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1/62

CARMONA NATIONAL HIGH SCHOOLCarmona, Cavite

TOPIC PLANNER-G7 MATHEMATICSS.Y. 2013-2014

Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ %ir&t Gra'in(

)erio'

In!*+&ive

ate&

Toi!&Content

&

Reeren!e/& In&tr+!tiona*

Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&

va*+ation A&&i(nment

Set An

intro'+!tion

e&!rie an'

i**+&trate 5e**

'e6ne' &et&,

&+&et&, +niver&a*

an' n+** &et,7&e venn 'ia(ram to

rere&ent &et& an'

&+&et&

7nion an'

Inter&e!tion o

&et&

e&!rie an' 'e6ne

+nion an'

inter&e!tion)erorm t"e &et

oeration& on +nion

an' inter&e!tion o

&et&

7&e venn 'ia(ram torere&ent t"e +nion

an' inter&e!tion o


2/62

&et&Com*ement

o a &et

e&!rie an' 'e6ne

t"e !om*ement o a

&et%in' t"e

!om*ement o a

(iven &et

7&e venn 'ia(ram to

rere&ent t"e

!om*ement o a &et)ro*em

&o*vin(

invo*vin( &et&

So*ve 5or' ro*em&

invo*vin( &et& 5it"

t"e +&e o venn

'ia(ramA* &et oeration&

to &o*ve variet o

5or' ro*em&Rea* N+mer e&!rie overvie5 o

rea* n+mer &&tem%+n'amenta*

oeration& on

Inte(er&

To eorm

+n'amenta*

oeration& on

inte(er&

A''ition

S+tra!tion

M+*ti*i!ation

ivi&ion)roertie& on

oeration& o

To &tate an'

i**+&trate t"e


3/62

inte(er& 'i8erent roertie&

o t"e oeration& on

inte(er&Rationa*

n+mer in t"e

n+mer *ine

To 'e6ne an'

i**+&trate rationa*

n+mer& an'

arran(e t"em on an+mer *ine

%orm& o

rationa*

n+mer&

To erorm

oeration& on

rationa* n+mer&

A''ition

S+tra!tion

M+*ti*i!ation

ivi&ion

)roertie& o

t"e oeration

on Rationa*

n+mer&

To i**+&trate

roertie& o rationa*

n+mer&

)rin!ia* root&

an' irrationa*

n+mer&

To 'e&!rie t"e

rin!ia* root& an'

te** 5"et"er t"e are

rationa* or irrationa*

T"e a&o*+te

va*+e o a

n+mer

To 6n' t"e a&o*+te

va*+e o a n+mer

S+&et& o

rea* n+mer&

To 'e&!rie,

rere&ent an'


4/62

!omare t"e 'i8.

S+&et& o rea* no&.

Si(ni6!ant

'i(it& an'

&!ienti6!notation

To 'etermine

&i(ni6!ant 'i(it in a

(iven &it+ation

To 5rite ver *ar(e

or &ma** n+mer& in

&!ienti6! notation9or'

ro*em&

invo*vin( rea*

n+mer&

To &o*ve ro*em&

invo*vin( rea*

n+mer&

S&tem o

Mea&+rement

1.e&!rie 5"at it

mean& to mea&+re

2. I**+&trate t"e

'eve*oment o

mea&+rement rom

rimitive to t"e

re&ent internationa*

&&tem o +nit

3. e&timate or


5/62

aro:imate *en(t"

4. 7&e aroriate

in&tr+ment& to

mea&+re *en(t"

;. Covert *en(t"

mea&+rement rom

one +nit to anot"er,in!*+'in( t"e n(*i&"

&&tem


6/62

&&tem4. So*ve

ro*em&

invo*vin(

5ei("tma&&

an'

vo*+me!aa!it

Mea&+rin(

An(*e&, Time

an'

Temerat+re

1. &timate or

aro:imate

mea&+re& o

an(*e, time

an'

temerat+re2. 7&e

aroriate

in&tr+ment&

to mea&+re

an(*e&, time

an'

temerat+re3. So*ve

ro*em&

invo*vin(

time, &ee',

temerat+re

an' +ti*itie&

+&a(e /meter

rea'in(


7/62



Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Se!on' Gra'in(

)erio'

In!*+&ive

ate&

Toi!&Content& Reeren!e/& In&tr+!tiona*

Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&


A*(erai!

:re&&ion&

e6ne a*(erai!

e:re&&ion&Tran&*ation o vera*

"ra&e& to

mat"emati!a*

e:re&&ion& an' vi!e

ver&a

Tran&*ate vera*

"ra&e into

a*(erai!

e:re&&ion an' vi!e

ver&ava*+atin( a*(erai!

e:re&&ion

va*+ate a*(erai!

e:re&&ion& or

(iven va*+e& o t"e

varia*e&)o*nomia*&

La5& o e:onent

)ro'+!t r+*e-

o5er r+*e

1.I**+&trate t"e *a5&

o e:onent an'

t"eir roertie&

2. i'enti t"e a&e,

!oe>!ient an'


8/62

)o5er o a

ro'+!t r+*e ?+otient r+*e )o5er o a

@+otient r+*e

e:onent&

Oeration& on

o*nomia*& A''ition S+tra!tion M+*ti*i!ation ivi&ion

1. e6ne

o*nomia*&,!on&tant&,

varia*e& an'

!oe>!ient2. e6ne an'

i**+&trate

monomia*,

inomia*,

trinomia*3. )erorm

oeration& on

o*nomia*&Se!ia* ro'+!t&

)ro'+!t o t5o

inomia*& S@+are o a

inomia* )ro'+!t o t"e

&+m an'

'i8eren!e o

t5o term& C+e o

inomia*

1. I**+&trate t"e

ro'+!t o

t5o

inomia*&2. 7&e t"e

ro'+!t o

t5o

inomia*& to

&o*ve

ro*em&3. I**+&trate t"e

&@+are o ainomia*

4. 7&e t"e


9/62

&@+are o a

inomia* to

&o*ve

ro*em&;. I**+&trate t"e

ro'+!t o

&+m an''i8eren!e o

t5o term&


10/62

n(*i&"

&enten!e& to

mat"emati!a

* &enten!e&

an' vi!e

ver&a

)roertie& o

e@+a*it

State an' a* t"e

'i8erent roertie&

o e@+a*it

So*vin( e@+ation&

+&in( a''ition an'&+tra!tion

So*ve &im*e

e@+ation& +&in(a''ition an'

&+tra!tion

So*vin( e@+ation&

+&in( m+*ti*i!ation

an' 'ivi&ion

So*ve &im*e

e@+ation& +&in(

m+*ti*i!ation an'

'ivi&ion


11/62

So*vin( m+*ti-&te

e@+ation&

So*ve &im*e

e@+ation& +&in( a

!omination o o+r

+n'amenta*oeration&

9or' )ro*em&

N+mer A(e 9or

7niorm

motion Mi:t+re

D+&ine&& an'

inve&tment Geometr

1. 7&e

e@+ation& to

&o*ve 5or'

ro*em&2. Ana*Ee 5or'

ro*em& an'

mani+*ate

e@+ation

Linear ine@+a*itie&an' oen &enten!e&

in one varia*e

So*ve ine@+a*itie&an' (ra" t"eir

&o*+tion &et&


12/62

A&o*+te va*+e in

oen &enten!e

So*ve *inear

e@+a*itie& an'

ine@+a*itie&

invo*vin( a&o*+te

va*+e


13/62


TOPIC PLANNER-G7 MATHEMATICS

S.Y. 2013-2014

Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ T"ir' Gra'in(

)erio'

In!*+&ive

ate&

Toi!&Conten

t&

Reeren!e/&

In&tr+!tiona*

Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&


Da&i!

!on!et& an'

term&

e&!rie t"e i'ea o oint,

*ine an' *ane

7n'e6ne'

term

)oint

Line

)*ane

1. I**+&trate t"e i'ea o

oint, *ine an' *ane2. Name t"e &+&et& o a

*ine Se(ment

ra

An(*e& 1. 'e6ne an' i**+&trate

an(*e&2. name t"e art& o an

an(*e3. 'etermine t"e

mea&+re o an an(*e


14/62

+&in( a rotra!tor4. i**+&trate t"e 'i8erent

in'& o an(*e& a!+te

ri("t ot+&e

)o*(on&

i8erent

in'& o

o*(on

1. 'e6ne an' i**+&trate

'i8erent in'& o

o*(on&, a!!or'in( to

t"e n+mer o &i'e&2. i'enti t"e art& o a

re(+*ar o*(onConve: an'

Non !onve:o*(on

i8erentiate !onve: rom

non !onve: o*(on

Trian(*e& 1. e6ne an' i**+&trate trian(*e& it& a&i! art& it& &e!on'ar art&2. !*a&&i trian(*e&

a!!or'in( to an(*e&

an' &i'e&

?+a'ri*atera*& 1. 'e6ne an' i**+&trate

@+a'ri*atera*&

2. name t"e 'i8erentin'& o @+a'ri*atera*&


15/62

Cir!*e& 1. e6ne !ir!*e2. I**+&trate, name an'

i'enti an' 'e6ne t"e

term& re*ate' to t"e

!ir!*e



Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ %o+rt" Gra'in(

)erio'

In!*+&ive

ate&

Toi!&Content

&

Reeren!e/& In&tr+!tiona*

Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&


Stati&ti!& an'

a&i! term&

e6ne t"e o**o5in(

term Stati&ti!&

)o+*ation


16/62

Sam*e

ata Ot"er re*ate'

term&

Sam*in(Te!"ni@+e& :*ain t"e 'i8erent&am*in( te!"ni@+e&

Co**e!tin(

ata

Co**e!t &tati&ti!a*

'ata an' or(aniEe

t"em in a ta*e

Con&tr+!tin(re@+en!

ta*e

Con&tr+!t re@+en!'i&tri+tion ta*e


17/62


18/62

+n(ro+e'

'ata

'ata

Mea&+re o

!entra*

ten'en!ie& or

(ro+e' 'ata

%in' t"e mea&+re o

!entra* ten'en!

+&in( (ro+e' 'ata


TOPIC PLANNER- MATHEMATICS IIIS.Y. 2013-2014

Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ %ir&t Gra'in(

)erio'


19/62

In!*+&ive

ate&


Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&

va*+ation A&&i(nmen

t

7n'e6ne' Term&

)oint

Line

Se(ment&

ra& )*ane

Se(ment& an' ra&

1. e&!rie t"e

i'ea o oint,

*ine an' *ane2. I**+&trate oint,

*ine an' *ane&3. e6ne, i'enti

an' name t"e

&+&et o a *ine

Ra& an' an(*e& 1. e6ne an'

i**+&trate an(*e&2. Name t"e art&

o an(*e&Mea&+re o an(*e& etermine t"e

mea&+re o an an(*e+&in( a rotra!tor

C*a&&i6!ation o an(*e& I**+&trate 'i8erent

in'& o an(*e&

A!+te Ri("t ot+&e

)o*(on& 1. i**+&trate

'i8erent in'&

o o*(on&

a!!or'in( to t"e

n+mer o &i'e& i'enti


20/62

t"e art&

o a

re(+*ar

o*(on

Conve: an' non !onve:

o*(on

i8erentiate !onve:

an' non !onve:

o*(on&

Trian(*e& I**+&trate

trian(*e

it& a&i!

art& it&

&e!on'ar

art&

C*a&&i6!ation otrian(*e&

C*a&&i trian(*e&a!!or'in( to#

an(*e& &i'e&

?+a'ri*atera*& e6ne, name an'

i**+&trate t"e 'i8erent

in'& o @+a'ri*atera*&

S+m o mea&+re& o t"einterior an(*e& o

etermine t"e &+m ot"e mea&+re o t"e


21/62


22/62


23/62



Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Se!on' Gra'in(

)erio'

In!*+&ive

ate&


Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&

va*+ation A&&i(nmen

t

Det5eene&& an'

Co**inearit o oint&

I**+&trate et5eene&&

an' !o**inearit o

oint&

Con(r+ent &e(ment&

an' mi'oint o a

&e(ment

1. 'e6ne

!on(r+ent

&e(ment& an'mi'oint o a

&e(ment


24/62

2. i**+&trate

!on(r+ent

&e(ment& an'

mi'oint o a

&e(ment3. orm !on!*+&ion

+on i'entiin(

mi'oint o a

&e(ment

Di&e!tor o an an(*e e6ne, name an'

i**+&trate i&e!tor o

an an(*e

Fin'& o an(*e air& 1. 'e&!rie an'

i**+&trate t"e

'i8erent in'&

o an(*e air& &+*ementar !om*ementar !on(r+ent

a'a!ent

*inear air

verti!a* an(*e&

)eren'i!+*arit 1. 'e6ne

eren'i!+*ar

*ine&2. i'enti ri("t

an(*e& orme'


25/62


26/62

A*ternate

interior an(*e& A*ternate

e:terior an(*e& Corre&on'in(

an(*e& An(*e& on t"e

&ame &i'e o

tran&ver&a*

)ro*em& +&in(

'e6nition& an'

roertie& invo*vin(

re*ation&"i& et5een

&e(ment& an' et5een

an(*e&

So*ve )ro*em& +&in(

'e6nition& an'

roertie& invo*vin(

re*ation&"i& et5een

&e(ment& an'

et5een an(*e&

)roertie& o

Con(r+en!e

I**+&trate an' &o*ve

ro*em& invo*vin(

Ree:ive

roert Smmetri!

roert Tran&itive

roert


27/62

Con(r+ent trian(*e& 1. e6ne an'

i**+&trate

!on(r+ent

trian(*e&2. Name t"e

!orre&on'in(

art& o

!on(r+ent

trian(*e&)roertie& o

!on(r+en!e

1. i8erentiate

in!*+'e' an(*e

an' in!*+'e'

&i'e2. 7&e in'+!tive

&i**& to rove

!on(r+en!eet5een

trian(*e&Trian(*e Con(r+en!e

SSS

SAS

ASA

SAA

A* 'e'+!tive &i**&

to &"o5 !on(r+en!e

et5een trian(*e&

+&in(#

SSS

SAS ASA

SAA


28/62

Si'e an(*e re*ation& in

a trian(*e

I**+&trate t"e

re*ation&"i o t"e

&i'e& an' an(*e& in a

trian(*e

Con(r+ent &i'e&

in a trian(*e

im* t"at

an(*e& oo&ite

t"em are

!on(r+ent Con(r+ent

an(*e& in a

trian(*e im*

t"at t"e &i'e&

oo&ite t"em

are !on(r+ent

Non !on(r+ent&i'e& in a

trian(*e im*

t"at t"e an(*e&

oo&ite t"em

are not

!on(r+ent Non !on(r+ent

an(*e& in a

trian(*e im*

t"at t"e &i'e&

oo&ite t"emare not

!on(r+ent


29/62

Ine@+a*itie& in a Trian(*e Name an' 'etermine

t"e

&ma**e&t an(*e

o a trian(*e *ar(e&t an(*e o

a trian(*e

Ine@+a*it in an

i&o&!e*e& trian(*e

)rove ine@+a*it

roertie& in an

i&o&!e*e& trian(*e

Con'ition& or Trian(*e

!on(r+en!e

7&e t"e !on'ition& or

trian(*e !on(r+en!e to

rove#

!on(r+ent

&e(ment& !on(r+ent

an(*e&


30/62

)ro*em& invo*vin(

&e(ment& an' an(*e&

So*ve ro+tine an' non-

ro+tine ro*em&




)erio'

In!*+&ive

ate&


Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&

va*+ation A&&i(nmen

t

?+a'ri*atera*& 1. 'e&!rie a

@+a'ri*atera*


31/62


32/62


33/62

)roortiona* &e(ment& 1. e6ne

roortiona*

&e(ment&2. A* t"e

'e6nition o

roortiona*

&e(ment& to

6n' +nno5n*en(t"&

Da&i! roortiona*it

t"eorem an' it&

!onver&e

I**+&trate an' veri

t"e a&i!

roortiona*it

t"eorem an' it&

!onver&e

Simi*ar Trian(*e& 1. e6ne &imi*ar

trian(*e&2. A* t"e

'e6nition o

&imi*ar trian(*e&

in eterminin( i

t5o trian(*e&

are &imi*ar %in'in( t"e

*en(t" o n &i'e

or mea&+re o

an an(*e o a

trian(*eSimi*arit T"eorem 1.=eri t"e &imi*arit


34/62


35/62


36/62



Name o Tea!"er# $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ %o+rt" Gra'in(

)erio'

In!*+&ive

ate&


Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&

va*+ation A&&i(nmen

t

T"e Cir!*e/ a re!a** 1. I'enti a maor an'

minor ar! an' !entra*

an(*e&2. 'etermine t"e


37/62


38/62

T5o &e!ant *ine&

@+ation o t"e *ine erive t"e e@+ation o

t"e *ine (iven t5o

oint& o t"e *ine T5o oint orm

)oint &*oe orm

S*oe inter!et

orm

)oint o Inter&e!tion etermine

a*(erai!a** t"e oint

o inter&e!tion o t5o

*ine&


39/62


40/62


41/62

tan(en! 5it" a

(iven *ine)ro*em& invo*vin(

!ir!*e&

So*ve ro+tine an' non

ro+tine ro*em&

invo*vin( !ir!*e&


42/62


43/62

Linear %+n!tion&

/: Km:

e6ne t"e *inear

+n!tion /: K m:

Re5rite in t"e orm

/:Km: an' vi!e

ver&a

Gra" o *inear +n!tion ra5 t"e (ra" o a

*inear +n!tion (iven

t"e o**o5in(#

An t5o oint&

J an'

inter!et& S*oe an' one

oint S*oe an' t"e -

inter!etGiven# /:K m: etermine t"e

o**o5in(, (iven t"e#

S*oe

Tren'#

in!rea&in( or

'e!rea&in( J an'

inter!et& Some oint&


44/62


45/62


46/62


47/62

Gra" o @+a'rati!

+n!tion

1. 'ra5 t"e (ra"

o a @+a'rati!

+n!tion +&in(

t"e# =erte:

A:i& o&mmetr

ire!tion o

oenin( o t"e

(ra"

Given oint&

2. Ana*Ee t"e

e8e!t& on t"e

(ra" o!"an(e& in a, "

an' in /: K

a /:-"2

ero& o @+a'rati!

+n!tion

%in' t"e Eero& o

@+a'rati! +n!tion #

%a!torin(

?+a'rati!

orm+*a


48/62


49/62

'i i i


50/62

'ivi&ion

Remain'er

t"eorem

%a!tor T"eorem I**+&trate t"e a!tort"eorem

ero& o o*nomia*

+n!tion& o 'e(ree

(reater t"an 2

%in' t"e Eero& o

o*nomia* +n!tion&

o 'e(ree (reater t"an

2 #

%a!tor t"eorem

%a!torin(

Snt"eti!

'ivi&ion

ere&&e'

e@+ation&


51/62

Gra" o o*nomia*

+n!tion& o 'e(ree

(reater t"an 2

ra5 t"e Gra" o

o*nomia* +n!tion&

o 'e(ree (reater t"an

2


TOPIC PLANNER- MATHEMATICS IVS.Y. 2013-2014


)erio'

In!*+&ive

ate&


Materia*&

Learnin(

Cometen!

N+mer

Oe!tive& A!tivitie&

Strate(ie&

va*+ation A&&i(nmen

t

:onentia* %+n!tion& I'enti !ertain

re*ation&"i& 5"i!"

are e:onentia*

)o. Gro5t"

over time

Gro5t" o


52/62

Gro5t" o

a!teria over

time

Ot"er&

Tren' o :onentia*

%+n!tion&

Given a ta*e o

or'ere' air&, &tate

5"et"er t"e tren' i&

e:onentia* or not

Gra" o e:onentia*

+n!tion

ra5 t"e (ra" o

e:onentia* +n!tion

)roertie& o

e:onentia* +n!tion

e&!rie &ome

roertie& o t"e

e:onentia* +n!tion,

/: K a:

a 1

0 a 1


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54/62

2. e&!rie &ome


55/62

2. e&!rie &ome

roertie& o

t"e *o(arit"mi!

+n!tion rom it&

(ra"

La5& o Lo(arit"m& 1. A* t"e *a5&

o *o(arit"m&

2. So*ve &im*e

*o(arit"mi!

e@+ation&

)ro*em& invo*vin(

e:onentia* an'

*o(arit"mi! +n!tion&

So*ve ro*em&

invo*vin( e:onentia*

an' *o(arit"mi!

+n!tion&

Cir!+*ar %+n!tion e6ne t"e o**o5in(# 7nit !ir!*e

Ar! *en(t"&


56/62

(

7nit mea&+re o

an an(*eConver&ion rom 'e(ree

to ra'ian an' vi!e ver&a

Convert rom 'e(ree

to ra'ian an' vi!e

ver&a

An(*e& in &tan'ar'

o&ition, !otermina*

an(*e&

Reeren!e an(*e&

I**+&trate an(*e& in

Stan'ar'

o&ition Cotermina*

an(*e& Reeren!e

an(*e&Rotation& a*on( t"e +nit

!ir!*e

=i&+a*iEe rotation&

a*on( t"e +nit !ir!*e

an' re*ate t"e&e toan(*e mea&+re&

/ !*o!5i&e or !o+nter

!*o!5i&e 'ire!tion&

Len(t" o an ar! An(*e& eon'

3


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58/62


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ro*em& invo*vin(

i "t t i *


60/62

ri("t trian(*e&

trian(*e& +&in(

t"e *a5 o &ine&

trian(*e& +&in(

t"e *a5 o

!o&ine&

Stati&ti!& 1. e6ne# &tati&ti!& &am*e

o+*ation2. (ive t"e "i&tor

an' imortan!e

o t"e &t+' o

&tati&ti!&

S+mmation 7&e t"e r+*e& o

&+mmation to 6n'

&+m

Sam*in( Te!"ni@+e& :*ain t"e 'i8erent&am*in( te!"ni@+e&


61/62

!"ara!teri&ti!&

o a &et o 'ata


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o a &et o 'ata

+&in( t"e

mea&+re& o

variai*it

Stati&ti!a* 'ata Ana*Ee, interret,

'ra5 !on!*+&ion, mae

re'i!tion&, mae

re!ommen'ation&'e!i

&ion

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