
ept
of a
func
tion
and
the
use
i)
Rub
ber b
ands
ii)
M
anila
pap
er
iii)
Mar
ker p
ens
Is th
e st
uden
t abl
e to
exp
lain
con
cept
of
the
func
tion?
8
(b)
Rep
rese
nt fu
nctio
ns
pict
oria
lly.
i)
The
teac
her t
o de
mon
stra
te h
ow to
re
pres
ent f
unct
ions
pi
ctor
ially
.ii)
St
uden
ts in
divi
dual
ly
to re
pres
ent f
unct
ions
pi
ctor
ially
.
i) C
olou
red
chal
ksii)
Pic
ture
s/
illus
tratio
ns o
f fu
nctio
ns
Is th
e st
uden
t ab
le to
illu
stra
te
func
tions
pi
ctor
ially
?
(c)
Iden
tify
func
tions
am
ong
rela
tions
i) T
he te
ache
r to
guid
e st
uden
ts th
roug
h qu
estio
ns a
nd a
nsw
ers
to d
iscu
ss c
ondi
tions
fo
r a re
latio
n to
be
a fu
nctio
n
i)
Pict
ures
and
ill
ustra
tions
ii)
G
raph
siii
) M
anila
pap
eriv
) M
arke
r pen
s
Is th
e st
uden
t abl
eto
iden
tify
func
tions
am
ong
rela
tions
?
103
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts i
n gr
oups
to
iden
tify
func
tions
am
ong
rela
tions
.
2.2
Dom
ain
and
Ran
ge o
f a
Func
tion
The
stud
ent s
houl
d be
able
to:
(a)
Stat
e th
e do
mai
n of
a
func
tion
i)
The
teac
her,
thro
ugh
ques
tion
and
answ
ers
to g
uide
a d
iscu
ssio
n on
iden
tifyi
ng th
e do
mai
n of
func
tions
.ii)
St
uden
ts to
do
exer
cise
s rel
atin
g to
the
dom
ain
of
func
tions
.
i) I
llust
ratio
ns o
f fu
nctio
nsii)
C
olou
red
chal
ks
iii)
Man
ila p
aper
iv)
Mar
ker p
ens
Is th
e st
uden
t ab
le to
stat
e th
e do
mai
n of
a
func
tion?
6
(b)
Stat
e th
e ra
nge
of a
fu
nctio
ni)
The
teac
her t
hrou
gh
ques
tions
and
ans
wer
s, to
gui
de a
dis
cuss
ion
on th
e ra
nge
of
func
tions
.ii)
Stu
dent
to d
o ex
erci
ses
rela
ting
to th
e ra
nge
of
func
tions
.
i)
Illus
tratio
ns o
f fu
nctio
nsii)
C
olou
red
chal
ks
iii)
Man
ila p
aper
iv)
Mar
ker p
ens
Is th
e st
uden
t abl
e to
stat
e th
e ra
nge
of a
func
tion?
2.3
Gra
phic
func
tion
The
stud
ent s
houl
d be
ab
le to
dra
w g
raph
s of
func
tions
.
i)
The
teac
her t
o gu
ide
stud
ents
to
draw
the
grap
hs o
f st
ep fu
nctio
ns a
nd
poly
nom
ial f
unct
ions
up
to th
e th
ird d
egre
e.
i)
Gra
ph p
aper
ii)
M
athe
mat
ical
in
stru
men
tsiii
) Col
oure
d ch
alks
iv
) Sq
uare
d pa
per
Is th
e st
uden
t abl
eto
dra
w g
raph
of
the
func
tions
?
6
104
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts t
o dr
aw
the
grap
hs o
f ste
p fu
nctio
ns a
nd
poly
nom
ial f
unct
ions
up
to th
e th
ird d
egre
e.iii
) The
teac
her t
o gu
ide
st
uden
ts to
dis
cuss
the
beha
vior
of g
raph
s of
func
tions
.iv
) Stu
dent
s to
stat
e th
e be
havi
or o
f gra
phs o
f fu
nctio
ns.
2.4
Inve
rse
of a
Fu
nctio
nTh
e st
uden
t sho
uld
be
able
to:
(a) E
xpla
in th
e in
vers
e of
a fu
nctio
n.
i) T
he te
ache
r to
expl
ain
the
inve
rse
of
func
tions
and
the
use
of th
e in
vers
e fu
nctio
n no
tatio
n.ii)
Stu
dent
s to
do
exer
cise
s inv
olvi
ng
inve
rse
of fu
nctio
ns.
i)
Gra
phs
ii)
Pic
ture
s or
illus
tratio
ns o
f fu
nctio
nsiii
) C
olou
red
cha
lks
iv)
Man
ila p
aper
Is th
e st
uden
t ab
le to
exp
lain
th
e in
vers
e of
a
func
tion?
12
(b) S
how
the
inve
rse
of a
func
tion
pict
oria
lly.
i) T
he te
ache
r to
guid
e st
uden
ts to
show
the
inve
rse
of a
func
tion
pict
oria
llyii)
Stu
dent
s to
expl
ain
the
beha
vior
of p
ictu
res o
f in
vers
es o
f one
to o
ne
func
tions
.
i)
Col
oure
d ch
alks
ii)
Illus
tratio
n of
a
f
unct
ion
iii)
Man
ila p
aper
iv)
Mar
ker p
ens
Is th
e st
uden
t ab
le to
illu
stra
te
inve
rse
func
tions
pi
ctor
ially
?
105
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nts t
o dr
aw
pict
ures
of i
nver
se
func
tions
.
(c)
Find
the
inve
rse
of
a fu
nctio
n.i)
Th
e te
ache
r to
guid
e st
uden
ts to
find
the
inve
rse
of a
func
tion
ii) S
tude
nts i
n gr
oups
to
find
the
inve
rse
of
func
tions
iii)
Stud
ents
to p
rese
nt
grou
p w
ork
on in
vers
e fu
nctio
nsiv
) Stu
dent
s to
solv
e pr
oble
ms i
nvol
ving
in
vers
e of
func
tions
in
real
life
situ
atio
n
i)
Col
oure
d ch
alks
ii)
G
eobo
ard
iii)
Gra
ph p
aper
s iv
) Sq
uare
d pa
per
v)
Rub
ber b
ands
Is th
e st
uden
t abl
e to
find
the
inve
rse
of a
func
tion?
(d)
Dra
w a
gra
ph o
f th
e in
vers
e of
a
func
tion.
i) Th
e te
ache
r to
dem
onst
rate
how
to
draw
the
grap
h of
the
inve
rse
of a
func
tion.
ii)
Stud
ents
in g
roup
s to
draw
gra
phs o
f inv
erse
of
func
tions
.iii
) St
uden
t to
pres
ent
grou
p w
ork
on g
raph
s an
d di
scus
s the
ir pr
oper
ties.
i) G
raph
pap
ers/
bo
ard
ii)
Squ
ared
pap
er
iii)
Geo
boar
div
) R
ubbe
r ban
ds
Is th
e st
uden
t abl
e to
dra
w g
raph
s of
inve
rse
func
tions
?
106
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv) S
tude
nts i
ndiv
idua
lly
to d
raw
the
grap
h of
in
vers
e of
a fu
nctio
n.(e
) St
ate
the
dom
ain
and
rang
e of
in
vers
e of
fu
nctio
ns.
i) St
uden
ts in
gro
ups t
o di
scus
s the
con
cept
of
dom
ain
and
rang
e of
in
vers
e fu
nctio
ns.
ii)
The
teac
her t
o gu
ide
stud
ents
to st
ate
dom
ain
and
rang
e of
inve
rse
func
tions
fr
om p
icto
rial
repr
esen
tatio
ns a
nd
grap
hs.
iii)
Stud
ents
to so
lve
prob
lem
s on
iden
tifyi
ng a
nd st
atin
g th
e do
mai
n an
d ra
nge
of in
vers
e fu
nctio
ns.
i)
Gra
phs
ii)
Pict
oria
l ill
ustra
tions
of
func
tions
iii)
Mar
ker p
ens
iv)
Man
ila p
aper
Is th
e st
uden
t ab
le to
stat
e th
e do
mai
n an
d ra
nge
of in
vers
e of
fu
nctio
ns?
3.0
STAT
ISTI
CS
3.1
Mea
nTh
e st
uden
t sho
uld
be
able
to:
(a)
Cal
cula
te th
e m
ean
from
a se
t of
dat
a, fr
eque
ncy
dist
ribut
ion
tabl
e an
d hi
stog
ram
.
i) Th
e te
ache
r to
guid
e st
uden
ts to
obt
ain
stat
istic
al d
ata
such
as
HIV
/ AID
S, R
oad
Safe
ty E
duca
tion,
C
hild
Lab
our a
nd
Gen
der
ii) T
he te
ache
r to
guid
e th
e st
uden
ts to
use
i) G
raph
pap
erii)
Squ
ared
pap
eriii
) Sq
uare
d bo
ards
/ pap
ers
iv)
Geo
boar
dv)
R
ubbe
r ban
dsvi
) C
alcu
lato
rs
Is th
e st
uden
t ab
le to
cal
cula
te
the
mea
n fr
om a
se
t of d
ata
from
a
freq
uenc
y di
strib
utio
n ta
ble
and
hist
ogra
m?
8
107
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
the
data
obt
aine
d to
ex
plai
n th
e co
ncep
t of
mea
n.iii
) T
he te
ache
r to
guid
e st
uden
ts to
cal
cula
te
the
mea
n fr
om
freq
uenc
y di
strib
utio
n fo
r ung
roup
ed a
nd
grou
ped
data
iv)
Stud
ents
to c
alcu
late
th
e m
ean
give
n fr
eque
ncy
dist
ribut
ion
tabl
es.
v)
The
teac
her t
o gu
ide
stud
ents
to c
alcu
late
th
e m
ean
from
hi
stog
ram
svi
) St
uden
ts to
cal
cula
te
the
mea
n fr
om
hist
ogra
ms.
(vii)
Stu
dent
s to
com
pare
th
e m
ean
obta
in fr
om
data
, fr
eque
ncy
dist
ribut
ion
tabl
es a
nd h
isto
gram
.(v
iii)S
tude
nts t
o ca
lcul
ate
the
mea
n us
ing
data
from
real
life
si
tuat
ion
Cha
rt w
ith d
ata
of
H I
V/ A
I D
S ro
ad
safe
ty
educ
atio
n , c
hild
la
bour
, gen
der
108
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Inte
rpre
t the
mea
n ob
tain
ed fr
om a
set
of d
ata,
freq
uenc
y di
strib
utio
n ta
bles
an
d hi
stog
ram
.
i) St
uden
ts in
gro
ups
to in
terp
ret t
he
mea
n ob
tain
ed fr
om
stat
istic
al d
ata
on
HIV
/AID
S, R
oad
safe
ty e
duca
tion,
chi
ld
labo
ur, g
ende
r.ii)
Stu
dent
s to
com
pare
th
e m
ean
obta
ined
fr
om ra
w d
ata,
fr
eque
ncy
dist
ribut
ions
an
d hi
stog
ram
s.iii
) E
ach
grou
p to
pre
sent
th
eir fi
ndin
gs in
cla
ss.
iv)
The
teac
her t
o le
ad th
e di
scus
sion
afte
r the
pr
esen
tatio
n.
Cha
rt w
ith
stat
istic
al re
ports
on
HIV
/ AID
S,
gend
er, r
oad
safe
ty e
duca
tion,
en
viro
nmen
t, ch
ild
labo
ur.
Is th
e st
uden
t abl
e to
inte
rpre
t the
m
ean?
3.2
Med
ian
The
stud
ent s
houl
d be
ab
le to
:(a
) Exp
lain
the
conc
ept
of m
edia
n.
i) T
he te
ache
r to
guid
e st
uden
ts to
use
the
data
obt
aine
d
to
expl
ain
the
conc
ept o
f m
edia
nii)
Stu
dent
s to
iden
tify
and
stat
e th
e m
edia
n fr
om ra
w st
atis
tical
da
ta.
i)
Gra
ph p
aper
s ii)
G
raph
boa
rd
iii) S
quar
ed p
aper
iv)
Geo
met
rical
inst
rum
ents
Is th
e st
uden
t ab
le to
exp
lain
th
e co
ncep
t of
med
ian?
10
109
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) C
alcu
late
the
med
ian
from
a se
t of
dat
a.
i) Th
e te
ache
r to
guid
e st
uden
ts to
cal
cula
te
the
med
ian
from
un
grou
ped
data
. ii)
Stu
dent
s to
solv
e pr
oble
ms i
nvol
ving
ca
lcul
atin
g th
e m
edia
n fr
om u
ngro
uped
dat
a
Cha
rt w
ith
stat
istic
al d
ata
Is th
e st
uden
t ab
le to
cal
cula
te
the
med
ian
from
un
grou
ped
data
?
(c)
Find
the
med
ian
usin
g fr
eque
ncy
dist
ribut
ion
tabl
es
and
cum
ulat
ive
curv
e.
i) Th
e te
ache
r to
guid
e st
uden
ts to
est
imat
e th
e m
edia
n fr
om
freq
uenc
y di
strib
utio
n ta
bles
and
cum
ulat
ive
curv
e.ii)
Stu
dent
s in
grou
ps to
fin
d th
e m
edia
n us
ing
freq
uenc
y di
strib
utio
n ta
bles
of s
ingl
e an
d gr
oupe
d da
ta a
nd
cum
ulat
ive
curv
e.iii
) St
uden
ts to
pre
sent
th
eir w
ork
in c
lass
iv)
The
teac
her t
o gu
ide
the
disc
ussi
on o
n th
e gr
oup
pres
enta
tion.
i)
Gra
ph p
aper
ii)
Squa
red
pape
r iii
) G
raph
boa
rdiv
) G
eobo
ard
v)
Rub
ber b
ands
vi)
Col
oure
d ch
alks
Is th
e st
uden
t abl
e to
find
the
med
ian
usin
g fr
eque
ncy
dist
ribut
ion
tabl
e an
d cu
mul
ativ
e cu
rve?
110
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AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d) I
nter
pret
the
med
ian
obta
ined
from
the
data
.
i) St
uden
ts in
gro
ups t
o in
terp
ret t
he m
edia
n ob
tain
ed fr
om th
e st
atis
tical
dat
aii)
The
teac
her t
o gu
ide
stud
ents
to p
rese
nt
thei
r gro
up w
ork
in
clas
siii
) St
uden
ts in
divi
dual
ly
to so
lve
prob
lem
s in
volv
ing
med
ian
i)
Gra
phs
ii)
Cha
rts w
ith
stat
istic
al d
ata
on H
IV/A
IDS,
ro
ad sa
fety
ed
ucat
ion,
ge
nder
, en
viro
nmen
t, ch
ild la
bour
iii) G
raph
pa
per/b
oard
Is th
e st
uden
t abl
e to
inte
rpre
t the
m
edia
n?
3.3
Mod
eTh
e st
uden
t sho
uld
be
able
to:
(a) E
xpla
in th
e co
ncep
t of
mod
e.
i) Th
e te
ache
r to
guid
e st
uden
ts to
us
e st
atis
tical
dat
a ob
tain
ed to
exp
lain
the
conc
ept o
f mod
e.ii)
Stu
dent
s to
iden
tify
and
stat
e th
e m
ode
from
stat
istic
al d
ata
Cha
rt w
ith d
iffer
ent
stat
istic
al d
ata
Is th
e st
uden
t abl
e to
exp
lain
the
conc
ept o
f mod
e?
12
(b) C
alcu
late
the
mod
e.i)
The
teac
her t
o gu
ide
stud
ents
to c
alcu
late
th
e m
ode
from
a se
t of
data
ii) S
tude
nts t
o ca
lcul
ate
the
mod
e fr
om
grou
ped
data
i) S
quar
ed p
aper
ii) G
eobo
ard
iii) C
olou
red
ch
alks
iv
) Gra
ph p
aper
/bo
ard
v) R
ubbe
r ban
ds
Is th
e st
uden
t abl
e to
cal
cula
te th
e m
ode
and
mod
al
clas
s fro
m a
set o
f da
ta?
111
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii)
The
teac
her t
o gu
ide
stud
ents
to id
entif
y th
e m
odal
cla
ssiv
) St
uden
ts to
use
mod
al
clas
s to
estim
ate
the
mod
e.(c
) Fi
nd th
e m
ode
usin
g fr
eque
ncy
dist
ribut
ion
tabl
e an
d a
hist
ogra
m.
i) T
he te
ache
r to
guid
e st
uden
ts to
est
imat
e th
e m
ode
from
a
hist
ogra
m a
nd a
fr
eque
ncy
dist
ribut
ion
tabl
e.ii)
Stu
dent
s in
grou
ps to
fin
d th
e m
ode
from
fr
eque
ncy
dist
ribut
ion
tabl
es a
nd h
isto
gram
s.
i)
Squa
red
pape
rii)
G
eobo
ard
iii)
Col
oure
d
chal
ks
iv)
Rub
ber b
ands
v)
M
anila
pap
er
vi)
Mar
ker p
ens
vii)
Gra
ph p
aper
Is th
e st
uden
t abl
e to
find
the
mod
e us
ing
a fr
eque
ncy
dist
ribut
ion
tabl
e an
d hi
stog
ram
?
(d)
Inte
rpre
t the
mod
e ob
tain
ed fr
om th
e da
ta
i) S
tude
nts i
n gr
oups
to
inte
rpre
t the
mod
e ob
tain
ed fr
om a
set o
f da
ta, d
istri
butio
ns a
nd
hist
ogra
ms.
ii) S
tude
nts i
ndiv
idua
lly
to so
lve
prob
lem
s in
volv
ing
the
mod
e an
d m
odal
-cla
ss.
i) S
tatis
tical
gra
ph
ii) C
harts
with
st
atis
tical
dat
a
Is th
e st
uden
t abl
e to
inte
rpre
t the
m
ode?
112
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
4.0
RAT
ES A
ND
VAR
IATI
ON
S4.
1 R
ates
The
stud
ents
shou
ld b
e ab
le to
:(a
) R
elat
e ra
tes o
f qu
antit
ies o
f di
ffere
nt k
inds
.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e di
ffere
nt k
inds
of
rate
s in
orde
r to
rela
te
quan
titie
s.ii)
St
uden
ts to
solv
e pr
oble
ms o
n di
ffere
nt
kind
s of r
ates
.
Obj
ects
of d
iffer
ent
kind
sIs
the
stud
ent a
ble
to re
late
qua
ntiti
es
of d
iffer
ent k
inds
?
8
(b) R
elat
e qu
antit
ies o
f th
e sa
me
kind
.i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
the
sam
e ki
nd o
f ra
tes i
n or
der t
o re
late
qu
antit
ies.
i) D
iffer
ent
curr
enci
esii)
Obj
ects
of t
he
sam
e ki
nd
Is th
e st
uden
t abl
e to
rela
te q
uant
ities
of
the
sam
e ki
nd?
(c)
Con
vert
Tanz
ania
n cu
rren
cy in
to o
ther
cu
rren
cies
.
i)
The
teac
her a
nd
stud
ents
to o
btai
n cu
rren
cy c
onve
rsio
n ra
tes f
rom
new
spap
ers,
mag
azin
es, r
adio
, TV,
ba
nks,
post
offi
ce.
ii) T
he te
ache
r to
guid
e st
uden
ts to
col
lect
di
ffere
nt c
urre
ncie
s iii
) The
teac
her t
o sh
ow
stud
ents
how
to
conv
ert T
anza
nian
sh
illin
gs in
to o
ther
cu
rren
cies
and
vic
e ve
rsa
i)
New
spap
ers
ii)
Mag
azin
es
iii)
Tele
visi
oniv
) R
adio
v)
Diff
eren
t cu
rren
cies
Is th
e st
uden
t ab
le to
con
vert
Tanz
ania
n cu
rren
cy in
to
othe
r cur
renc
ies?
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
to c
onve
rt Ta
nzan
ian
shill
ings
to
othe
r cur
renc
ies a
nd
vice
ver
sa.
4.2
Varia
tion
The
stud
ent s
houl
d be
ab
le to
:(a
) Exp
lain
the
conc
ept
of d
irect
var
iatio
n.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
ings
whi
ch v
ary
dire
ctly
.ii)
The
teac
her t
o gu
ide
stud
ents
to w
rite
dire
ct
prop
ortio
n in
sym
bolic
fo
rmiii
) Stu
dent
s to
use
the
sym
bol o
f dire
ct
prop
ortio
n in
writ
ing
prop
ortio
ns.
i) M
anila
pape
rii)
Mar
ker p
ens
iii) P
hysi
cal
obje
cts
Is th
e st
uden
t abl
e to
exp
lain
the
conc
ept o
f dire
ct
varia
tion?
20
(b) S
olve
pro
blem
s on
dire
ct v
aria
tion.
i)
The
teac
her t
o gu
ide
stud
ents
in fo
rmin
g an
d so
lvin
g eq
uatio
ns
from
dire
ct v
aria
tion
ii)
Stud
ents
to so
lve
ques
tions
from
dire
ct
varia
tion
Phys
ical
obj
ects
Is th
e st
uden
t abl
eto
solv
e pr
oble
ms
on d
irect
va
riatio
n?
114
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Dra
w g
raph
s of
dire
ct v
aria
tion.
i) Th
e te
ache
r thr
ough
qu
estio
ns a
nd a
nsw
ers
to g
uide
stud
ents
to
draw
gra
phs o
f dire
ct
varia
tions
.ii)
St
uden
ts to
dra
w
grap
hs o
f dire
ct
varia
tions
iii)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss th
e be
havi
or o
f the
gra
phs
of d
irect
var
iatio
ns
i) G
raph
pap
ers/
boar
dii)
Mat
hem
atic
al
inst
rum
ents
iii) C
olou
red
chal
ksiv
) Geo
boar
dv)
R
ubbe
r ban
ds
Is th
e st
uden
t abl
e to
dra
w g
raph
s of
dire
ct v
aria
tions
?
(d) E
xpla
in th
e co
ncep
t of
inve
rse
varia
tion.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
ings
whi
ch v
ary
inve
rsel
y.ii)
The
teac
her t
o gu
ide
stud
ents
to w
rite
inve
rse
prop
ortio
ns in
sy
mbo
lic fo
rmiii
) St
uden
ts to
use
the
sym
bols
α to
writ
e in
vers
es p
ropo
rtion
s
i) Ph
ysic
al o
bjec
ts
ii)
Man
ila p
aper
iii)
Mar
ker p
ens
Is th
e st
uden
t abl
e to
exp
lain
the
conc
ept o
f inv
erse
va
riatio
n?
115
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AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(e) S
olve
pro
blem
s on
inve
rse
varia
tions
.i)
The
teac
her t
o gu
ide
stud
ents
to fo
rm a
nd
solv
e eq
uatio
ns fr
om
inve
rse
varia
tions
.ii)
St
uden
ts in
divi
dual
ly
to d
raw
gra
phs o
f in
vers
e va
riatio
ns.
i)
Man
ila p
aper
ii)
M
arke
r pen
sIs
the
stud
ent a
ble
to so
lve
prob
lem
s on
inve
rse
varia
tions
?
(f)
Dra
w g
raph
s re
latin
g in
vers
e va
riatio
ns.
i) Th
e te
ache
r to
guid
e st
uden
ts th
roug
h qu
estio
ns a
nd a
nsw
ers,
to d
raw
gra
phs o
f in
vers
e va
riatio
ns.
ii) S
tude
nts i
ndiv
idua
lly
to d
raw
gra
phs o
f in
vers
e va
riatio
ns a
nd
stat
e th
eir b
ehav
ior.
i) G
raph
pap
er
ii) M
athe
mat
ical
in
stru
men
tsiii
) Col
oure
d ch
alks
Is th
e st
uden
t abl
e to
dra
w g
raph
s re
latin
g in
vers
e va
riatio
n?
(g) U
se jo
int v
aria
tion
in so
lvin
g pr
oble
ms.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
jo
int v
aria
tion
as a
qu
antit
y w
hich
var
ies
join
tly w
ith tw
o or
m
ore
varia
bles
.ii)
Th
e te
ache
r to
guid
e st
uden
ts in
form
ing
and
solv
ing
equa
tions
fr
om jo
int v
aria
tions
iii)
Stud
ents
to so
lve
ques
tions
from
join
t va
riatio
ns.
i)
Squa
red
pape
rii)
G
eobo
ard
iii)
Rub
ber b
ands
iv)
Gra
ph b
oard
Is th
e st
uden
t ab
le to
use
join
t va
riatio
n in
so
lvin
g pr
oble
m?
116
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
5.0
SEQ
UEN
CES
A
ND
SER
IES
5.1
Sequ
ence
sTh
e st
uden
t sho
uld
be
able
to :
(a)
Expl
ain
the
conc
ept
of se
quen
ce.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
conc
ept o
f a se
quen
ceii)
St
uden
ts to
ext
end
term
s of g
iven
se
quen
ces.
iii)
The
teac
her t
o gu
ide
stud
ents
to fi
nd n
th th
e
term
of a
sequ
ence
.iv
) St
uden
ts in
divi
dual
ly
to n
th s
olve
pro
blem
s on
the
ter
m o
f a
sequ
ence
s.
i) N
umbe
r car
dsii)
Num
ber
patte
rns i
n as
cend
ing
and
desc
endi
ng
orde
riii
) M
athe
mat
ical
ta
bles
iv)
Scie
ntifi
c po
cket
sv)
C
alcu
lato
rsvi
) C
olou
red
chal
ks
i) Is
the
stud
ent
able
to e
xpla
in
the
conc
ept o
f a
sequ
ence
?
ii) Is
the
stud
ent
able
to fi
nd th
e nth
term
of a
se
quen
ce?
12
(b)
Iden
tify
an
arith
met
ic
prog
ress
ion
(AP)
an
d ge
omet
ric
prog
ress
ion
(GP)
.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
mea
ning
of A
.P a
nd
G.P
.ii)
The
teac
her t
o gu
ide
stud
ents
in g
roup
s to
iden
tity
AP
and
GP
from
oth
er se
quen
ces
iii)
Stud
ents
indi
vidu
ally
to
solv
e pr
oble
ms
dist
ingu
ishi
ng A
P’s
and
GP’
s
i) N
umbe
r car
dsii)
Col
oure
d ch
alks
iii) M
athe
mat
ical
ta
bles
iv) S
cien
tific
pock
etv)
Cal
cula
tors
Is th
e st
uden
t ab
le to
iden
tify
an a
rithm
etic
pr
ogre
ssio
nan
d ge
omet
ric
prog
ress
ion?
117
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
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D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Find
the
gene
ral
term
of a
n A
P.i)
The
teac
her t
o gu
ide
stud
ents
to d
eriv
e th
e fo
rmul
a fo
r the
gen
eral
te
rm o
f an
A.P
.ii)
St
uden
ts to
use
the
nint
h te
rm fo
rmul
a to
so
lve
prob
lem
s.
Col
oure
d ch
alks
Is th
e st
uden
t ab
le to
find
the
gene
ral t
erm
of
an a
rithm
etic
pr
ogre
ssio
n?
(d)
Find
the
gene
ral
term
of a
GP.
i) Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
to fi
nd th
e ge
nera
l ter
m o
f a G
Pii)
St
uden
ts to
use
the
form
ula
for t
he n
th
term
of a
GP
to so
lve
prob
lem
s
i) M
athe
mat
ical
ta
bles
ii)
Man
ila p
aper
\iii
) M
arke
r pen
siv
) Sc
ient
ific
pock
et
calc
ulat
ors
Is th
e st
uden
t ab
le to
find
the
gene
ral t
erm
of
a g
eom
etric
pr
ogre
ssio
n?
5.2
Serie
sTh
e st
uden
t sho
uld
be
able
to:
(a)
Der
ive
the
form
ula
for a
sum
of
an a
rithm
etic
pr
ogre
ssio
n.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
conc
ept o
f a se
ries
ii) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
of su
m o
f A.P
iii)
Stud
ents
indi
vidu
ally
to
solv
e pr
oble
ms
usin
g fo
rmul
a fo
r the
su
m o
f an
AP.
i) S
cien
tific
pock
et
calc
ulat
ors
ii) M
athe
mat
ical
ta
bles
i) Is
the
stud
ent
able
to d
eriv
e th
e fo
rmul
a of
sum
of a
n ar
ithm
etic
pr
ogre
ssio
n?ii)
Is th
e st
uden
t ab
le to
solv
e pr
oble
ms
rela
ted
to th
e su
m o
f an
AP?
12
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ING
ST
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TE
AC
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RN
ING
R
ESO
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S
ASS
ESS
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NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Cal
cula
te th
e ar
ithm
etic
mea
n.i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
how
to fi
nd th
e ar
ithm
etic
mea
n.ii)
The
teac
her t
o gu
ide
stud
ents
to d
eriv
e th
e fo
rmul
a fo
r the
ar
ithm
etic
mea
niii
) St
uden
ts in
divi
dual
ly
to u
se a
rithm
etic
m
ean
form
ula
to so
lve
prob
lem
s
Col
oure
d ch
alk
Is th
e st
uden
t abl
e to
cal
cula
te th
e ar
ithm
etic
mea
n?
(c)
Der
ive
the
form
ula
for t
he su
m o
f a
geom
etric
pr
ogre
ssio
n.
i) Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
for t
he su
m o
f a
GP
ii)
The
teac
her t
o gu
ide
stud
ents
in g
roup
s to
solv
e pr
oble
ms u
sing
th
e fo
rmul
a of
the
sum
of
G.P
iii)
Stud
ents
indi
vidu
ally
to
solv
e pr
oble
ms
usin
g th
e fo
rmul
a fo
r th
e su
m o
f a G
P.
i) C
olou
red
chal
k ii)
Mat
hem
atic
al
tabl
esiii
) Sci
entifi
poc
ket
calc
ulat
ors
i) Is
the
stud
ent
able
to d
eriv
e th
e fo
rmul
a fo
r the
sum
of
a ge
omet
ric
prog
ress
ion?
ii) I
s the
stud
ent
able
to fi
nd th
e su
m o
f a G
P?
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AC
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ING
R
ESO
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S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
Cal
cula
te th
e ge
omet
ric m
ean.
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
for t
he
geom
etric
mea
nii)
St
uden
ts to
use
the
geom
etric
mea
niii
) St
uden
ts to
use
the
geom
etric
mea
n fo
rmul
a to
solv
e pr
oble
ms
i) M
athe
mat
ical
ta
bles
ii) S
cien
tific
pock
et
calc
ulat
ors
Is th
e st
uden
t abl
e to
cal
cula
te th
e ge
omet
ric m
ean?
5.3
Com
poun
d In
tere
stTh
e st
uden
t sho
uld
be a
ble
to c
alcu
late
co
mpo
und
inte
rest
us
ing
form
ula.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
mea
ning
of c
ompo
und
inte
rest
.ii)
The
teac
her t
o gu
ide
stud
ents
to d
eriv
e th
e co
mpo
und
inte
rest
fo
rmul
a us
ing
the
know
ledg
e ob
tain
ed
from
the
G.P
serie
siii
) Stu
dent
s to
do
calc
ulat
ions
usi
ng th
e co
mpo
und
inte
rest
fo
rmul
a
i) M
athe
mat
ical
ta
bles
ii) S
cien
tific
pock
ets
calc
ulat
ors
Is th
e st
uden
t abl
e to
cal
cula
te th
e co
mpo
und
inte
rest
us
ing
form
ula?
3
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R
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ESS
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F PE
RIO
DS
6.0
CIR
CLE
S6.
1 D
efini
tion
of T
erm
sTh
e st
uden
t sho
uld
be
able
to d
efine
diff
eren
t te
rms o
f circ
les.
i) Th
e te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
on
the
mea
ning
of
circ
le, c
hord
, ra
dius
, dia
met
er,
circ
umfe
renc
e, a
rc,
cent
re, s
ecto
r and
se
gmen
t of a
circ
le.
ii)
Stud
ents
indi
vidu
ally
to
synt
hesi
ze th
e re
spon
ses i
nto
mea
ning
s of t
he te
rms.
iii) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ap
plic
atio
n of
circ
les
in d
aily
life
.
i)
Com
pass
es
ii)
Rul
eriii
) C
olou
red
chal
ks
Is th
e st
uden
t abl
e to
defi
ne d
iffer
ent
term
s of c
ircle
s?
3
6.2
Cen
tral A
ngle
The
stud
ent s
houl
d be
ab
le to
:(a
) D
eriv
e th
e fo
rmul
a fo
r the
leng
th o
f an
arc
.
i) Th
e te
ache
r to
dem
onst
rate
the
cent
ral a
ngle
by
usin
g a
diag
ram
ii) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
rela
tions
hip
betw
een
cent
ral a
ngle
and
the
ar
c it
inte
rcep
tsiii
) Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
for t
he le
ngth
of
an
arc.
i) C
olou
red
chal
ks
ii)
Rul
eriii
) Pr
otra
ctor
iv
) C
ompa
sses
i) Is
the
stud
ent
able
to d
eriv
e th
e
form
ula
for t
he le
ngth
of
an
arc?
ii) Is
the
stud
ent
able
to a
pply
th
e fo
rmul
a fo
r th
e le
ngth
of a
n ar
c in
solv
ing
prob
lem
s?
10
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
in g
roup
s to
solv
e pr
oble
ms r
elat
ed
to th
e fo
rmul
a fo
r the
le
ngth
of a
n ar
c.v)
St
uden
ts to
pre
sent
th
eir w
ork
in c
lass
for
eval
uatio
n.(b
) C
alcu
late
the
cent
ral a
ngle
.i)
The
teac
her t
o gu
ide
stud
ents
to fi
nd th
e m
easu
re o
f the
cen
tral
angl
e us
ing
the
form
ula.
ii)
Stud
ents
indi
vidu
ally
to
cal
cula
te th
e ce
ntra
l an
gle
in d
iffer
ent r
eal
life
situ
atio
ns u
sing
th
e fo
rmul
a.
i) C
ompa
sses
ii) C
olou
red
chal
ks
iii)
Rul
er
Is th
e st
uden
t abl
e to
cal
cula
te th
e ce
ntra
l ang
le?
(c)
Expl
ain
the
conc
ept
of ra
dian
mea
sure
.i)
The
teac
her t
o de
mon
stra
te th
e ra
dian
m
easu
re.
ii) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e m
eani
ng o
f rad
ian
mea
sure
.iii
) St
uden
ts to
est
imat
e th
e ra
dian
mea
sure
by
mea
surin
g di
ffere
nt
cylin
ders
or c
ircle
s.
i)
Thre
adii)
C
ompa
sses
iii
) R
uler
iv)
Prot
ract
or
v)
Cyl
inde
rs
Is th
e st
uden
t abl
e to
exp
lain
the
conc
ept o
f rad
ian
mea
sure
?
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ST
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TE
AC
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RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
Con
vert
radi
ans t
o de
gree
s and
vic
e ve
rsa.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
con
vert
radi
ans
to d
egre
es a
nd d
egre
es
to ra
dian
s.ii)
St
uden
ts to
solv
e pr
oble
ms o
n co
nver
ting
radi
ans
to d
egre
es a
nd v
ice
vers
a.
i) M
athe
mat
ical
ta
bles
ii) S
cien
tific
pock
et
calc
ulat
ors
iii) M
anila
pap
eriv
) M
arke
r pen
s
Is th
e st
uden
t abl
e to
con
vert
radi
ans
to d
egre
es a
nd
vice
ver
sa?
6.3
Ang
les
Prop
ertie
sTh
e st
uden
t sho
uld
be
able
to:
(a)
Prov
e ci
rcle
th
eore
ms o
f in
scrib
ed a
ngle
s
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e m
eani
ng o
f an
insc
ribed
ang
le.
ii)
The
teac
her t
o gu
ide
stud
ents
to p
rove
the
theo
rem
“Th
e an
gle
whi
ch a
n ar
c su
bten
ds
at th
e ce
nter
is d
oubl
e th
at w
hich
it su
bten
ds
at a
ny p
oint
on
the
rem
aini
ng p
art o
f the
ci
rcum
fere
nce”
.iii
) St
uden
ts in
gro
ups t
o so
lve
prob
lem
s rel
ated
to
the
theo
rem
i) C
ompa
sses
ii)
Rul
ers
iii) C
olou
red
chal
ks
iv) M
anila
pap
erv)
Mar
ker p
ens
Is th
e st
uden
t ab
le to
pro
ve th
e ci
rcle
theo
rem
s of
insc
ribed
ang
le?
10
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ING
ST
RAT
EG
IES
TE
AC
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D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv) T
he te
ache
r to
guid
e st
uden
ts to
pro
ve th
e th
eore
m “
Ang
les i
n th
e sa
me
segm
ent o
f a
circ
le a
re e
qual
”.v)
Stu
dent
s in
grou
ps to
so
lve
prob
lem
s rel
ated
to
the
theo
rem
vi) T
he te
ache
r to
guid
e st
uden
ts to
pro
ve
the
theo
rem
” Th
e an
gle
subt
ende
d in
a
sem
icirc
le is
a ri
ght
angl
e”.
vii)S
tude
nts i
n gr
oups
to
solv
e pr
oble
ms r
elat
ed
to th
e th
eore
m.
viii)
The
teac
her t
o gu
ide
stud
ents
to p
rove
th
e th
eore
m ”
The
oppo
site
ang
les o
f a
cycl
ic q
uadr
ilate
ral a
re
supp
lem
enta
ry”
ix)
Stu
dent
s in
grou
ps to
so
lve
prob
lem
s rel
ated
to
the
theo
rem
.
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RN
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R
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UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) A
pply
the
circ
le
theo
rem
s in
solv
ing
rela
ted
prob
lem
s.
i) Th
e te
ache
r to
guid
e st
uden
ts to
solv
e pr
oble
ms i
nvol
ving
th
e fo
ur a
ngle
th
eore
ms.
ii) S
tude
nts i
ndiv
idua
lly
to u
se th
e ci
rcle
th
eore
ms i
n so
lvin
g pr
oble
ms i
nvol
ving
al
l the
four
ang
le
theo
rem
s
i)
Com
pass
es
ii)
Rul
erIs
the
stud
ent
able
to a
pply
the
circ
le th
eore
ms
in so
lvin
g re
late
d pr
oble
ms?
6.4
Cho
rd
Pr
oper
ties o
f a
Circ
le
The
stud
ent s
houl
d be
ab
le to
:(a
) Ide
ntify
cho
rd
prop
ertie
s of a
ci
rcle
.
i) T
he te
ache
r to
guid
e
stud
ents
to d
iscu
ss th
e ch
ord
prop
ertie
s of a
ci
rcle
usi
ng d
iagr
ams.
ii) S
tude
nts i
ndiv
idua
lly
to st
ate
chor
d pr
oper
ties o
f a c
ircle
i)
Com
pass
es
ii)
Rul
eriii
) Col
oure
d ch
alks
iv
) Se
t squ
are
v)
Man
ila p
aper
svi
) M
arke
r pen
s
Is th
e st
uden
t abl
e to
iden
tify
chor
d pr
oper
ties o
f a
circ
le?
9
(b) P
rove
the
theo
rem
on
the
perp
endi
cula
r bi
sect
or to
a c
hord
.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
proo
f of t
he th
eore
m
on th
e pe
rpen
dicu
lar
bise
ctor
of a
cho
rd.
ii) T
he te
ache
r to
guid
e st
uden
ts to
use
the
theo
rem
on
the
perp
endi
cula
r bis
ecto
r of
cho
rd to
solv
e re
late
d pr
oble
ms.
i)
Com
pass
es
ii)
Rul
eriii
) Col
oure
d ch
alks
iv
) Se
t squ
are
v)
Man
ila p
aper
s vi
) M
arke
r pen
s
i) Is
the
stud
ent
able
to p
rove
th
e th
eore
m
on th
e pe
rpen
dicu
lar
bise
ctor
of t
he
chor
dii)
Is th
e st
uden
t ab
le to
solv
e pr
oble
m
rela
ted
to th
e
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RN
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UR
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ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii)
Stud
ents
to so
lve
prob
lem
s rel
ated
to th
e pe
rpen
dicu
lar b
isec
tor
of a
cho
rd
perp
endi
cula
r bi
sect
or o
f a
chor
d?
(c) P
rove
the
theo
rem
on
par
alle
l cho
rds.
i) T
he te
ache
r to
gui
de st
uden
ts to
pr
ove
the
theo
rem
“
para
llel c
hord
s
in
terc
ept c
ongr
uent
ar
cs”
ii) T
he te
ache
r to
guid
e st
uden
ts in
gro
ups
to u
se th
e th
eore
m
on p
aral
lel c
hord
s to
solv
e re
late
d pr
oble
ms.
iii)
Stu
dent
s to
pre
sent
thei
r gro
up
wor
k in
cla
ss fo
r ev
alua
tion.
iv)
Stud
ents
indi
vidu
ally
to
solv
e pr
oble
ms o
n pa
ralle
l cho
rds
i)
Com
pass
es
ii)
Rul
eriii
) C
olou
red
c
halk
s iv
) S
et sq
uare
v)
Man
ila p
aper
s vi
) M
arke
r pen
s
i) Is
the
stud
ent
able
to p
rove
th
e th
eore
m o
n pa
ralle
l cho
rds?
ii) Is
the
stud
ent
able
to so
lve
prob
lem
re
latin
g pa
ralle
l ch
ords
?
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AC
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)A
pply
the
theo
rem
s on
cho
rds i
n so
lvin
g re
late
d pr
oble
ms.
i) T
he te
ache
r to
guid
e st
uden
ts to
use
the
chor
d th
eore
ms t
o so
lve
rela
ted
prob
lem
s in
gro
up.
ii) S
tude
nts t
o pr
esen
t th
eir g
roup
wor
k in
cl
ass.
iii)
Stud
ents
to so
lve
prob
lem
s on
chor
d th
eore
ms i
ndiv
idua
lly.
i) C
ompa
sses
ii) R
uler
iii) S
et sq
uare
Is th
e st
uden
t abl
e to
app
ly c
hord
pr
oper
ties a
nd
theo
rem
s to
solv
e pr
oble
ms?
6.5
Tang
ent
Pr
oper
ties
The
stud
ent s
houl
d be
able
to:
(a)
Des
crib
e a
tang
ent
to a
circ
le.
i) T
he te
ache
r to
illus
trate
a ta
ngen
t to
a ci
rcle
usi
ng d
iagr
ams
ii) S
tude
nts t
o dr
aw
diffe
rent
tang
ents
to
the
give
n ci
rcle
i) M
athe
mat
ical
in
stru
men
ts
ii) M
anila
pap
er
iii) M
arke
r pen
s
i) I
s the
stud
ent
able
to
desc
ribe
a ta
ngen
t to
a ci
rcle
?ii)
Is t
he st
uden
t ab
le to
dra
w
a ta
ngen
t to
a ci
rcle
?
12
(b)
Iden
tify
tang
ent
prop
ertie
s of a
ci
rcle
.
i) Th
e te
ache
r to
g
uide
stud
ents
to
d
iscu
ss th
e ta
ngen
t
pr
oper
ties u
sing
di
agra
ms
ii)
Stud
ents
to li
st
tang
ent p
rope
rties
of a
circ
le
i) R
uler
ii) C
ompa
sses
iii) C
olou
red
chal
ks
Is th
e st
uden
t abl
e to
iden
tify
tang
ent
prop
ertie
s of a
ci
rcle
?
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Prov
e ta
ngen
t th
eore
ms.
i) T
he te
ache
r to
guid
e st
uden
ts to
pro
ve
the
theo
rem
“ T
wo
tang
ents
from
an
exte
rnal
poi
nt to
a
circ
le a
re e
qual
”.ii)
Stu
dent
s in
grou
ps to
so
lve
prob
lem
s rel
ated
to
tang
ents
from
an
exte
rnal
poi
nts t
o a
circ
leiii
) Stu
dent
s to
do
indi
vidu
al w
ork
on
tang
ents
from
an
exte
rnal
poi
nt to
a
circ
leiv
) Th
e te
ache
r to
guid
e st
uden
ts to
pro
ve th
e th
eore
m “
Alte
rnat
e se
gmen
t the
orem
”v)
St
uden
ts in
gro
ups
to so
lve
prob
lem
s re
late
d on
the
alte
rnat
e se
gmen
t the
orem
.vi
) St
uden
ts to
do
indi
vidu
al w
ork
on
the
alte
rnat
e se
gmen
t th
eore
m.
i)
Set
squa
reii)
C
ompa
sses
iii
) M
anila
pap
er
iv)
Mar
ker p
ens
Is th
e st
uden
t abl
e pr
ove
tang
ent
theo
rem
s?
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ING
ST
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IES
TE
AC
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D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
App
ly th
eore
ms
rela
ting
to ta
ngen
t to
a c
ircle
in
solv
ing
prob
lem
s.
i)
The
teac
her t
o gu
ide
stud
ents
to u
se ta
ngen
t th
eore
ms i
n so
lvin
g re
late
d pr
oble
ms.
ii)
Stud
ents
to so
lve
prob
lem
s rel
ated
to
tang
ents
to a
circ
le.
Mat
hem
atic
alin
stru
men
tsIs
the
stud
ent a
ble
to a
pply
theo
rem
s re
late
d to
tang
ents
to
a c
ircle
in
solv
ing
prob
lem
s?
7.0
THE
EART
H
AS
A S
PHER
E7.
1 Fe
atur
es a
n Lo
catio
n of
Pl
aces
The
stud
ent s
houl
d be
ab
le to
:(a
) Des
crib
e th
e eq
uato
r, gr
eat
circ
les,
smal
l ci
rcle
s, m
erid
ian,
la
titud
es a
nd
long
itude
s.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
the
mea
ning
of t
he
Equa
tor,
mer
idia
n,
latit
udes
, lon
gitu
des,
grea
t circ
les a
nd sm
all
circ
les o
n a
glob
e.ii)
The
stud
ents
to
draw
dia
gram
s sh
owin
g th
e Eq
uato
r, m
erid
ian,
latit
udes
and
lo
ngitu
des.
i)
Glo
beii)
O
rang
esiii
) W
ater
mel
on
iv)
Mod
els o
f a
skel
eton
sphe
re
and
soft
gras
sv)
A
tlas
vi)
Col
oure
d C
halk
s’vi
i) G
raph
s pap
ers
Is th
e st
uden
t ab
le to
des
crib
e th
e eq
uato
r, gr
eat
circ
les,
smal
l ci
rcle
s, m
erid
ian,
la
titud
e an
d lo
ngitu
de?
6
(b) L
ocat
e a
plac
e on
th
e ea
rth’s
surf
ace.
i) Th
e te
ache
r to
illus
trate
how
to lo
cate
a
plac
e on
a g
lobe
.ii)
The
teac
her t
o gu
ide
stud
ents
to
loca
te p
lace
s alo
ng
the
Equa
tor,
the
Gre
enw
ich
mer
idia
n,
latit
udes
and
lo
ngitu
des.
i) G
lobe
ii)
A
tlas
iii)
Col
oure
d
c
halk
s iv
) G
raph
pap
ers
Is th
e st
uden
t abl
e to
loca
te a
pla
ce
on th
e ea
rth’s
su
rfac
e?
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii)
Stud
ents
to lo
cate
pl
aces
alo
ng th
e Eq
uato
r and
the
Gre
enw
ich
in g
roup
s.iv
) Th
e te
ache
r to
guid
e st
uden
ts to
find
the
plac
e on
the
glob
e gi
ven
its la
titud
e an
d lo
ngitu
de.
v)
Stud
ents
to fi
nd p
lace
s on
the
glob
e.
7.2
Dis
tanc
es
Alo
ng G
reat
C
ircle
s
The
stud
ents
shou
ld b
e ab
le to
:(a
) C
alcu
late
dis
tanc
es
alon
g gr
eat c
ircle
s.
i) Th
e te
ache
r to
guid
e st
uden
ts to
cal
cula
te
dist
ance
s alo
ng g
reat
ci
rcle
sii)
St
uden
ts in
gro
ups t
o fin
d di
stan
ces a
long
gr
eat c
ircle
siii
) St
uden
ts to
pre
sent
th
eir w
ork
in c
lass
iv)
Stud
ents
to c
alcu
late
th
e di
stan
ces b
etw
een
two
plac
es a
long
gre
at
circ
les
i)
Mag
netic
co
mpa
ssii)
C
ompa
sses
iii
) R
uler
iv)
Thre
adv)
Pr
otra
ctor
Is th
e st
uden
t abl
e to
cal
cula
te th
e di
stan
ce a
long
gr
eat c
ircle
s?
6
130
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) S
olve
nav
igat
ion
rela
ted
prob
lem
s.i)
The
teac
her t
o gu
ide
stud
ents
in so
lvin
g na
viga
tion
rela
ted
prob
lem
sii)
Stu
dent
s in
grou
ps to
ca
lcul
ate
navi
gatio
n re
late
d pr
oble
ms u
sing
sc
ale
draw
ing
and
Pyth
agor
as th
eore
m.
iii)
Stud
ents
to p
rese
nts
thei
r gro
up w
ork
in th
e cl
ass.
iv)
Stud
ents
to d
o in
divi
dual
wor
k on
na
viga
tion
prob
lem
s by
scal
e dr
awin
g.
i)
Prot
ract
orii)
M
athe
mat
ical
ta
bles
iii)
Nav
igat
ion
com
pass
esiv
) G
yros
cope
Is th
e st
uden
t abl
e to
solv
e na
viga
tion
prob
lem
s?
7.3
Dis
tanc
es
alon
g sm
all
circ
les
The
stud
ents
shou
ldbe
abl
e to
cal
cula
te
dist
ance
s alo
ng sm
all
circ
les.
i) T
he te
ache
r to
guid
e st
uden
ts to
find
the
gene
ral f
orm
ula
for
radi
us o
f sm
all c
ircle
s.ii)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
how
to fi
nd th
e di
stan
ce a
long
smal
l ci
rcle
siii
) T
he te
ache
r to
guid
e st
uden
ts in
gro
ups t
o fin
d di
stan
ce a
long
sm
all c
ircle
s
i)
Wat
er m
elon
ii)
Ora
nges
iii)
Com
pass
esiv
) C
olou
red
Cha
lks
v)
Mod
els m
ade
of st
raw
s, w
ires o
r sof
t gr
ass
vi)
Glo
bevi
i) M
anila
pap
ers
viii)
Mar
ker p
ens
Is th
e st
uden
t abl
eto
cal
cula
te th
e di
stan
ces a
long
sm
all c
ircle
s?
8
131
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AC
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
to so
lve
prob
lem
s usi
ng th
e fo
rmul
a fo
r the
radi
us
of a
smal
l circ
lev)
St
uden
ts to
find
the
dist
ance
bet
wee
n tw
o po
ints
on
the
sam
e la
titud
e.
8.0
AC
CO
UN
TS8.
1 D
oubl
e En
tryTh
e st
uden
ts sh
ould
be a
ble
to:
(a) E
xpla
in th
e m
eani
ng
of d
oubl
e en
try.
i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss th
e pr
inci
ples
of d
oubl
e en
try sy
stem
usi
ng
real
life
exa
mpl
es ii
) Th
e te
ache
r to
dem
onst
rate
acc
ount
s sh
owin
g th
e de
bit s
ide
and
the
cred
it si
deiii
) St
uden
ts to
con
stru
ct
and
labe
l the
cre
dit
and
debi
t sid
eiv
) St
uden
ts to
exp
lain
th
e m
eani
ng o
f dou
ble
entry
i)
Rul
erii)
D
iffer
ent
ledg
er b
ooks
i) Is
the
stud
ent
able
to e
xpla
in
the
mea
ning
of
doub
le e
ntry
?
ii) I
s the
stud
ent
able
to
cons
truct
and
la
bel t
he c
redi
t an
d de
bit
acco
unts
?
10
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) D
escr
ibe
diffe
rent
ty
pes o
f led
ger.
i) T
he te
ache
r to
disp
lay
diffe
rent
type
s of
ledg
ers a
nd a
sk
stud
ents
exp
lain
the
mea
ning
of l
edge
rii)
Th
e te
ache
r to
lead
st
uden
ts to
exp
lain
di
ffere
nt ty
pes o
f le
dger
s suc
h as
cas
h ac
coun
t, ca
pita
l, pu
rcha
ses,
sale
s, ex
pens
es a
nd st
ock
iii)
Stud
ents
to
dist
ingu
ish
diffe
rent
ty
pes o
f led
gers
Diff
eren
t typ
es o
f le
dger
sIs
the
stud
ent
able
to d
escr
ibe
diffe
rent
type
s of
ledg
ers?
(c) C
onst
ruct
a le
dger
.i)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
how
to q
ualif
y an
d la
bel c
redi
t and
deb
it ac
coun
tii)
Stu
dent
s to
cons
truct
an
d qu
alify
the
debi
t an
d cr
edit
acco
unt
i)
Ledg
er b
ooks
ii)
Col
oure
d
c
halk
s
Is th
e st
uden
t ab
le to
con
stru
ct a
le
dger
?
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d) P
ost e
ntrie
s in
the
ledg
er.
i) T
he te
ache
r to
dem
onst
rate
how
to
post
ent
ries i
n th
e le
dger
ii) T
he te
ache
r to
orga
nize
th
e st
uden
ts in
smal
l gr
oups
to p
ost e
ntrie
s in
the
ledg
er
i)
Ledg
erii)
C
olou
red
chal
ks
iii)
Sam
ples
of
vouc
hers
Is th
e st
uden
t abl
e to
pos
t ent
ries i
n th
e le
dger
?
(e) C
lose
the
sim
ple
acco
unts
i) T
he te
ache
r to
guid
e st
uden
ts to
clo
se
acco
unts
ii) S
tude
nts t
o ex
erci
se o
n cl
osin
g ac
coun
ts
Ledg
er b
ooks
Is th
e st
uden
t abl
e to
clo
se th
e si
mpl
e ac
coun
ts?
8.2
Tria
l Bal
ance
The
stud
ents
shou
ld b
e ab
le to
:(a
) Exp
lain
the
conc
ept
of tr
ial b
alan
ce.
i) T
he te
ache
r to
lead
st
uden
ts to
dis
cuss
th
e m
eani
ng o
f a tr
ial
bala
nce
ii) S
tude
nts t
o di
scus
s the
us
e of
a tr
ial b
alan
ceiii
) Stu
dent
s to
expl
ain
the
conc
ept o
f tria
l ba
lanc
e
Ledg
er b
ooks
Is th
e st
uden
t abl
e to
exp
lain
the
conc
ept o
f tria
l ba
lanc
e?
12
134
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) C
onst
ruct
tria
l ba
lanc
e.i)
The
teac
her t
o de
mon
stra
te h
ow to
co
nstru
ct a
nd q
ualif
y a
trial
bal
ance
ii) T
he te
ache
r to
guid
e st
uden
ts to
do
exe
rcis
es o
n co
nstru
ctin
g an
d qu
alify
ing
a tri
al
bala
nce
i)
Cal
cula
tors
ii)
Bal
ance
shee
tIs
the
stud
ent a
ble
to c
onst
ruct
a tr
ial
bala
nce
?
(c) P
ost d
ebit
bala
nces
an
d cr
edit
bala
nces
.i)
Th
e te
ache
r to
dem
onst
rate
to
stud
ents
how
to p
ost
debi
t bal
ance
s and
cr
edit
bala
nces
ii) S
tude
nts i
n gr
oups
to
do
exer
cise
s on
post
ing
debi
t bal
ance
s an
d cr
edit
bala
nces
i)
Ledg
er b
ooks
ii)
Sam
ples
of
repo
sts o
n bu
sine
ss
trans
actio
ns
Is th
e st
uden
t ab
le to
pos
t deb
it ba
lanc
es a
nd c
redi
t ba
lanc
es ?
(d) C
heck
the
bala
nces
.i)
The
teac
her t
o gu
ide
stud
ents
to c
heck
the
bala
nces
.ii)
St
uden
ts in
divi
dual
ly
to d
o ex
erci
ses o
n ch
ecki
ng th
e ba
lanc
es
Ledg
er b
ooks
Is th
e st
uden
t ab
le to
che
ck th
e ba
lanc
es?
135
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AC
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
8.3
Trad
ing
Profi
t an
d Lo
ssTh
e st
uden
t sho
uld
be
able
to:
(a)
Asc
erta
in g
ross
pr
ofit/l
oss u
sing
tra
ding
acc
ount
.
i) T
he te
ache
r to
dem
onst
rate
how
to
asce
rtain
gro
ss p
rofit
/ lo
ss u
sing
trad
ing
acco
unt.
ii) S
tude
nts i
ndiv
idua
lly
to a
scer
tain
gro
ss
profi
t/los
s in
tradi
ng
acco
unts
.
i)
Rul
erii)
Le
dger
boo
ksIs
the
stud
ent a
ble
to a
scer
tain
gro
ss
profi
t/los
s usi
ng
tradi
ng a
ccou
nt?
6
(b)
Asc
erta
in n
et p
rofit
/ lo
ss.
i) T
he te
ache
r to
dem
onst
rate
how
to
asce
rtain
net
pro
fit/
loss
usi
ng p
rofit
or
loss
acc
ount
sii)
Stu
dent
s ind
ivid
ually
to
asc
erta
inin
g ne
t pr
ofit/l
oss i
n pr
ofit o
r lo
ss a
ccou
nt
i)
Cal
cula
tors
ii)
Bal
ance
s she
ets
Is th
e st
uden
t abl
e to
asc
erta
in n
et
profi
t/los
s ?
8.4
Bal
ance
She
etTh
e st
uden
t sho
uld
be
able
to:
(a)
Con
stru
ct a
bal
ance
sh
eet.
i) T
he te
ache
r to
dem
onst
rate
the
mea
ning
of a
bal
ance
sh
eet
ii) T
he te
ache
r to
guid
e st
uden
ts to
con
stru
ct a
ba
lanc
e sh
eet
iii) S
tude
nts t
o co
nstru
ct a
ba
lanc
e sh
eet
i) Va
rious
bal
ance
sh
eets
ii)
Rul
eriii
) Man
ila sh
eets
Is th
e st
uden
t ab
le to
con
stru
ct a
ba
lanc
e sh
eet?
6
136
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Post
ent
ries i
n a
ba
lanc
e sh
eet.
i) T
he te
ache
r to
dem
onst
rate
how
to
post
ent
ries i
n th
e ba
lanc
e sh
eet.
ii) S
tude
nts i
n gr
oups
to
pos
t ent
ries i
n th
e ba
lanc
e sh
eet
iii)
Stud
ents
to p
rese
nt
thei
r gro
up w
ork
in
clas
s for
eva
luat
ion.
iv)
Stud
ents
indi
vidu
ally
to
pos
t ent
ries i
n th
e ba
lanc
e sh
eet.
i) Va
rious
bal
ance
sh
eets
ii)
Man
ila sh
eets
iii)
Mar
ker p
ens
Is th
e st
uden
t abl
e to
pos
t ent
ries i
n a
bala
nce
shee
t?
(c) I
nter
pret
in
form
atio
n fr
om
the
bala
nce
shee
t.
i) Th
e te
ache
r to
guid
e st
uden
ts to
inte
rpre
t in
form
atio
n fr
om th
e ba
lanc
e sh
eet.
ii) T
he te
ache
r to
guid
e st
uden
ts o
n pr
epar
ing
bala
nce
shee
ts.
iii)
Stud
ents
to d
o ex
erci
se
on in
terp
retin
g ba
lanc
e sh
eets
.
i) B
alan
ce sh
eets
sa
mpl
eii)
Pu
blis
hed
Bal
ance
shee
tsiii
) Pr
inci
ples
of
acc
ount
s m
anua
l
Is th
e st
uden
t ab
le to
inte
rpre
t in
form
atio
n fr
om
the
bala
nce
shee
t ?
137
FORM FOUR
CLASS LEVEL COMPENTENCESStudent should have the ability to:
1. Solve general mathematical problems on coordinate geometry. 2. Perform mathematical experiments and predict outcome .3. Compute surfarce area and volume of objects .4. Draw graphs and three dimensional figures.5. Do computations on matrices and vectors.
CLASS LEVEL OBJECTIVESBy the end of Form Four course the student should be able to:
1. Apply mathematical knowledge and skills to form lines , calculate distance between two points and problems on parallel and perpendicular lines in two dimensional geometry
2. Drive and apply the formulae for surfarce area and volume of geometrical figures3. Find the sum , difference and scalar multiplication of vectors and hence use the
knowledge to solve practical problems.4. Use 2 x 2 matrices to solve simultaneous equations and solve problems on
transformations.5. Calculate the probability of an even and perform simple combination of probabilities6. Draw graph of sine and cosine functions and apply sine and cosine rules to solve
problems.7. Use oblique projections to draw three dimensional figures and find the angle
between a line and a plane and the angle between two planes.
138
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
1.0
CO
OR
DIN
ATE
GEO
MET
RY
1.1
Equa
tion
of a
Li
neTh
e st
uden
t sho
uld
be a
ble
to d
eriv
e th
e ge
nera
l equ
atio
n of
a
stra
ight
line
.
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
a lin
ear e
quat
ion
in th
e ge
nera
l for
m
ax +
by
+ c
= 0.
ii)
Stud
ents
to re
writ
e lin
ear e
quat
ions
in th
e ge
nera
l for
m
i)
Gra
ph p
aper
sii)
Sq
uare
d pa
pers
iii
) G
eobo
ard
iv)
Rub
ber b
ands
v)
Gra
ph b
oard
Is th
e st
uden
t ab
le to
der
ive
the
equa
tion
of a
st
raig
ht li
ne in
the
gene
ral f
orm
?
3
1.2
Mid
poin
t of a
Li
ne S
egm
ent
The
stud
ent s
houl
d be
abl
e to
det
erm
ine
the
coor
dina
tes o
f th
e m
idpo
int o
f a li
ne
segm
ent.
i) Th
e te
ache
r to
guid
e th
e st
uden
ts th
roug
h qu
estio
ns a
nd a
nsw
ers
to fo
rm a
form
ula
for
mid
poin
t of a
line
se
gmen
t.ii)
St
uden
ts to
find
the
mid
poin
ts o
f a g
iven
lin
e se
gmen
t
i) G
raph
pap
erii)
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
find
the
mid
poin
t of a
line
se
gmen
t?
3
1.3
Dis
tanc
e B
etw
een
two
poin
ts o
n a
plan
e
The
stud
ent s
houl
d be
ab
le to
cal
cula
te th
e di
stan
ce b
etw
een
two
poin
ts o
n a
plan
e.
i) T
he te
ache
r to
guid
e st
uden
ts in
usi
ng
Pyth
agor
as th
eore
m
to fo
rm a
dis
tanc
e fo
rmul
a.ii)
Stu
dent
s to
appl
y th
e fo
rmul
a to
cal
cula
te
dist
ance
s on
the
x-y
pl
ane.
i)
Gra
ph p
aper
s/bo
ard
ii)
Squa
red
pape
rsiii
) G
eobo
ard
iv)
Rub
ber b
ands
v)
M
athe
mat
ical
ta
bles
Is th
e st
uden
t abl
e to
cal
cula
te th
e di
stan
ce b
etw
een
two
poin
ts in
a
plan
e?
3
139
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
1.4
Para
llel a
nd
Perp
endi
cula
r Li
nes
The
stud
ent s
houl
d be
ab
le to
:(a
) C
ompu
te g
radi
ents
in
ord
er to
de
term
ine
the
cond
ition
s for
any
tw
o lin
es to
be
para
llel.
i) S
tude
nts i
n gr
oups
to
calc
ulat
e th
e gr
adie
nts
of d
iffer
ent l
ines
.ii)
Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
resu
lts o
f the
gra
dien
ts
for t
he p
aral
lel l
ines
iii)
The
teac
her t
o gu
ide
stud
ents
to g
ener
aliz
e th
e co
nditi
ons f
or
lines
to b
e pa
ralle
l.iv
) St
uden
ts to
do
prob
lem
s on
para
llel
lines
i)
Gra
ph p
aper
ii)
Mat
hem
atic
al
inst
rum
ents
iii)
Geo
boar
div
) R
ubbe
r ban
dsv)
Sq
uare
d pa
per
vi)
Gra
ph b
oard
Is th
e st
uden
t ab
le to
app
ly
cond
ition
s for
pa
ralle
l lin
es to
so
lve
prob
lem
s?
10
(b)
Com
pute
gra
dien
ts
in o
rder
to
dete
rmin
e th
e co
nditi
ons f
or a
ny
two
lines
to b
e pe
rpen
dicu
lar.
i)
Stud
ents
in g
roup
s to
calc
ulat
e th
e gr
adie
nt
of d
iffer
ent l
ines
.ii)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss th
e re
sults
of t
he g
radi
ents
fo
r the
per
pend
icul
ar
lines
iii) T
he te
ache
r to
guid
e st
uden
ts to
gen
eral
ize
the
cond
ition
s fo
r lin
es to
be
perp
endi
cula
r
i) Th
in w
ireii)
Gra
ph b
oard
iii) G
raph
pap
eriv
) M
athe
mat
ical
inst
rum
ent
Is t
he st
uden
t ab
le to
app
ly th
eco
nditi
ons f
or
perp
endi
cula
r lin
es in
solv
ing
prob
lem
s?
140
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
to d
o pr
oble
ms o
n pe
rpen
dicu
lar l
ines
(c) S
olve
pro
blem
s on
par
alle
l and
pe
rpen
dicu
lar l
ines
.
i) T
he te
ache
r to
guid
e st
uden
ts to
solv
e pr
oble
ms o
n pa
ralle
l an
d pe
rpen
dicu
lar
lines
.ii)
Stu
dent
s to
solv
e pr
oble
ms o
n pa
ralle
l an
d pe
rpen
dicu
lar l
ines
in
real
life
.
i) G
raph
pap
erii)
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t abl
e to
solv
e pr
oble
ms
on p
aral
lel a
nd
perp
endi
cula
r lin
e in
real
life
?
2.0
AR
EA A
ND
PE
RIM
ETER
2.1
Are
a of
any
Tr
iang
leTh
e st
uden
t sho
uld
be
able
to:
(a)
Der
ive
the
form
ula
for t
he a
rea
of a
ny
trian
gle.
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
area
of t
riang
le u
sing
ba
se a
nd h
eigh
t.ii)
Stu
dent
s to
solv
e pr
oble
ms u
sing
the
area
form
ula
of a
tri
angl
eiii
) Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
area
of a
ny tr
iang
le
whe
n tw
o si
des a
nd
an in
clud
ed a
ngle
are
gi
ven.
i) G
eobo
ard
ii) S
quar
ed p
aper
iii
) Gra
ph-b
oard
iv
) Mat
hem
atic
al
inst
rum
ents
v)
Man
ila p
aper
vi
) M
arke
r pen
svi
i) R
ubbe
r ban
ds
Is th
e st
uden
t ab
le to
der
ive
the
form
ula
for
the
area
of a
ny
trian
gle?
6
141
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AC
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G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iv)
Stud
ents
to so
lve
prob
lem
s usi
ng
(b)
App
ly th
e fo
rmul
a to
find
the
area
of
any
trian
gle.
i) T
he te
ache
r to
dem
onst
rate
the
appl
icat
ion
of a
form
ula
to
find
the
area
of a
ny
trian
gle.
ii)
Stud
ents
to a
pply
the
form
ula
to c
alcu
late
th
e ar
ea o
f any
tria
ngle
in
solv
ing
prob
lem
s.
i) C
harts
ii) G
raph
pap
eriii
) Rul
er
Is th
e st
uden
t ab
le to
app
ly
the
form
ula
to
calc
ulat
e ar
eas o
f tri
angl
es?
2.2
Are
a of
a
Rho
mbu
sTh
e st
uden
t sho
uld
be
able
to:
(a) D
eriv
e th
e fo
rmul
a fo
r find
ing
the
area
of
rhom
bi in
term
s of
the
diag
onal
s.
i) T
he te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
th
e ty
pes o
f tria
ngle
s m
ake
by th
e di
agon
als
of a
rhom
bus.
ii) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
for a
rea
of
a rh
ombu
s usi
ng it
s di
agon
als.
i) G
eobo
ard
ii) G
raph
boa
rd
iii) M
athe
mat
ical
in
stru
men
ts
Is th
e st
uden
t ab
le to
der
ive
the
area
form
ula
for
a rh
ombu
s and
sq
uare
?
6
142
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TIV
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) S
tude
nt to
ded
uce
the
form
ula
for fi
ndin
g th
e ar
ea o
f a sq
uare
from
th
e ar
ea o
f a rh
ombu
s.
(b) A
pply
the
form
ula
to fi
nd th
e ar
eas o
f qu
adril
ater
als.
Stud
ents
to a
pply
fo
rmul
ae in
find
ing
area
s of
qua
drila
tera
ls.
i)
Play
grou
nd
ii)
Dec
orat
ions
iii
) Ti
les
iv)
Mat
s v)
Pi
lots
vi)
Bui
ldin
gs
mod
els
Is th
e st
uden
t ab
le to
app
ly
the
form
ula
to
find
the
area
s of
quad
rilat
eral
s?
2.3
Perim
eter
of
a R
egul
ar
Po
lygo
n
The
stud
ent s
houl
d be
ab
le to
:(a
) D
eriv
e th
e fo
rmul
a fo
r find
ing
the
leng
th o
f a si
de o
f a
regu
lar p
olyg
on.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
the
rela
tions
hip
betw
een
a ce
ntra
l ang
le a
nd th
e ch
ord
subt
endi
ng it
.ii)
Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ula
for t
he le
ngth
of
a si
de o
f a re
gula
r po
lygo
n.iii
) St
uden
ts to
solv
e pr
oble
ms o
n th
e le
ngth
of a
side
of a
re
gula
r pol
ygon
.
i)
Geo
boar
dii)
M
athe
mat
ical
in
stru
men
tsiii
) M
anila
pap
eriv
) M
arke
r pen
s
Is th
e st
uden
t ab
le to
der
ive
the
form
ula
for
the
leng
th o
f a
side
of a
regu
lar
poly
gon?
6
143
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CIF
IC
OB
JEC
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ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) A
pply
the
form
ula
to d
eter
min
e th
e pe
rimet
er o
f a
regu
lar p
olyg
on.
i) S
tude
nts t
o de
duce
the
form
ula
for p
erim
eter
of
a re
gula
r pol
ygon
.ii)
St
uden
ts to
app
ly th
e fo
rmul
a to
cal
cula
te
the
perim
eter
of
regu
lar p
olyg
ons
i) M
athe
mat
ical
in
stru
men
tsii)
M
anila
pap
eriii
) M
arke
r pen
s
Is th
e st
uden
t ab
le to
app
ly
the
form
ula
for
the
perim
eter
of
regu
lar p
olyg
ons?
2.4
Are
a of
a
Reg
ular
Poly
gon
The
stud
ent s
houl
d be
ab
le to
(a
) D
eriv
e th
e fo
rmul
a fo
r find
ing
the
area
of a
regu
lar
poly
gon.
i) S
tude
nts t
o de
rive
the
form
ula
for t
he a
rea
of
regu
lar p
olyg
on g
iven
di
ffere
nt si
des.
ii) T
he te
ache
r to
guid
e th
e st
uden
ts to
der
ive
the
form
ula
of th
e ar
ea
of a
regu
lar p
olyg
on
i) M
anila
pap
erii)
M
arke
r pen
s iii
) M
athe
mat
ical
ta
bles
iv)
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
der
ive
the
form
ula
for
findi
ng th
e ar
ea o
f re
gula
r pol
ygon
s?
6
(b) A
pply
the
form
ula
to c
alcu
late
the
area
of a
regu
lar
poly
gon.
i) S
tude
nts i
n gr
oups
to
app
ly th
e fo
rmul
a in
find
ing
the
area
of
regu
lar p
olyg
ons
foun
d in
dai
ly li
fe.
ii)
Stud
ents
to p
rese
nt
thei
r gro
up w
ork
in
clas
s.iii
) The
teac
her t
o gu
ide
disc
ussi
on o
n th
e pr
esen
ted
wor
k.
i) M
athe
mat
ical
in
stru
men
tsii)
M
athe
mat
ical
ta
ble
Is th
e st
uden
t abl
e to
app
ly fo
rmul
a to
cal
cula
te
area
of r
egul
ar
poly
gons
?
144
TOPI
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OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
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AC
HIN
G
AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
2.5
Are
a of
Sim
ilar
Pol
ygon
sTh
e st
uden
t sho
uld
be
able
to:
(a)
Find
the
ratio
of
area
s of s
imila
r po
lygo
ns.
i) T
he te
ache
r to
guid
e st
uden
ts to
find
the
ratio
of t
he a
reas
of
two
sim
ilar t
riang
les
whe
re k
is th
e ra
tio o
f th
eir c
orre
spon
ding
si
des.
ii) S
tude
nts i
n gr
oups
to
com
pare
ratio
for a
rea
of si
mila
r rec
tang
les
and
squa
res.
iii) T
he te
ache
r to
guid
e st
uden
ts to
gen
eral
ize
thei
r res
ults
to ra
tio o
f ar
eas o
f any
sim
ilar
poly
gons
.
i) M
athe
mat
ical
in
stru
men
ts.
ii)
Mat
hem
atic
al
tabl
es.
iii)
Man
ila p
aper
iv
) M
arke
r pen
s v)
G
eo b
oard
vi)
Rub
ber b
ands
Is th
e st
uden
t abl
e to
der
ive
the
ratio
fo
r are
a of
sim
ilar
poly
gons
?
6
(b)
Solv
e pr
oble
ms
rela
ted
to ra
tio fo
r ar
eas o
f sim
ilar
poly
gons
.
i) T
he te
ache
r to
guid
e st
uden
ts in
solv
ing
prob
lem
s rel
ated
to
ratio
of a
reas
of s
imila
r po
lygo
ns.
ii) S
tude
nts t
o so
lve
prob
lem
s rel
ated
to
ratio
of a
rea
of si
mila
r po
lygo
ns.
i) M
athe
mat
ical
in
stru
men
ts.
ii)
Mat
hem
atic
al
tabl
es
Is th
e st
uden
t abl
e to
solv
e pr
oble
ms
rela
ted
to ra
tio o
f ar
eas o
f sim
ilar
poly
gons
?
145
TOPI
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OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
3.0
THR
EE
D
IMEN
SIO
NA
L FI
GU
RES
3.1
Thre
e D
imen
sion
alFi
gure
The
stud
ent s
houl
d be
ab
le to
:(a
) Cla
ssify
thre
e di
men
sion
al
figur
es.
i) S
tude
nts t
o co
llect
va
rious
thre
e di
men
sion
al o
bjec
ts.
ii) T
he te
ache
r to
guid
e st
uden
ts to
cla
ssify
th
e ob
ject
s int
o co
nes,
pyra
mid
s, pr
ism
s and
cy
linde
rs
i)
Man
ila c
ard
ii)
Con
esiii
) Pyr
amid
s iv
) Pr
ism
sv)
C
ylin
ders
Is th
e st
uden
t ab
le to
cla
ssify
th
ree
dim
ensi
onal
fig
ures
?
6
(b)
List
the
char
acte
ristic
s of
each
cla
ss.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e ch
arac
teris
tics o
f ea
ch c
lass
of t
hree
di
men
sion
al o
bjec
ts.
ii) S
tude
nts t
o lis
t the
ch
arac
teris
tics o
f cl
asse
s of t
hree
di
men
sion
al fi
gure
s.
Thre
e di
men
sion
alob
ject
s/m
odel
sIs
the
stud
ent
able
to li
st th
e ch
arac
teris
tics o
f th
ree
dim
ensi
onal
ob
ject
s?
3.2
Con
stru
ctio
n of
Th
ree
D
imen
sion
al
Figu
res
The
stud
ent s
houl
d be
ab
le to
con
stru
ct th
ree
dim
ensi
onal
figu
res.
i) Th
e te
ache
r to
guid
e st
uden
ts to
sket
ch n
ets
of th
ree
dim
ensi
onal
fig
ures
.ii)
St
uden
ts to
con
stru
ct
thre
e di
men
sion
al
figur
es in
gro
ups b
y us
ing
sim
ple
mat
eria
l su
ch a
s pap
ers,
man
ila
card
s, st
raw
s and
st
icks
.
i)
Pap
ers
ii)
Man
ila c
ards
iii)
Stra
ws
iv)
Stic
ks
v)
Glu
evi
) S
ciss
ors
vii)
Thr
ead
viii)
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t ab
le to
con
stru
ct
thre
e di
men
sion
al
obje
cts?
4
146
TOPI
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CS
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CIF
IC
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii)
Stud
ents
to d
ispl
ay
thei
r thr
ee d
imen
sion
al
figur
es fo
r eva
luat
ion
3.3
Sket
chin
g
Thre
e
D
imen
sion
al
Figu
res
The
stud
ent s
houl
d be
ab
le to
:(a
) Sk
etch
thre
e di
men
sion
al
figur
es.
i) T
he te
ache
r to
dem
onst
rate
how
to
dra
w sk
etch
es o
f th
ree
dim
ensi
onal
fig
ures
usi
ng o
bliq
ue
proj
ectio
ns.
ii) S
tude
nts t
o sk
etch
th
ree
dim
ensi
onal
fig
ures
usi
ng o
bliq
ue
proj
ectio
ns.
i) M
athe
mat
ical
in
stru
men
tii)
M
anila
pap
ers
iii) M
arke
r pen
s
Is th
e st
uden
t ab
le to
sket
ch
thre
e di
men
sion
al
figur
es?
12
(b)
Iden
tify
prop
ertie
s of
thre
e di
men
sion
al
figur
es.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
pl
anes
, edg
es a
nd
diag
onal
s in
thre
e di
men
sion
al o
bjec
ts/
figur
esii)
Stu
dent
s to
iden
tify
and
stat
e th
e pl
anes
, edg
es,
verti
ces a
nd d
iago
nals
in
thre
e di
men
sion
al
figur
es.
i) B
oxes
ii)
Tin
siii
) Bui
ldin
gs
mod
els
iv) C
ar m
odel
sv)
Th
ree
dim
ensi
onal
m
odel
s
Is th
e st
uden
t ab
le to
iden
tify
the
prop
ertie
s of
thre
e di
men
sion
al
figur
es?
147
TOPI
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CS
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CIF
IC
OB
JEC
TIV
ES
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AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
Find
the
angl
e be
twee
n a
line
and
a pl
ane.
i) T
he te
ache
r to
guid
e st
uden
ts to
loca
te a
nd
find
the
angl
e be
twee
n a
line
and
a pl
ane.
ii) S
tude
nts t
o fin
d th
e an
gle
betw
een
lines
an
d pl
anes
of d
iffer
ent
thre
e di
men
sion
al
figur
es.
i)
Thre
e di
men
sion
al
obje
cts/
mod
els.
ii)
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t abl
e to
find
the
angl
e be
twee
n a
line
and
a pl
ane?
(d) C
alcu
late
the
an
gle
betw
een
two
plan
es.
i) T
he te
ache
r to
guid
e st
uden
ts to
vi
sual
ize
and
disc
uss
inte
rsec
ting
plan
es
of th
ree
dim
ensi
onal
fig
ures
.ii)
The
teac
her t
o gu
ide
stud
ents
to c
alcu
late
th
e an
gle
betw
een
two
inte
rsec
ting
plan
es.
iii) S
tude
nts t
o ca
lcul
ate
the
angl
e be
twee
n tw
o in
ters
ectin
g pl
anes
i) Th
ree
dim
ensi
onal
ob
ject
s/m
odel
s ii)
M
athe
mat
ical
in
stru
men
ts
Is th
e st
uden
t abl
e to
cal
cula
te th
e an
gle
betw
een
two
plan
es?
148
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OPI
CS
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IC
OB
JEC
TIV
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AC
HIN
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AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
3.4
Surf
ace A
rea
of T
hree
D
imen
sion
al
Obj
ects
The
stud
ent s
houl
d be
ab
le to
:(a
) D
eriv
e th
e fo
rmul
ae
for c
alcu
latin
g th
e su
rfac
e ar
ea o
f pr
ism
s, cy
linde
rs,
and
pyra
mid
s and
co
ne.
i) Th
e te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ulae
of s
urfa
ce
area
of p
rism
s, cy
linde
rs, p
yram
ids
and
cone
s.ii)
The
teac
her t
o gu
ide
stud
ents
to c
alcu
late
th
e su
rfac
e ar
eas o
f pr
ism
s, cy
linde
rs a
nd
pyra
mid
s .iii
) Stu
dent
s in
grou
ps,
to c
alcu
late
the
surf
ace
area
s of
pris
ms,
cylin
ders
and
py
ram
ids.
i) T
hree
di
men
sion
al
obje
cts
ii) M
athe
mat
ical
ta
bles
iii) M
athe
mat
ical
in
stru
men
tsiv
) Sci
entifi
c po
cket
ca
lcul
ator
s
Is th
e st
uden
t abl
e to
der
ive
form
ula
for c
alcu
latin
g su
rfac
e ar
eas o
f pr
ism
s, cy
linde
rs
pyra
mid
s and
co
nes?
6
(b) A
pply
the
form
ulae
to
cal
cula
te th
e su
rfac
e ar
ea o
f sp
here
s.
i) Th
e te
ache
r to
guid
e st
uden
ts to
use
the
form
ula
in c
alcu
latin
g su
rfac
e ar
ea o
f a
sphe
re.
ii) S
tude
nts t
o ca
lcul
ate
the
surf
ace
area
of
sphe
res
i)
The
glob
e ii)
O
rang
esiii
) Wat
er-m
elon
iv
) M
odel
s
Is th
e st
uden
t abl
e to
cal
cula
te th
e su
rfac
e ar
ea o
f sp
here
s?
149
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
3.5
Volu
me
of th
ree
Dim
ensi
onal
O
bjec
ts
The
stud
ent s
houl
d be
ab
le to
:(a
) D
eriv
e th
e fo
rmul
ae
for c
alcu
latin
g vo
lum
e of
pris
ms,
cylin
ders
, pyr
amid
s an
d co
nes.
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
form
ulae
for fi
ndin
g th
e vo
lum
e of
pris
ms,
cylin
ders
, pyr
amid
s an
d co
nes.
ii) T
he te
ache
r to
guid
e a
disc
ussi
on o
n ho
w
to fi
nd th
e vo
lum
e of
pr
ism
s and
cyl
inde
rs
by u
sing
the
base
are
a an
d th
e he
ight
.iii
) Stu
dent
s to
calc
ulat
e th
e vo
lum
e of
pris
ms
and
cylin
ders
.
i) Th
ree
dim
ensi
onal
fig
ures
/mod
els
ii)
Mat
hem
atic
al
tabl
es.
iii) M
athe
mat
ical
in
stru
men
ts.
iv)
Scie
ntifi
c po
cket
ca
lcul
ator
s.
Is th
e st
uden
t ab
le to
der
ive
the
form
ulae
fo
r vol
ume
of
pris
ms,
cylin
ders
, py
ram
ids a
nd
cone
s?
6
(b) A
pply
the
form
ulae
to
cal
cula
te
the
volu
me
of
cylin
ders
pyr
amid
s an
d co
nes.
i) T
he te
ache
r to
guid
e st
uden
ts to
app
ly th
e fo
rmul
a of
a c
one
and
pyra
mid
, pris
ms a
nd
cylin
der
ii) S
tude
nts t
o ap
ply
the
form
ula
to c
alcu
late
the
volu
me
of c
ones
and
pyr
amid
s
i) M
athe
mat
ical
ta
ble
ii) S
cien
tific
pock
et
calc
ulat
ors
Is th
e st
uden
t ab
le to
cal
cula
te
the
volu
me
of
pris
ms,
cylin
ders
py
ram
ids a
nd
cone
s?
150
TOPI
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OPI
CS
SPE
CIF
IC
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JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
4.0
PRO
BA
BIL
ITY
4.1
Prob
abili
ty o
f an
Eve
ntTh
e st
uden
t sho
uld
be
able
to(a
) Det
erm
ine
the
prob
abili
ty o
f an
even
t thr
ough
ex
perim
ents
.
i) T
he te
ache
r to
guid
e st
uden
ts to
per
form
th
e ex
perim
ents
such
as
rolli
ng a
die
or
toss
ing
a co
in in
ord
er
to d
evel
op th
e co
ncep
t of
pro
babi
lity
of a
n ev
ent.
ii) S
tude
nts t
o pe
rfor
m
expe
rimen
ts o
n pr
obab
ility
and
reco
rd
thei
r res
ults
.iii
) The
teac
her t
o gu
ide
stud
ent t
o us
e th
e re
sults
obt
aine
d to
de
fine
prob
abili
ty
i)
Coi
n ii)
D
ieiii
) C
olou
red
obje
cts
iv)
Clo
thv)
C
ards
vi
) G
ames
Is th
e st
uden
t abl
e to
det
erm
ine
the
prob
abili
ty o
f an
even
t thr
ough
ex
perim
ent?
12
(b)
Inte
rpre
t ex
perim
enta
l re
sults
in re
latio
n to
real
life
oc
curr
ence
s.
i) T
he te
ache
r to
guid
e st
uden
ts th
roug
h qu
estio
ns a
nd
answ
ers t
o in
terp
ret
expe
rimen
tal r
esul
ts in
re
al li
fe si
tuat
ion.
ii) S
tude
nts i
n gr
oups
to
do e
xper
imen
t usi
ng
larg
e nu
mbe
r of t
rials
i)
Coi
n ii)
D
ieiii
) C
olou
red
obje
cts
iv)
Clo
thv)
Pl
ayin
g ca
rds
vi)
Gam
es
Is th
e st
uden
t ab
le to
inte
rpre
t ex
perim
enta
l re
sults
in re
latio
n to
real
life
oc
curr
ence
s?
151
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OB
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AC
HIN
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AN
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c) W
rite
the
form
ula
for fi
ndin
g th
e pr
obab
ility
of a
n ev
ent.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
writ
e th
e fo
rmul
a of
the
prob
abili
ty fo
r an
even
t fro
m th
e ex
perim
enta
l res
ults
.ii)
Stu
dent
s ind
ivid
ually
to
writ
e th
e fo
rmul
a fo
r fin
ding
pro
babi
lity
of
an e
vent
i)
Gam
es
ii)
Coi
ns
iii)
Die
iv)
Col
oure
d ob
ject
s v)
Pl
ayin
g ca
rds
Is th
e st
uden
t ab
le to
writ
e th
e fo
rmul
a fo
r fin
ding
pro
babi
lity
of a
n ev
ent?
(d) A
pply
the
form
ula
to c
alcu
late
the
prob
abili
ty o
f an
even
t.
i) T
he te
ache
r to
guid
e st
uden
ts to
app
ly th
e fo
rmul
a fo
r find
ing
the
prob
abili
ty o
f an
even
t.ii)
The
teac
her t
o gu
ide
stud
ents
to d
iscu
ss
how
to fi
nd th
e pr
obab
ilitie
s of e
vent
to
occ
ur o
r not
to
occu
r.iii
) Stu
dent
s to
solv
e pr
oble
ms o
n pr
obab
ility
.
Cha
rtsIs
the
stud
ent a
ble
to c
alcu
late
the
prob
abili
ty o
f an
even
t?
152
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
4.2
Com
bine
d Ev
ents
The
stud
ent s
houl
d be
ab
le to
:(a
) Pe
rfor
m
expe
rimen
ts o
f tw
o co
mbi
ned
even
ts.
i) T
he te
ache
r to
guid
e st
uden
ts to
per
form
the
activ
ities
of d
oing
two
even
ts a
t the
sam
e tim
e in
ord
er to
exp
lain
the
conc
ept o
f com
bine
d ev
ents
.ii)
Stu
dent
s to
perf
orm
ex
perim
ents
and
re
cord
the
resu
lts
i)
Coi
n ii)
D
ieiii
) C
olou
red
obje
cts
iv)
Clo
th g
ames
Is th
e st
uden
t ab
le to
per
form
ex
perim
ents
of
two
com
bine
d ev
ents
?
12
(b)
Dra
w a
thre
e di
agra
m o
f co
mbi
ned
even
ts.
i) T
he te
ache
r to
guid
e st
uden
ts to
per
form
th
e ac
tiviti
es o
f doi
ng
two
even
ts a
t the
sa
me
time
in o
rder
to
find
the
prob
abili
ty
of c
ombi
ned
even
ts
by th
e us
e of
a tr
ee
diag
ram
.ii)
Stu
dent
s to
solv
e pr
oble
ms o
n pr
obab
ility
of
com
bine
d ev
ents
by
the
use
of th
ree
diag
ram
s.
i)
Die
ii)
Play
ing
card
siii
) C
olou
red
obje
cts
iv)
Coi
nsv)
C
loth
vi
) R
uler
vi
i) G
ames
Is th
e st
uden
t ab
le to
dra
w a
tre
e di
agra
m o
f co
mbi
ne e
vent
s?
153
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c) F
ind
the
prob
abili
ty
of tw
o co
mbi
ned
even
ts u
sing
the
form
ula.
i) Th
e te
ache
r to
guid
e st
uden
ts to
find
the
prob
abili
ty o
f tw
o co
mbi
ned
even
ts u
sing
th
e fo
rmul
a.ii)
Stu
dent
s to
calc
ulat
e th
e pr
obab
ility
of t
wo
com
bine
d ev
ents
by
form
ula
i)
Coi
ns
ii)
Die
iii)
Gam
esiv
) Po
pula
tion
reco
rds
v)
Wea
ther
fo
reca
st
Is th
e st
uden
t ab
le to
find
the
prob
abili
ty o
f tw
o co
mbi
ned
even
ts?
(d)
App
ly th
e kn
owle
dge
of
prob
abili
ty to
de
term
ine
the
occu
rren
ce o
f ev
ents
in re
al li
fe
situ
atio
n.
i) T
he te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
on
app
licat
ion
of
the
know
ledg
e of
pr
obab
ility
in re
al li
fe
situ
atio
n.ii)
Stu
dent
s to
appl
y th
e kn
owle
dge
of p
roba
bilit
y to
pr
edic
t out
com
es o
f oc
curr
ence
s in
real
lif
e.
i)
Gen
etic
sii)
Po
pula
tion
reco
rds
iii)
Wea
ther
fo
reca
st
Is th
e st
uden
t ab
le to
app
ly
the
know
ledg
e of
pro
babi
lity
to d
eter
min
e th
e oc
curr
ence
of
even
ts in
real
life
si
tuat
ion?
154
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
5.0
TRIG
ON
OM
ETRY
5.1
Trig
onom
etric
R
atio
sTh
e st
uden
t sho
uld
be
able
to:
(a)
Det
erm
ine
the
sine
, cos
ine
and
tang
ent o
f an
angl
e m
easu
red
in th
e cl
ockw
ise
and
antic
lock
wis
e di
rect
ions
.
i) T
he te
ache
r to
guid
e th
e st
uden
ts to
dis
cuss
th
e si
gn o
f sin
es,
cosi
nes a
nd ta
ngen
t fo
r ang
les i
n th
e fo
ur
quad
rant
sii)
Stu
dent
s in
grou
ps
to fi
nd si
ne, c
osin
e an
d ta
ngen
t of a
ngle
s m
easu
red
in a
ny
dire
ctio
n.
i) M
athe
mat
ical
ta
bles
ii)
Trig
onom
etric
ta
bles
iii)
Cal
cula
tors
Is th
e st
uden
t abl
e to
det
erm
ine
the
trigo
nom
etric
ra
tios o
f a g
iven
an
gle?
7
(b) A
pply
trig
onom
etric
ra
tios t
o so
lve
prob
lem
s in
daily
lif
e.
i) T
he te
ache
r tog
uide
st
uden
ts to
do
activ
ities
whi
ch
invo
lve
appl
icat
ions
of
trig
onom
etric
ratio
s in
dai
ly li
fe su
ch a
s fin
ding
hei
ghts
of
tow
ers,
build
ings
, m
ount
ains
and
wid
th
of ri
vers
. ii)
Stu
dent
s to
wor
k in
divi
dual
ly to
use
tri
gono
met
ric ra
tios i
n so
lvin
g pr
oble
ms.
i)
Trea
dle
whe
el
ii)
Clin
omet
eriii
) R
ope
iv)
Rul
ev)
Ta
pe m
easu
re
vi)
Trig
onom
etric
ta
bles
vii)
Prot
ract
or
Is th
e st
uden
t abl
e to
find
dis
tanc
es
indi
rect
ly
by a
pply
ing
trigo
nom
etric
ra
tios?
155
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) T
he te
ache
r to
guid
e st
uden
ts to
solv
e pr
oble
ms u
sing
tri
gono
met
ric ta
bles
or
scal
e dr
awin
g5.
2 Si
ne a
nd
Cos
ine
Func
tions
The
stud
ent s
houl
d be
ab
le to
(a)
Find
sine
s and
co
sine
s of a
ngle
s θ
such
that
-720
o ≤ θ
≤ 7
20o
i) T
he te
ache
r to
guid
e st
uden
ts to
pre
pare
ta
ble
of v
alue
s of
sine
and
cos
ine
of
angl
e q
such
that
-720
o ≤ θ
≤ 7
20o
ii) T
he te
ache
r to
guid
e st
uden
ts to
dra
w th
e gr
aph
of si
ne a
nd
cosi
ne fu
nctio
ns u
sing
ta
ble
of v
alue
s.iii
) The
teac
her t
o us
e qu
estio
ns a
nd a
nsw
ers
to d
iscu
ss fe
atur
es o
f th
e gr
aphs
of s
ine
and
cosi
ne fu
nctio
ns
i)
Rul
erii)
G
raph
pap
eriii
) Sq
uare
d pa
pers
iv)
Gra
ph b
oard
Is th
e st
uden
tab
le to
find
sine
and
cos
ine
of
a gi
ven
angl
e?
6
(b)
Inte
rpre
t the
gra
phs
of si
ne a
nd c
osin
e fu
nctio
ns.
i) T
he te
ache
r to
guid
e st
uden
ts to
inte
rpre
t th
e gr
aphs
of s
ine
and
cosi
ne fu
nctio
ns b
y us
ing
wor
ds su
ch a
s ev
en o
r odd
func
tions
, an
d pe
riodi
c or
non
pe
riodi
c fu
nctio
n.
Gra
phs o
f sin
es a
nd
cosi
nes
Is th
e st
uden
t ab
le to
inte
rpre
t co
rrec
tly g
raph
s of
sine
and
cos
ine
func
tions
?
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AN
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts t
o id
entif
y ev
en o
r odd
func
tions
an
d pe
riodi
c or
non
pe
riodi
c fu
nctio
n
5.3
Sine
and
C
osin
e R
ules
The
stud
ent s
houl
d be
ab
le to
:(a
) D
eriv
e th
e si
ne a
nd
cosi
ne ru
les.
i) T
he te
ache
r to
guid
e st
uden
ts to
der
ive
the
sine
rule
.ii)
Stu
dent
s in
grou
ps to
so
lve
prob
lem
s usi
ng
the
sine
rule
s.iii
) The
teac
her t
o gu
ide
stud
ents
to d
eriv
e th
e co
sine
rule
.iv
) Stu
dent
s in
grou
ps to
so
lve
prob
lem
s usi
ng
the
cosi
ne ru
le.
v) T
he te
ache
r to
dem
onst
rate
how
to
solv
e pr
oble
ms
rela
ted
to th
e si
ne o
r co
sine
rule
by
draw
ing
cons
truct
ion.
vi
) Stu
dent
s to
solv
e pr
oble
ms r
elat
ed
to si
ne o
r cos
ine
rule
by
draw
ing
or
cons
truct
ion
i)
Rul
erii)
C
olou
red
chal
kIs
the
stud
ent a
ble
to d
eriv
e th
e si
ne
and
cosi
ne ru
les?
7
157
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) A
pply
the
sine
and
co
sine
rule
s in
solv
ing
prob
lem
s on
tria
ngle
s.
i) T
he te
ache
r to
guid
e st
uden
ts to
use
the
sine
and
cos
ine
rule
s in
solv
ing
real
life
pr
oble
ms i
ndiv
idua
llyii)
Stu
dent
s ind
ivid
ually
to
app
ly si
ne a
nd
cosi
ne ru
les t
o so
lve
rela
ted
prob
lem
s
i) R
ules
ii) C
olou
red
chal
ksIs
the
stud
ent
able
to a
pply
the
sine
and
cos
ine
rule
s in
solv
ing
trian
gles
?
5.4
Com
poun
d A
ngle
sTh
e st
uden
t sho
uld
be a
ble
to a
pply
th
e co
mpo
und
angl
e fo
rmul
ae fo
r si
ne, c
osin
e an
d ta
ngen
t in
solv
ing
trigo
nom
etric
pr
oble
ms.
i) T
he te
ache
r to
expl
ain
the
com
poun
d an
gles
fo
r sin
e an
d co
sine
.ii)
The
teac
her t
o de
mon
stra
te to
st
uden
ts th
e us
e of
co
mpo
und
angl
e fo
rmul
ae in
solv
ing
and
sim
plify
ing
trigo
nom
etric
pr
oble
ms.
iii)
Stud
ents
in g
roup
s to
solv
e an
d si
mpl
ify
trigo
nom
etric
pr
oble
ms u
sing
co
mpo
und
angl
e fo
rmul
ae.
i) C
harts
of
trigo
nom
etric
fo
rmul
ae fo
r co
mpo
und
angl
es.
ii) T
rigon
omet
ric
tabl
es
Is th
e st
uden
t ab
le to
app
ly th
e co
mpo
und
angl
e fo
rmul
ae to
solv
e tri
gono
met
ric
prob
lem
s?
4
158
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AC
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
6.0
VEC
TOR
S6.
1 D
ispl
acem
ent
and
Posi
tion
Vect
ors
The
stud
ent s
houl
d be
ab
le to
:(a
) Ex
plai
n th
e co
ncep
t of a
vec
tor
quan
tity.
i) T
he te
ache
r to
guid
e st
uden
ts th
roug
h qu
estio
ns a
nd a
nsw
ers
to e
xpla
in th
e co
ncep
t of
a v
ecto
r qua
ntity
.ii)
Stu
dent
s in
grou
ps to
di
scus
s the
diff
eren
ce
betw
een
the
vect
or a
nd
scal
ar q
uant
ities
.
i)
Gra
ph b
oard
ii)
Rul
eriii
) G
raph
pap
ers
iv)
Set s
quar
ev)
Col
oure
d ch
alks
vi
) G
eo b
oard
vii)
Rub
ber b
ands
viii)
Squ
ared
pap
er
Is th
e st
uden
t ab
le to
exp
lain
th
e co
ncep
t of a
ve
ctor
qua
ntity
?
8
(b)
Dis
tingu
ish
betw
een
disp
lace
men
t and
po
sitio
n ve
ctor
s.
i) T
he te
ache
r to
guid
e st
uden
ts in
dis
cuss
ing
the
mea
ning
of
disp
lace
men
t eq
uiva
lent
and
pos
ition
ve
ctor
s.ii)
Stu
dent
s in
grou
ps to
di
stin
guis
h be
twee
n di
spla
cem
ent p
ositi
on
and
equi
vale
nt v
ecto
rs
in tw
o di
men
sion
s
i) G
eo b
oard
ii) G
raph
s pap
ers
iii) M
athe
mat
ical
in
stru
men
ts
Is th
e st
uden
t abl
e to
dis
tingu
ish
betw
een
disp
lace
men
t and
po
sitio
n ve
ctor
s?
(c)
Res
olve
any
ve
ctor
into
i an
d j
com
pone
nts.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
reso
lve
a gi
ven
vect
or in
to i
and
j co
mpo
nent
sii)
Stu
dent
s ind
ivid
ually
to
reso
lve
give
n i
and
j vec
tors
into
co
mpo
nent
s.
i)
Gra
ph p
aper
ii)
Col
oure
d
ch
alks
iii)
Mat
hem
atic
al
inst
rum
ents
Is th
e st
uden
t abl
e to
reso
lve
any
vect
orin
to i
and
jco
mpo
nent
s?
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
6.2
Mag
nitu
de a
nd
Dire
ctio
n of
a
Vect
or
The
stud
ent s
houl
d be
abl
e to
cal
cula
te
the
mag
nitu
de a
nd
dire
ctio
n of
a v
ecto
r.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
find
the
mag
nitu
de a
nd
dire
ctio
n of
a v
ecto
rii)
Stu
dent
s ind
ivid
ually
to
cal
cula
te th
e m
agni
tude
and
di
rect
ion
of a
vec
tor.
i) M
athe
mat
ical
ta
ble
ii) M
athe
mat
ical
in
stru
men
ts
Is th
e st
uden
t ab
le to
cal
cula
te
the
mag
nitu
de
and
dire
ctio
n of
a
vect
or?
4
6.3
Sum
and
D
iffer
ence
of
Vect
ors
The
stud
ent s
houl
d be
ab
le to
:(a
) Fi
nd th
e su
m o
f tw
o or
mor
e ve
ctor
s.
i) T
he te
ache
r to
dem
onst
rate
how
to
find
the
sum
of
two
or m
ore
vect
ors
diag
ram
mat
ical
ly.
ii) S
tude
nts t
o fin
d th
e su
m o
f giv
en v
ecto
rs
by d
raw
ing.
iii) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
find
the
sum
of
vect
ors w
ithou
t usi
ng
diag
ram
siv
) Stu
dent
s in
grou
ps
to fi
nd th
e su
m o
f ve
ctor
s with
out u
sing
di
agra
ms
Gra
ph p
aper
M
athe
mat
ical
in
stru
men
ts
Is th
e st
uden
t abl
e to
find
the
sum
of
two
or m
ore
vect
ors?
6
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ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b)
Find
the
diffe
renc
e of
vec
tors
.i)
The
teac
her t
o ex
plai
n th
e m
eani
ng o
f op
posi
te v
ecto
r.ii)
The
teac
her t
o de
mon
stra
te h
ow to
fin
d di
agra
mm
atic
ally
th
e di
ffere
nce
of
vect
ors b
y us
ing
oppo
site
vec
tors
.iii
) Stu
dent
s to
find
the
diffe
renc
e of
giv
en
vect
ors b
y dr
awin
g.iv
) The
teac
her t
o gu
ide
stud
ents
to
disc
uss h
ow to
find
th
e di
ffere
nce
of
vect
ors w
ithou
t usi
ng
diag
ram
s.v)
Stu
dent
s in
grou
ps to
fin
d th
e di
ffere
nce
betw
een
vect
ors
with
out u
sing
di
agra
ms.
i)
Geo
boar
dii)
R
ubbe
r ban
dsiii
) R
uler
iv)
Col
oure
d ch
alks
v)
G
raph
pap
ers
vi)
Squa
red
pape
rs
vii)
Gra
ph b
oard
Is th
e st
uden
t ab
le to
find
the
diffe
renc
e of
ve
ctor
s?
6.4
Mul
tiplic
atio
n of
a V
ecto
r by
a Sc
alar
The
stud
ent s
houl
d be
abl
e to
mul
tiply
a
vect
or b
y a
scal
ar.
i) Th
e te
ache
r to
use
exam
ples
to d
iscu
ss
with
stud
ents
how
to
mul
tiply
a v
ecto
r by
a sc
alar
.
i) C
olou
red
chal
ks
ii) R
uler
Is th
e st
uden
t ab
le to
mul
tiply
a
vect
or b
y a
scal
ar?
4
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii)
The
teac
her t
hrou
gh
ques
tions
and
ans
wer
s to
dem
onst
rate
how
to
mul
tiply
a v
ecto
r by
a sc
alar
.6.
5 A
pplic
atio
n of
Ve
ctor
sTh
e st
uden
t sho
uld
be
able
to a
pply
vec
tors
in
solv
ing
sim
ple
prob
lem
s on
velo
citie
s, di
spla
cem
ents
and
fo
rces
.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e us
e of
vec
tors
in
solv
ing
sim
ple
prob
lem
s on
velo
citie
s.ii)
The
teac
her t
o de
mon
stra
te h
ow
to fi
nd b
earin
gs
by d
raw
ing
and
mea
surin
g.iii
) Stu
dent
s to
do
exer
cise
s on
appl
icat
ion
of v
ecto
rs
in so
lvin
g re
al li
fe
prob
lem
s.
i)
Rul
erii)
P
rotra
ctor
iii)
Col
oure
d ch
alks
iv
) M
agne
tic
com
pass
v)
Set
squa
revi
) S
quar
ed p
aper
vi
i) G
raph
boa
rd
viii)
Gra
ph p
aper
s
Is th
e st
uden
t abl
e to
app
ly v
ecto
rs in
so
lvin
g pr
oble
ms
on v
eloc
ities
, di
spla
cem
ents
and
fo
rces
?
5
7.0
MAT
RIC
ES A
ND
TR
AN
SFO
RM
A-
TIO
NS
7.1
Ope
ratio
ns o
n M
atric
esTh
e st
uden
t sho
uld
be
able
to:
(a) E
xpla
in th
e co
ncep
t of
a m
atrix
.
i) S
tude
nts t
o co
llect
pr
ice
lists
of i
tem
s.ii)
The
teac
her t
o gu
ide
the
stud
ents
on
how
to
org
aniz
e th
e ite
ms
and
pric
es in
col
umns
an
d ro
ws (
rect
angu
lar
arra
y).
i) C
olou
red
chal
ksii)
Pric
es o
f ite
ms
Is th
e st
uden
t ab
le to
exp
lain
th
e co
ncep
t of
mat
rix?
16
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AC
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
iii) T
he te
ache
r to
guid
e st
uden
ts to
exp
lain
the
mea
ning
of m
atrix
.(b
) A
dd m
atric
es o
f or
der u
p to
2 ×
2.
i) T
he te
ache
r to
dem
onst
rate
how
to
add
mat
rices
of o
rder
up
to 2
× 2
.ii)
Stu
dent
s in
pairs
to
solv
e pr
oble
ms o
n ad
ditio
n of
2 ×
2
mat
rices
Cha
rts o
f mat
rices
Is th
e st
uden
t ab
le to
add
2 ×
2
mat
rices
?
(c) S
ubtra
ct m
atric
es o
f or
der u
p to
2 ×
2.
i) T
he te
ache
r to
dem
onst
rate
how
to
subt
ract
mat
rices
of
orde
r up
to 2
× 2
.ii)
Stu
dent
s in
grou
ps
to
Sol
ve p
robl
ems o
n su
btra
ctio
n of
mat
rices
of
ord
er u
p to
2 ×
2
Cha
rts o
f mat
rices
Is th
e st
uden
t ab
le to
subt
ract
m
atric
es o
f ord
er
up to
2 ×
2?
(d)
Mul
tiply
a m
atrix
of
ord
er 2
× 2
by
a sc
alar
.
i) T
he te
ache
r to
dem
onst
rate
the
mul
tiplic
atio
n of
a
2 ×
2 m
atrix
by
a sc
alar
. ii)
Stu
dent
s in
pairs
to
solv
e pr
oble
ms o
n m
ultip
licat
ion
of 2
× 2
m
atric
es b
y sc
alar
s.
i) C
olou
red
chal
k ii)
Cha
rts o
f m
atric
es
Is th
e st
uden
t abl
e to
mul
tiply
a
2 ×
2 m
atrix
by
a sc
alar
?
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(e)
Mul
tiply
two
mat
rices
of o
rder
up
to 2
× 2
i) T
he te
ache
r to
dem
onst
rate
the
mul
tiplic
atio
n of
two
mat
rices
of o
rder
up
to
2 ×
2ii)
Stu
dent
s in
pairs
to
do
exer
cise
s on
mul
tiply
ing
two
mat
rices
of o
rder
up
to
2 ×
2
i)
Cha
rts o
f m
atric
esii)
C
olou
red
chal
k
Is th
e st
uden
t abl
e to
mul
tiply
two
mat
rices
of o
rder
up
to 2
× 2
?
7.2
Inve
rse
of a
M
atrix
The
stud
ent s
houl
d be
ab
le to
:(a
) C
alcu
late
the
dete
rmin
ant o
f a
2 ×
2 m
atrix
.
i) T
he te
ache
r to
dem
onst
rate
how
to
cal
cula
te th
e de
term
inan
t of a
2 ×
2
mat
rix.
ii) S
tude
nts i
n gr
oups
to
cal
cula
te th
e de
term
inan
ts o
f giv
en
2 ×
2 m
atric
es.
Cha
rts o
f de
term
inan
ts o
f m
atric
es
Is th
e st
uden
t abl
e to
cal
cula
te th
e de
term
inan
t of a
2
× 2
mat
rix?
9
(b)
Find
the
inve
rse
of
a 2
× 2
mat
rix.
i) Th
e te
ache
r to
guid
e st
uden
ts in
find
ing
the
inve
rse
of a
mat
rix.
ii) S
tude
nts i
n sm
all
grou
ps to
find
the
inve
rse
of g
iven
mat
rix
Cha
rts o
f inv
erse
s of
mat
rices
Is th
e st
uden
t abl
e to
find
the
inve
rse
of a
2 ×
2 m
atrix
?
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EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
App
ly 2
× 2
m
atric
es to
solv
e si
mul
tane
ous
equa
tions
.
i) T
he te
ache
r to
guid
e st
uden
ts to
dis
cuss
th
e ap
plic
atio
n of
2
× 2
mat
rices
in
solv
ing
sim
ulta
neou
s eq
uatio
ns.
ii) S
tude
nts i
n sm
all
grou
ps to
app
ly
2 ×
2 m
atric
es in
so
lvin
g si
mul
tane
ous
equa
tions
Is th
e st
uden
t abl
e to
app
ly 2
× 2
m
atric
es to
solv
e si
mul
tane
ous
equa
tions
?
7.3.
Mat
rices
and
Tran
sfor
mat
ions
The
stud
ent s
houl
d be
ab
le to
:(a
) Tra
nsfo
rm a
ny
poin
t P (x
, y) i
nto
),
(1
11
yx
p b
y pr
e- m
ultip
lyin
g
x y⎛ ⎝⎜
⎞ ⎠⎟ w
ith a
tra
nsfo
rmat
ion
mat
rix
Τ=
ab
cd
⎛ ⎝⎜⎞ ⎠⎟
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
mul
tiply
a
2 ×
2 m
atrix
and
a
colu
mn
mat
rix.
ii) T
he te
ache
r to
use
exam
ples
to
dem
onst
rate
a
trans
form
atio
n of
a p
oint
by
a tra
nsfo
rmat
ion
mat
rix.
iii)
Stud
ents
in p
airs
to
tran
sfor
m th
e gi
ven
poin
ts b
y us
ing
diffe
rent
tra
nsfo
rmat
ion
mat
rices
i) C
olou
rded
ch
alks
ii)
Gra
ph b
oard
iii
) M
athe
mat
ical
ta
bles
iv
) R
uler
v)
Geo
boar
dvi
) R
ubbe
r ban
dsvi
i) G
raph
pap
ers
viii)
Squ
ared
pap
er
Is th
e st
uden
t ab
le to
tran
sfor
m
a po
int b
y pr
e-
mul
tiply
ing
its
colu
mn
trans
form
atio
n m
atrix
by
a m
atrix
?
16
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RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) A
pply
the
mat
rix
÷÷ ���� ��
10
01
I
to re
flect
a p
oint
P(
x,y)
in th
e x
– ax
is
i) T
he te
ache
r to
guid
e st
uden
ts to
refle
ct a
po
int p
(x, y
) in
the
x
-axi
s usi
ng th
e m
atrix
÷÷ ���� ��
10
01
I
ii) S
tude
nts t
o w
ork
indi
vidu
ally
in
refle
ctin
g gi
ven
poin
ts
in x
-axi
s usi
ng th
e ap
prop
riate
mat
rix
i)
Rul
erii)
G
eobo
ard
iii)
Rub
ber b
ands
iv)
Gra
ph p
aper
sv)
S
quar
ed
pape
rsvi
) G
raph
boa
rd
vii)
Mat
hem
atic
al
tabl
e
Is th
e st
uden
t ab
le to
app
ly th
e m
atrix
÷÷ ��
�� ��
10
01
I to re
flect
a p
oint
P(
x,y)
in th
e x
–ax
is?
(c) A
pply
the
mat
rix
÷÷ ���� ��
10
01
I
t
o re
flect
a p
oint
p
(x, y
) in
the
y –
axis
i) Th
e te
ache
r to
guid
e st
uden
ts to
refle
ct a
po
int p
(x, y
) in
the
y-ax
is u
sing
the
mat
rix
÷÷ ���� ��
10
01
I
ii) S
tude
nts t
o w
ork
indi
vidu
ally
in
refle
ctin
g gi
ven
poin
ts
in th
e y-
axis
usi
ng th
e ap
prop
riate
mat
rix.
i)
Geo
boa
rd
ii)
Rul
eiii
) Col
ourd
cha
lk
iv)
Rub
ber b
ands
v)
M
athe
mat
ical
tabl
es
Is th
e st
uden
t ab
le
to a
pply
the
mat
rix
÷÷ ���� ��
10
01
I to re
flect
the
poin
t P(
x, y
) in
the
y ax
is?
166
TOPI
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CS
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CIF
IC
OB
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TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(d)
Use
a m
atrix
op
erat
or to
rota
te
any
poin
t P(x
,y)
thro
ugh
90o ,
180o ,2
70o a
nd 3
60o
abou
t the
orig
in
i) T
he te
ache
r to
use
exam
ples
to
dem
onst
rate
the
rota
tion
of a
poi
nt
p(
x , y
) thr
ough
90o ,
180o ,
270o a
nd 3
60o
abou
t the
orig
in u
sing
th
e ro
tatio
n m
atri
T=
sinθ
cosθ
cosθ
sinθ
⎛ ⎝⎜⎞ ⎠⎟
ii) S
tude
nts i
n gr
oups
to
rota
te v
ario
us
poin
ts th
roug
h 90
o , 28
0o , 27
0o and
360
o ab
out t
he o
rigin
us
ing
the
appr
opria
te
trans
form
atio
n m
atrix
i)
Geo
boa
rd
ii)
Rul
eiii
) G
raph
pap
er
iv)
Rub
ber b
ands
v)
M
athe
mat
ical
ta
bles
Is t
he st
uden
t ab
le to
rota
tea
poin
t P(x
, y)
thro
ugh
90o ,
180o 2
70o ,
360o a
bout
the
orig
in b
y us
ing
a m
atrix
?
(e)
Use
the
enla
rgem
ent m
atrix
Ε=
ΚΟ
ΟΚ
⎛ ⎝⎜⎞ ⎠⎟
in e
nlar
ging
figu
res
i) Th
e te
ache
r to
use
exam
ples
to
dem
onst
rate
the
enla
rgem
ent o
f figu
res
usin
g a
mat
rix .
Ε=
ΚΟ
ΟΚ
⎛ ⎝⎜⎞ ⎠⎟
i)
Geo
boar
dii)
C
olou
red
chal
k iii
) R
ule
iv)
Rub
ber b
ands
m
atrix
.
Ε=
ΚΟ
ΟΚ
⎛ ⎝⎜⎞ ⎠⎟
Is th
e st
uden
t ab
le to
enl
arge
a
figur
e gi
ven
an e
nlar
gem
ent
fact
or o
f the
fo
rm?
167
TOPI
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B-T
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CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
ii) S
tude
nts i
n pa
irs to
en
larg
e gi
ven
figur
es
usin
g th
e en
larg
emen
t m
atrix
8.0
LIN
EAR
PR
OG
RA
M-
MIN
G
8.1
Sim
ulta
neou
sEq
uatio
nsTh
e st
uden
t sho
uld
be
able
to:
(a)
Form
sim
ulta
neou
s eq
uatio
n fr
om w
ord
prob
lem
s.
i) T
he te
ache
r to
use
exam
ples
in g
uide
ing
a di
scus
sion
on
how
to fo
rmul
ate
linea
r sim
ulta
neou
s eq
uatio
ns fr
om w
ord
prob
lem
s.ii)
Stu
dent
s to
form
ulat
e lin
ear s
imul
tane
ous
equa
tion
from
wor
k pr
oble
ms i
ndiv
idua
lly.
i)
Gra
ph p
aper
ii)
Rul
eriii
) S
quar
e pa
pers
iv)
Geo
boar
dv)
R
ubbe
r ban
dsvi
) G
raph
boa
rd
Is th
e st
uden
t ab
le to
form
si
mul
tane
ous
equa
tions
from
w
ord
prob
lem
s?
6
(b)
Solv
e si
mul
tane
ous
equa
tions
gr
aphi
cally
i) Th
e te
ache
r to
guid
e st
uden
ts to
solv
e lin
ear s
imul
tane
ous
equa
tions
gra
phic
ally
.ii)
Stu
dent
s in
grou
ps
to so
lve
vario
us
linea
r sim
ulta
neou
s eq
uatio
ns fo
rmul
ated
fr
om w
ord
prob
lem
s gr
aphi
cally
.
i)
Gra
ph b
oard
ii)
Gra
ph p
aper
iii
) R
uler
iv)
Geo
boar
dv)
R
ubbe
r ban
dsvi
) C
olou
red
chal
k
Is th
e st
uden
t ab
le to
solv
e si
mul
tane
ous
equa
tions
gr
aphi
cally
?
168
TOPI
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B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
8.2
Ineq
ualit
ies
The
stud
ent s
houl
d be
ab
le to
:(a
) Fo
rm li
near
in
equa
litie
s in
two
unkn
owns
from
w
ord
prob
lem
s.
i) T
he te
ache
r to
guid
e st
uden
ts to
form
line
ar
ineq
ualit
ies i
n tw
o un
know
ns fr
om a
wor
d pr
oble
m.
ii) S
tude
nts i
n gr
oups
to
form
ulat
e lin
ear
ineq
ualit
ies i
n tw
o un
know
ns fr
om w
ord
prob
lem
s
i)
Man
ila p
aper
ii)
Cha
rtsIs
the
stud
ent
able
to fo
rm li
near
in
equa
litie
s in
two
unkn
owns
?
6
(b)
Find
the
solu
tion
set o
f sim
ulta
neou
s lin
ear i
nequ
aliti
es
grap
hica
lly.
i) Th
e te
ache
r to
dem
onst
rate
to
stud
ents
the
dete
rmin
atio
n of
fe
asib
le re
gion
of a
set
of li
near
ineq
ualit
ies
grap
hica
lly.
ii) S
tude
nts i
n gr
oups
to
solv
e pr
oble
ms
on d
eter
min
ing
the
solu
tion
of a
set o
f lin
ear i
nequ
aliti
es
grap
hica
lly
i)
Gra
ph b
oard
ii)
Gra
ph p
aper
siii
) G
eobo
ard
iv)
Rub
ber b
ands
v)
Rul
ervi
) C
olou
red
chal
ks
vii)
Pen
cil
viii)
Squ
ared
pap
er
Is th
e st
uden
t ab
le to
find
the
solu
tion
set o
f si
mul
tane
ous
ineq
ualit
ies
grap
hica
lly?
169
TOPI
CSU
B-T
OPI
CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
8.3
The
obje
ctiv
e Fu
nctio
nTh
e st
uden
t sho
uld
be a
ble
to fo
rm a
n ob
ject
ive
func
tion
from
w
ord
prob
lem
s.
i) Th
e te
ache
r to
guid
e st
uden
ts to
dis
cuss
ho
w to
form
ulat
e an
ob
ject
ive
func
tion
from
a w
ord
prob
lem
.ii)
St
uden
ts in
gro
ups
to fo
rm a
n ob
ject
ive
func
tion
from
giv
en
wor
d pr
oble
ms
Man
ila p
aper
Is th
e st
uden
t ab
le to
form
the
obje
ctiv
e fu
nctio
n fr
om a
giv
en w
ord
prob
lem
?
4
8.4
Max
imum
an
d M
inim
um
Valu
es
The
stud
ent s
houl
d be
ab
le to
:(a
) Lo
cate
cor
ner
poin
ts o
n th
e fe
asib
le re
gion
.
i) Th
e te
ache
r to
guid
e st
uden
ts to
det
erm
ine
the
coor
dina
tes o
f co
rner
poi
nts o
f the
fe
asib
le re
gion
.ii)
Stu
dent
s to
draw
th
e gr
aphs
of l
inea
r in
equa
litie
s for
mul
ated
fr
om a
wor
d pr
oble
m
and
dete
rmin
e th
e co
ordi
nate
s of p
oint
s of
the
visi
ble
regi
on.
i)
Gra
ph b
oard
ii)
Gra
ph p
aper
iii)
Geo
boar
div
) R
ubbe
r ban
dsv)
R
uler
vi)
Col
oure
d C
halk
vi
i) Sq
uare
d pa
per
Is th
e st
uden
t abl
e to
loca
te c
orne
r po
ints
of t
he
feas
ible
regi
on o
fa
linea
r pr
ogra
mm
ing
prob
lem
?
8
170
TOPI
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CS
SPE
CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(b) F
ind
the
min
imum
an
d m
axim
um
valu
es u
sing
the
obje
ctiv
e fu
nctio
n.
i) T
he te
ache
r to
illus
trate
the
max
imum
an
d m
inim
um v
alue
s us
ing
the
obje
ctiv
e fu
nctio
n gr
aphi
cally
.ii)
Stu
dent
s in
grou
ps
to p
ract
ice
on
dete
rmin
ing
the
max
imum
and
m
inim
um v
alue
s usi
ng
the
obje
ctiv
e fu
nctio
n gr
aphi
cally
.iii
) The
teac
her t
o gu
ide
stud
ents
to
disc
uss h
ow to
find
th
e m
axim
um a
nd
min
imum
val
ues b
y su
bstit
utin
g th
e co
rner
po
ints
of a
feas
ible
re
gion
in th
e ob
ject
ive
func
tion.
iv) S
tude
nts i
ndiv
idua
lly
to fi
nd th
e m
axim
um
and
min
imum
val
ues
of th
e gi
ven
prob
lem
s by
subs
titut
ing
the
corn
er p
oint
s in
the
obje
ctiv
e fu
nctio
ns.
i)
Rul
erii)
G
eobo
ard
iii)
Col
oure
d C
halk
s iv
) R
ubbe
r ban
dsv)
G
raph
pap
er
vi)
Squa
red
pape
r vi
i) G
raph
boa
rd
Is th
e st
uden
t ab
le to
find
th
e m
axim
um
or m
inim
um
valu
es o
f a
give
n ob
ject
ive
func
tion?
171
TOPI
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B-T
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CS
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CIF
IC
OB
JEC
TIV
ES
TE
AC
HIN
G
AN
D L
EA
RN
ING
ST
RAT
EG
IES
TE
AC
HIN
G
AN
D L
EA
RN
ING
R
ESO
UR
CE
S
ASS
ESS
ME
NT
NU
MB
ER
O
F PE
RIO
DS
(c)
App
ly li
near
pr
ogra
mm
ing
in
solv
ing
sim
ple
real
lif
e pr
oble
ms.
i) T
he te
ache
r to
guid
e st
uden
ts to
bra
inst
orm
on
dai
ly li
fe si
tuat
ion
in w
hich
line
ar
prog
ram
min
g is
ap
plic
able
.ii)
The
teac
her t
o gu
ide
stud
ents
to a
pply
the
linea
r pro
gram
min
g kn
owle
dge
to so
lve
daily
life
pro
blem
s.iii
) Stu
dent
s to
solv
e pr
oble
ms f
rom
thei
r da
ily li
fe o
n lin
ear
prog
ram
min
g.
i)
Gra
ph b
oard
ii)
G
raph
pap
eriii
) C
olou
red
chal
k iv
) P
enci
lv)
R
uler
vi)
Geo
boar
dvi
i) R
ubbe
r ban
ds
viii)
Squ
ared
pap
er
Is th
e st
uden
t abl
e to
app
ly li
near
pr
ogra
mm
ing
in
solv
ing
sim
ple
real
lif
e pr
oble
ms?
172