Yearly Plan for Mathematics 2013 2014 First Semester · PDF fileYearly Plan for Mathematics...

Yearly Plan for Mathematics 2013 – 2014 First Semester Grade 8

Teacher's Name & Signature: Senior Teacher's Signature: Supervisor's Signature: Principal's Signature:

Only minimum level of objectives are given in the yearly plan and more can be added further.

The teacher is strongly advised to give more examples and exercises (from the approved list of Math books) than the ones provided in the yearly plan.

The teacher may solve the problems in any scientific way (rather than the suggested methods in the yearly plan).

skrameR Assessment

tools Teaching

aids Teaching strategies

Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define and use equal sets.

Definition:

A Set B is equal sets if they contain the same elements (A = B).

e.g.(1) : Let X be a set of letters of the word "set" and Y be the set of the

letters of the word "test". Is X=Y? Give a reason.

X={s, e, t} and Y={t, e, s}

X=Y because each element of X belongs to Y and each

element of Y belongs to X.

e.g.(2) : Let A = {x : x is a digit of the number 531}

and B = {x : x is a digit of the number 251}

Is A=B? Give a reason.

A={1, 3, 5} and B={1, 2, 5}

A B because 3 is an element of A but doesn’t belong to B.

Or because 32 is an element of B but doesn’t belong to A.

e.g.(3) : Complete the following using " " or " " :

a) ….{ } b) {0}…..

c) {52, 73}….{2, 5, 3, 7} d) {a,b}….{b,a}

□ E

qu

al

Set

s

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define and use subsets.

Revision:

F={ , , }

Banana is an element of F.

Banana belongs to F ( We denote this by Banana F ).

Orange is not an element of F.

Orange does not belong to F ( Orange F).

Definition of a subset:

A Set X is a subset of a set Y if every element of X is an element of

Y. (We write Y X : Read" Y is a subset of X " )

For example: If A={ , } , B={ , }

and C={ , , , }

A C but B C .

Note that:

{ , }

{ } { , }

□ S

ub

sets

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(1) : List all subsets of the set X = {2, 5, 7}

The empty set, which is .

Sets containing one element : {2}, {5}, {7}

Sets containing two elements : {2, 5}, {2,7}, {5, 7}

Sets containing three elements : {2, 5, 7}

Thus, all subsets of X are : ,{2},{5},{7},{2, 5},{2,7},{5, 7},{2, 5, 7}

e.g.(2): Complete the following using " " or " " :

a) ….{a,b} b) {0}…..{ } c) {7}….{77} d) {a,b}….{b,a}

e.g.(3): Let . Complete the following using " " or " " or

" " or " " :

a) …. b) {23}….. c) {2}…. d) 22….

If the set A contains m elements ,

Then the number of all subsets of A = .

e.g.(4): Circle the correct answer. Let A={a , b , c} . The number of all

subsets of A is :

a) 3 b) 6 c) 8 d) 9

S

ub

sets

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Operation on sets:

1- Define and use intersection of sets

Definition:

Given two sets A and B, the intersection of A and B:

Is the set that contains elements that belong to A and to B at the same

time.

Shaded region is the intersection of A and B.

We denote the intersection of A and B as :

Read ( " A intersection B " )

e.g.(1) : Let and , find

?

Since . .

e.g.(2) : From the opposite Venn diagram, find .

□

Inte

rsec

tion

of

Set

s

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober

𝐀 𝐁






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(3) : Let X = {1, 2, 5, 6, 7, 9}, Y = {1, 3, 4, 5, 6, 8}

and Z = {3, 5, 6, 7, 8, 10}.

1) Find: a) d) X ∩ Y ∩ Z b) X ∩ Y c) Y ∩ Z d) X ∩ Z

2) Represent these sets by a Venn diagram.

Step 1 : Draw three overlapping circles to represent the three sets.

Step 2 : Write down the elements in the intersection X ∩ Y ∩ Z

We find that X ∩ Y ∩ Z = {5, 6}

Step 3 : Write down the remaining elements in the intersections:

X ∩ Y, Y ∩ Z and X ∩ Z.

X ∩ Y = {1, 5, 6}, Y ∩ Z = {3, 5, 6, 8} and X ∩ Z = {5, 6, 7}

Step 4 : Write down the remaining elements in the respective sets.

In

ters

ecti

on

of

Set

s

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

2- Define and use union of sets

Definition:

Given two sets A and B, the union of A and B:

Is the set that contains elements that belong

to either A or B or to both.

Shaded region is the union of A and B.

We denote the union of A and B as :

Read ( " A union B " )

e.g.(1) : Let A = { x : x is a number bigger than 4 and smaller than 8}

and B = { x : x is a positive number smaller than 7}. Find .

A = { 5, 6, 7} and B = { 1, 2, 3, 4, 5, 6}

= { 1, 2, 3, 4, 5, 6, 7}

e.g.(2) : From the opposite Venn diagram, find:

a)

= {1, 2, 3, 4, 5, 6}

b)

= {2, 3, 4, 5, 6, 7}

c)

={1, 2, 3, 4, 5, 6, 7}

□ U

nio

n o

f S

ets

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Activity:

Use the previous Venn diagram to recognize the intersection and union

properties on sets :

Property For any three sets A , B and C

Commutative Intersection

Union

Associative Intersection

Union

Distributive Intersection:

Union

□ U

nio

n o

f S

ets

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.: From the opposite Venn diagram,

find:

a)

b)

U

nio

n o

f S

ets

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

3- Use the difference operation

Definition:

Given two sets A and B, the difference of set B from set A :

Is the set of all elements in A but not in B.

Shaded region is the difference of B from A.

We denote A difference B as :

Notice : .

e.g.(1) : Let A = { b , e , f} and B = { e , k , r , s }. Find :

a)

b)

c) Draw a Venn diagram then shade the region that represents

.

e.g.(2) : Let , and . Draw a

Venn diagram to represent the sets X and Y.

□ D

iffe

ren

ce o

f S

ets

𝐀 𝐁






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Introduction:

Definition:

Given two nonempty sets A and B,

The set containing all the ordered pairs where the first element is

taken from A and the second element is taken from B is called the

Cartesian product of A and B and is denoted by , and read as

A cross B.

The set builder form of is : and y With taking care of .

e.g.(1) : Let A = {1, 3, 5} and B = {2, 4}. Find .

We can describe Cartesian product using two types of diagrams:

1. Mapping diagram

2. Cartesian diagram

C

art

esia

n P

rod

uct

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Cartesian product to a set by itself:

If Y is nonempty set then the Cartesian product to the set Y by Y is

denoted by , and read as Y cross Y.

The set builder form is : and y

e.g.(1) : Let Y = {2, 3}. Find .

1. Mapping diagram

2. Cartesian diagram

If A and B are two nonempty sets, then :

1. 2.

Where n(A) is the number of elements in the set A and n(B) is the

number of elements in the set B.

e.g.(2): Let A={a , b , c} . The number of elements in ( ) is :

a) 3 b) 6 c) 8 d) 9

C

art

esia

n P

rod

uct

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define and use the term relation.

Identify and express examples of relations in life situations.

Display a relation as :

- a set of ordered pairs - a mapping diagram - a Cartesian diagram

Consider the following example, where A and B are two sets :

Suppose : Rana has two brothers Mohammed and Saleh

Mariam has one brother Ahmed Fatima has one brother Karim

o If we define a relation R " is a brother of" between the elements of

A and B then clearly :

o These can be written in the form of a set R of ordered pairs as

o The relation R from A to B is a subset of ( R ).

□ □ □

Rel

ati

on

s

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(1): If R is a relation "is greater than" from A to B,

where A= {1, 2, 3, 5} and B = {1, 2, 6}.

a) Find R in the roster form.

R = {(2,1), (3, 1), (3, 2), (5, 1), (5, 2)}

b) Represent R by the Mapping diagram

e.g.(2): Given that A = {1, 2, 3}, B = {1, 2, 3, 4, 5, 6}. R is a relation

from A to B defined by

.

Find R in the roster form.

R={(1,2) , (2, 4) , (3, 6)}

e.g.(3): In the opposite figure, the

Cartesian diagram represents a

relation R from X to X. Write R in

the roster form.

R={(2, 2) , (3, 3) , (5, 5)}

So, R is a relation "equal to".

R

elati

on

s

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define and use the terms abscissa and ordinate

Define and use the domain of a relation.

Define and use the range of a relation.

Definitions:

The first element of an ordered pair is called its abscissa.

The second element of an ordered pair is called its ordinate.

Thus, for example, the abscissa of (4, 2) is 4, while the ordinate is 2.

If R is a relation between two sets then :

The Domain of R : is the set of all abscissas of each ordered pair.

The Range of R : is the set of all ordinates of each ordered pair.

e.g.(1): If R is a relation from B to B where and

. Find :

a) R in the roster form. R = {(1, 11), (3, 9), (5, 7)}

b) Domain of R. Domain of R = {1, 3, 5}

c) Range of R. Range of R = {7, 9, 11}

e.g.(2): Consider the graph of the relation S

shown in the given figure. What are

the domain and range of the relation S?

S={(1,2), (2,1), (2,4), (3,3), (4,4)}

The Domain of S = {1, 2, 3, 4}

The Range of S = {1, 2, 3, 4}

□ □ □

Dom

ain

an

d R

an

ge

of

a R

elati

on

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define a function.

The following Mapping diagrams represent three relations :

1) Write each relation in a roster form.

2) Which of these relations satisfies the following condition: each

element of A is connected to only one element of B.

Student should observe that in a function no two ordered pairs have the

same abscissa.

A relation from set A to B is said to be a function if:

Every element of A has a unique (only one) image in B.

e.g.(1) : If X= {1, 2, 3, 4} and Y={1, 3, 5, 7}. Determine which of the

following relations represents a function from X to Y:

a) R1={(2, 3) , (1, 1) , (3, 5) , (3, 7) , (4, 3)}

b) R2={(1, 7) , (2, 5) , (4, 1)}

c) R3={(2, 3) , (3, 3), (1, 5) , (4, 7)}

Solution:

a) R1 is not a function because has two images in Y (appears in

two ordered pairs (3,5) and (3,7) ).

b) R2 is not a function because has no image in Y.

c) R3 is a function because every element of X has only image in Y.

□ F

un

ctio

ns

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(2): Which of the following Cartesian diagrams represents a function

:

(a)

(b)

(c)

The mathematical symbol of a function:

A function from the set X to the set Y is written mathematically as:

and is read as : " is a function from X to Y"

If the ordered pair belongs to the function , then the element

is called "the image" of the element , and we denote that

by .

□ F

un

ctio

ns

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define the linear function.

Introduction :

a) Plot the points (ordered pairs) with coordinates : (1, 2) , (2, 3) ,

(3, 4) , (4, 5) and (5, 6)

b) Draw a straight line through these points.

c) Describe the relation between the x- and y-coordinates of these

points.

a) b)

c) The y-coordinate is always one more than the x-coordinate , so we can

write .

The function from X to Y is called a linear function (a function of

the first degree) if where and are constants

( ).

□ L

inea

r F

un

ctio

n

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1

Sep

tem

ber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Graph a linear function in the Cartesian coordinate plane.

Determine if an ordered pair is a solution to a linear function.

Read information from a graph of a linear function (a straight line).

e.g.(1) : a) Graph the linear function .

b) Complete the missing numbers in the coordinates of other

points that lie on the line : ( 4 , …. ) , ( …. , )

c) Will the point with coordinates lie on the line? Give

a reason for your answer.

Solution:

a) The table shows the coordinates of some ordered pairs (points)

on the line.

0 1 2

1 3 5

The points with coordinates and can be plotted, and a straight line drawn through

these points.

b) (4, 9) , ( , )

c) No, because

□ □ □

Gra

ph

of

Lin

ear

Fu

nct

ion

Un

it O

ne:

Set

s an

d R

elati

on

s

5

1 S

epte

mber

– 3

Oct

ober






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Identify and define rational numbers.

Revision:

The set of natural numbers is . If we add zero to the set of natural numbers, the result is the set of

whole numbers . Whole numbers and their opposites make up the set of integers

.

Definition of rational numbers:

A rational number is a number that can be expressed in the form

,

where and are integers and .

The set of rational numbers is denoted by .

Examples of rational numbers :

where and .

where and .

where and .

where and .

□ In

trod

uct

ion

to R

ati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y

𝑊






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Representing rational numbers of the form (

) on the number line.

e.g.(1): Represent the rational number

on the number line.

Step 1: Write the rational number in simplest form

.

Step 2: Draw a number line showing and because it lies

between them.

Step 3: Since the denominator is 5, divide the space between them

into 5 equal parts (each part represents

)

Step 4: Mark

at 2 units to the left of , we obtain the

number line as follow:

e.g.(2): Write the rational number that represent the letters:

A =

or

B = 2

or

C = 5

or

□

Rep

rese

nti

ng R

ati

on

al

Nu

mb

ers

on

Nu

mb

er L

ine

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Eid Al-Fetr

Leave

15 - 17

October

Comparing and ordering rational numbers.

To compare/order rational numbers :

Step 1: find the LCM (least common multiple) of all denominators.

Step 2: write equivalent fractions with the LCM as the denominator.

Step 3: compare the numerators : larger numerator = larger number

e.g.(1): Arrange the following rational numbers in ascending order:

Step 1: LCM = 12

Step 2:

Step 3:

The ascending order of these numbers is :

□

Com

pari

ng a

nd

Ord

erin

g R

ati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Eid Al-Fetr

Leave

15 - 17

October

Operations on rational numbers ( ).

a) Addition and Subtraction and their properties.

(involve revision: addition of integers)

Adding/subtracting rational numbers with a common denominator

If

and

are two rational numbers, then

where .

Step1: Add/subtract the numerators.

Step2: Write the sum/difference over the denominator.

Step3: Write the answer in simplest form.

e.g.(1): Find the value of each of the following in its simplest form :

a)

b)

c)

In simplest form :

In simplest form :

= (

)

(

)

e.g.(2): Find

.Write in simplest form.

□

Ad

dit

ion

an

d S

ub

tract

ion

of

Rati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Eid Al-Fetr

Leave

15 - 17

October

Adding/subtracting rational numbers with a different denominator.

Use the LCM of the denominators to rename the fractions with a

common denominator. Then add/subtract and simplify.

e.g.(1): Find

. Write in simplest form.

LCM of 6 and 8 is 24

Rename each fraction using LCM

e.g.(2) : The length of a rectangular land is

and its width is

. Find its perimeter.

The perimeter of the land (

)

(

)

(

)

(

)

A

dd

itio

n a

nd

Su

btr

act

ion

of

Rati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Eid Al-Fetr

Leave

15 - 17

October

Properties of Addition in :

The property Description in symbols

(For every rational numbers

,

and

)

Commutative

Example :

Associative (

)

)

Example : (

)

)

Additive identity

Additive identity is : Zero

Example :

Additive inverse

(

) (

)

is the additive inverse of

Example : The additive inverse of

is

The additive inverse of

is

[ (

)

]

Remark :

Subtraction operation can be changed to Addition operation in .

If

and

are rational numbers , then

A

dd

itio

n a

nd

Su

btr

act

ion

of

Rati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included


b) Multiplication and its properties.

(involve revision: Sign rules of Multiplication)

Multiplying with same signs Multiplying with different signs

Multiplying rational numbers.

If

and


where .

Simplify before multiplying (If possible)

Step1: Multiply the numerators.

Step2: Multiply the denominators.

Step3: Write the answer in simplest form (if possible).

e.g.(1): Find

in the simplest form.

e.g.(2): Ahmed spends

minutes to arrive his school. How many

minuets he needs to go and return back?

M

ult

ipli

cati

on

of

Rati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Properties of Multiplication in :

The property

Description in symbols

(For every rational numbers

,

and

)

where

Commutative

Example :

Associative (

)

)

Example : (

)

)

Distributive over

addition

(

) (

) (

)

Example :

(

)

)

Multiplicative

identity

Multiplicative identity is : 1

Example :

Multiplicative

inverse

(

) (

)

is the multiplicative inverse of

Example : The multiplicative inverse of

is

because(

)

M

ult

ipli

cati

on

of

Rati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6

Oct

ober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Hijri New

Year Leave

5 November


c) Division.

(involve revision: Sign rules of Division)

Dividing with same signs Dividing with different signs

Dividing rational numbers.

If

and


where .

Step1: KEEP the first fraction the same.

Step2: CHANGE to .

Step3: FLIP the second fraction over.

Step4: Write the answer in simplest form (if possible).

e.g.(1): Find in the simplest form.

a)

b)

c)

e.g.(2): Magda used

inches of wire for making 5 necklaces. How

much wire did she used for each necklace?

D

ivis

ion

of

Rati

on

al

Nu

mb

ers

Un

it T

wo :

Rati

on

al

Nu

mb

ers

4

6 O

ctober

– 6

Feb

ruar

y






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Define and use negative exponents.

Exponents Rules:

:

1. 2. :

3.

4. where

5.

6.

e.g.(1): Write each of the following in the simplest form (as a single

positive power) :

a)

b)

c)

e.g.(2) : Find the value of the following :

□ E

xp

on

ents

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Apply the rule of an algebraic term raised to a power.

Revision:

A variable :

is a letter or a symbol that is used to represent an unknown quantity.

Algebraic term :

is either a number or a number multiplied by one or more variables.

Examples : 3 , , and

e.g.: Write each of the following in simplest form :

a) b) c) d)

a)

b) Note:

c)

d)

□ E

xp

on

ents

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er

Order of operations on rational numbers involving negative exponents.

e.g.: Find the value of:

1)

2) [ ]

□






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Evaluate variable expressions with one variable using rational numbers.

Revision:

Algebraic expression :

contain any number of algebraic terms.

use signs of operation between the algebraic terms —addition,

subtraction, multiplication, and division.

do not contain an equality sign (=).

e.g. : Evaluate the expression when :

a)

b)

c)

□

Evalu

ati

ng V

ari

ab

le E

xp

ress

ion

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er

Evaluate variable expressions with 2 or more variables using rational

numbers.

e.g. (1) : Evaluate the expression if and

.

e.g. (2) : Evaluate

when

□






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

.

Revision:

Algebraic term: is a number or a number multiplied by one or more

variables raised to a nonnegative power .

Degree of a term: is the power of the variable.

Example of Algebraic Term

(Expressed in the Form )

Coefficient

Degree

3 5

1 14

7 0

1

A polynomial : is a single term or a finite sum of terms.

Types of polynomials :

A monomial is a polynomial that has one term.

A binomial is a polynomial that has two terms.

A trinomial is a polynomial that has three terms.

A Degree of a polynomial (in one variable) : is the highest power of

the variable in the polynomial.

Types of

polynomial Example

Descending order of

terms

Degree of

polynomial

Monomial 9

Binomial 2

Trinomial 8

□ I

ntr

od

uct

ion

to P

oly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Add and subtract polynomials with applications.

To add or subtract two polynomials, we combine like terms.

Two terms are like terms if they each have the same variables

and the corresponding variables are raised to the same powers.

Polynomials can be added/subtracted horizontally or vertically.

e.g.(1): Find :

a)

⏟ ⏟ ⏟ Group like terms.

Add like terms.

b)

When adding vertically, we line up the like terms :

e.g.(2): Find

Change the sign of each term of the second polynomial.

⏟ ⏟ ⏟ Group like terms.

Add like terms.

□ A

dd

itio

n a

nd

Su

btr

act

ion

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(3): Subtract from

When subtracting vertically, we line up the like terms :

Now change the sign of each term of the second polynomial and

add the like terms :

e.g.(4): Jamila traveled miles in the morning and

miles in the afternoon. Write a polynomial that represents the total

distance that she traveled.

A

dd

itio

n a

nd

Su

btr

act

ion

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Multiply a polynomial by a polynomial.

e.g.(1): Find : a) b)

a) [ ]

b) [ ]

e.g. (2) : Find the area of the given figure

when :

(Hint: Area of parallelogram = base x height)

Multiplication of polynomials :

To multiply polynomials, multiply each term of one polynomial by

every term of the polynomial, then combine like terms.

e.g.(3): Find: a) b)

a)

b) (

)

□ M

ult

ipli

cati

on

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er

𝑎𝑏 𝑐

𝑎






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(4): The length, width and height of a box are and

inches respectively. Write a polynomial that represents its

volume? (Hint: Volume of a box = length width height)

e.g.(5): Find:

⏟

Multiplication of polynomials can be performed vertically as follow :

e.g.(6): Find: (

Note: When multiplying vertically, it is important to align like terms

vertically before adding terms.

M

ult

ipli

cati

on

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Special Cases Products of two binomials:

Difference of Squares :

e.g.(7): Find a) b)

a)

Apply the formula .

Simplify each term.

b)

Apply the formula .

Simplify each term.

□ M

ult

ipli

cati

on

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er


Perfect Square Trinomials :

e.g.(8): Find a) b)

a)

Apply the formula .

Simplify each term.

b)

Apply the formula

Simplify each term.






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

National

Day Leave

27 – 28

November


Perfect Square Trinomials :

e.g.(9): Find a) b)

a) y

Apply the formula .

Simplify each term.

a)

Apply the formula .

Simplify each term.

□ M

ult

ipli

cati

on

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er

Factor polynomials :

Factoring out the Greatest Common Factor.

e.g.(1) : Factor out the Greatest Common Factor :

a) b)

a)

b)

□

Fact

ori

zati

on

of

Poly

no

mia

ls






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

National

Day Leave

27 – 28

November


Factoring Perfect Square Trinomial.

e.g.(1) : Factor the following perfect square trinomials :

a) b)

a)

Put the trinomial is in the form:

where and .

Factor as .

b)

Put the trinomial is in the form:

where and

Factor as .

□ F

act

ori

zati

on

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y–

2 D

ecem

ber






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

National

Day Leave

27 – 28

November


Factoring Difference of Squares Binomial.

e.g.(1) : Factor the following difference of squares binomials:

a) b)

a)

Put the binomial is in the form:

where and 3.

Factor as .

b)

Put the binomial is in the form:

where and .

Factor as .

□ F

act

ori

zati

on

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7

Feb

ruar

y– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

National

Day Leave

27 – 28

November

Divide a polynomial by a monomial.

Introduction: Dividing Monomials using Exponents Rules

e.g.(1) : Find the following in simplest form :

a)

b)

c) d)

a)

b)

e.g.(2) : Find the following in simplest form :

a)

b)

a)

Divide each term in the numerator by .

Simplify each term.

b)

Divide each term in the numerator by

Simplify each term.

□ D

ivis

ion

of

Poly

nom

ials

Un

it T

hre

e :

Poly

nom

ials

7 F

ebru

ary– 2

Dec

emb

er






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Determine the difference between gross pay and net pay.

Deductions : is the total amount of money you spend on .

Food , Telephone , Housing (rent) , Clothing, etc.

Gross Pay : is the total amount of money you get before deductions.

Salary or/and Other earnings as commission, doing

piecework and overtime pay.

Net Pay : is the amount of money you get after deductions.

Gross Pay for regular pay (salary) :

Some people get a salary, which is a fixed amount of money for

each time period worked, such as a day, week, month, or year.

e.g.(1) : Mariam is paid a salary of OMR 46

per week. How much gross pay does

Mariam receive for one year of

work?

Omani Rials.

e.g.(2) : Khalid works as a policeman and is paid a monthly salary of

OMR 540. What is his yearly gross pay?

Omani Rials.

□ G

ross

Pay a

nd

Net

Pay

Un

it F

ou

r :

Con

sum

er M

ath

emati

cs

3

Dec

emb

er –

26 D

ecem

ber

1 year = 12 months

1 year = 52 weeks

1 year = 365 days






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

e.g.(3) : Ahmed is paid OMR 4316 a year. Calculate his :

a) Weekly gross pay.

b) Monthly gross pay.

a)

83 Omani Rials.

b)

Omani Rials.

e.g.(4) : Said gets a salary of OMR 495 per month. Every month, he pays

OMR 220 for rent and OMR 75 for car monthly payment (loan).

a) Calculate his monthly deductions.

b) Calculate his monthly net pay.

a) Omani Rials.

b) Omani Rials.

G

ross

Pay a

nd

Net

Pay

Un

it F

ou

r :

Con

sum

er M

ath

emati

cs

3

Dec

emb

er –

26 D

ecem

ber






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Calculate earnings for doing piece work.

Piece work : work paid for each item (piece) produced/sold.

Or

e.g.(1) : Ahmed works in making furniture. He gets OMR 25 for each

chair, OMR 55 for each table and OMR 70 for each cabinet.

What are his earnings if he made 4 chairs, 2 tables and 2

cabinets?

Omani Rials.

e.g.(2) : Salim is paid OMR 280 per month plus OMR 3 for each item

he sells. Salim sold 24 items in November.

a) What were Salim’s gross earnings for November?

b) If Salim paid OMR 20 for electricity bill. What was his net

pay?

a)

Omani Rials.

b)

Omani Rials.

□ P

iece

Work

Un

it F

ou

r :

Con

sum

er M

ath

emati

cs

3

Dec

emb

er –

26 D

ecem

ber






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Calculate earnings for overtime pay.

Overtime work : work paid for overtime (additional) hours beyond

the regular working hours.

Or

e.g.(1) : Salim drives a truck for a monthly salary of OMR 220 plus

OMR 5 for any additional hour. If he worked 4 additional hours,

what would be his gross earnings?

Omani Rials.

□ O

ver

tim

e W

ork

Un

it F

ou

r :

Con

sum

er M

ath

emati

cs

3

Dec

emb

er –

26 D

ecem

ber






skrameR Assessment

tools Teaching


Objectives/Outcomes

Ach

iev

ed

Ob

jec

tive

To

pic

№ o

f

We

ek

s

Pe

rio

d

Of

tim

e

Revision

Lessons and

Exercises

are included

Pre-exams

leave 29-30

December

Calculate earnings for straight commission.

Straight commission work : work paid (as a percent) for sales.

Some salespeople earn a commission or both a salary plus a

commission.

Or

e.g.(1) : Ahmed earns a commission of on the sale of any house. If

he sells a house priced at OMR 60 000. What is his earning?

Omani Rials

e.g.(2) : Saleh earns OMR 250 per month plus 18% commission on

sales. He sold OMR 830 in the month of February. What is his

gross monthly earning for February?

Omani Rials

□ C

om

mis

sion

Un

it F

ou

r :

Con

sum

er M

ath

emati

cs

3 D

ecem

ber

– 2

6 D

ecem

ber

Rewrite the percent as a fraction :

Yearly Plan for Mathematics 2013 2014 First Semester · PDF fileYearly Plan for Mathematics...

Documents

Transcript of Yearly Plan for Mathematics 2013 2014 First Semester · PDF fileYearly Plan for Mathematics...