Mathematics Syllabus grade VIII for AKU - EB Schools
Aga Khan
Education Service Pakistan
Aga Khan Higher
Secondary Schools, GILGIT-BALTISTAN
Syllabus Curriculum
for Grade 8th
2018-2019
REVIEWED BY
Syed Anwar Ali Shah (AKHSS,
Gilgit)
Rizwan Karim (AKHSS,
Gahkuch)
Sulaiman Shah (AKHSS,
Sherquila)
AIMS
-
The students shall explore the nature in terms of mathematical
language.
-
The students shall be able to apply their learning of mathematics in
their daily life.
OBJECTIVES
-
The students shall be able to understand the problems existing in
nature and do the mathematical modeling of these problems.
-
The students shall develop understanding of basic concepts of math and
usage of symbols.
-
The students shall develop basic numerical skills to be accurate in
their measurements.
-
The students shall develop problem-solving skills in mathematics.
Term wise distribution of syllabus
|
First
Term April-Sept |
Allocated
Periods |
|
Second
Term Oct-Fe |
Allocated Periods |
|
|
Days(96) |
Reflections |
|
Days(89) |
reflections |
|
|
Concept of Fraction and Decimal
Fraction |
20 |
|
Factorization and algebraic
manipulation |
16 |
|
|
Sets |
30 |
|
Algebraic Equations |
18 |
|
|
Laws of Exponents |
13 |
|
Simultaneous
Linear Equations |
16 |
|
|
Financial Arithmetic |
15 |
|
Fundamentals
of geometry |
18 |
|
|
Algebraic Expressions and Algebraic
Formulae |
15 |
|
Practical
geometry |
15 |
|
|
Total |
93 |
|
|
83 |
|
|
Revision(days) |
3 |
|
Revision(days) |
6 |
|
Suggested Text Book:
1.
Grade 8 Mathematics AKHSSs.
Suggested reference Books:
1.
Mathematics 9 (3rd Edition) by Prof Shamshad Mohammad Lodhi
(late), Ms. Balqees Mohammad Din, Mohammad Habib, Ghulam Sarvar Sipra, Fahim
Hussain, Muhammad Anwar, Punjab Textbook Board, Lahore.
2.
Countdown Math Book 7 and 8
3.
New Syllabus D Mathematics 4,2 (3rd Edition) by Lee Peng Yee, The
Keng Seng, Looi Chin Keong. Oxford University Press (1995).
4.
Punjab Text Book for 9th
5.
Ilmi Book for 10th
6. Math wise Book 8th.
|
Concepts |
Specific Learning Objectives |
|
|
|
Date |
|
|
K |
U |
A |
|
|
|
First Term No of Days:
96 Semester durations: April
16 to September 30 |
|
||||
|
1- CONCEPT
OF FRACTION AN DECIMAL FRACTION 1.1. Introduction to Fraction. 1.2.
Decimal Fractions. |
The students should be able
to: 1.1.1.
Define fraction and demonstrate different fractions through pictorial
presentation. 1.1.2.
Explain proper and improper fraction through pictorial presentation. 1.1.3.
Demonstrate equivalent fractions through pictorial presentation (e.g.
½=2/4=4/8 etc.) 1.1.4.
Find desired fraction of any number or a fraction e.g. ½ of 10, ½ of
1/3 and 3/5 of 1 etc. and express these sets pictorially. 1.1.5.
Order of fractional numbers (ascending order/descending order) 1.1.6.
Add, Subtract, multiply and divide different fractions. 1.1.7.
Use BODMAS rule to simplify fractions 1.2.1 Read
and write decimal fractions (with pictorial presentation) 1.2.2 Order
decimal fractions. 1.2.3 Add,
Subtract, multiply and divide different decimal fractions. |
* * * |
* * * * |
* * * * * * * |
April 16 To May 11 |
|
2- SETS 2.1 Sets 2.2 Operations on Sets 2.3 Venn Diagram (Up to three sets) |
The students should be able
to: 2.1.1 Define set 2.1.2 Present any set in ·
Tabular form ·
Descriptive form ·
Set-builder notation 2.1.3 Recognize set of: ·
natural numbers (N) ·
whole numbers (W) ·
integers (Z) ·
rational numbers (Q) ·
even numbers (E) ·
odd numbers (O) ·
prime numbers (P) 2.1.4 Explain relationship between two sets ·
Disjoint ·
Overlapping ·
Subsets 2.2.1 solve related problems on union,
intersection, difference and compliment 2.2.2 Find subsets of any set 2.2.3 Define proper 2.2.4 Find power set P(A) of a set A and
explore the formula to find number of elements in power set keeping number of
elements of a set in a view. 2.3.1 Define and explain Venn Diagram. 2.3.2 Demonstrate different cases of Venn
diagram for two sets. 2.3.3 Demonstrate the following cases for
Venn diagram up to three sets Case I A, B and C all are overlapping, Case II All three sets are disjoint Case III First set is subset of 2nd and
Second is subset of 3rd. Case IV A
overlapped to B and B overlapped with C but A and C are disjoint. Case V Two
sets are overlapping, and they are subset of third set. Case VI Two
sets are disjoint and subsets of third set. 2.3.4. Express tabular form of a set related to
above cases in Venn diagram 2.3.5 Apply union, intersection, difference
and complement on the cases given above. |
* * * * |
* * * * * |
* * * * * |
May 12 To June 25 |
|
3- LAWS OF EXPONENTS/INDICES 3.1 Introduction 3.2 Scientific
Notation |
The students should be able
to: 3.1.1 Simplify expressions containing
exponents without using laws below. 3.1.2 Explore the following laws of
exponents to simplify expressions with real base and exponent 3.2.1 Define ordinary and scientific notation
of numbers 3.2.2 Identify ordinary and scientific
notation of numbers 3.2.3 Convert numbers from
ordinary and scientific notation of numbers (vice versa) 3.2.4 Apply operation on
scientific notation ·
Addition ·
Subtraction ·
Multiplication ·
Division |
* |
* * * |
* * * * |
June 25 To Aug. 17 |
|
4-
Financial Arithmetic’s 4.1 Percentage 4.2 Profit and Loss |
4.1.1
Define Percentage 4.1.2
Concert percentage into fraction
and decimal and vice versa. 4.1.3.
Find the required percentage of
any number (e.g. 2% of 10, 2.5% of 10 and 2 ½ % of 20 etc.) 4.1.5
Apply percentage in different real
life problems (Zakat, insurance and income tax etc.) 4.2.1
Define profit and loss. 4.2.2 Find profit and loss and profit or loss
percent. 4.2.3
Find cost price and sale price if
profit and loss or profit or loss percent are given. |
* * |
|
* * * * * |
Aug. 17 To Sep. 7 |
|
5- Algebraic
expression and algebraic formulae. 5.1 Algebraic Expressions 5.2 Polynomial 5.3 Operations on
polynomial 5.4 Basic Algebraic
Formulas |
The students should be able
to: 5.1.1 Recall constant,
variable, algebraic expression 5.1.2 Types of algebraic
expressions (polynomial, rational, irrational) 5.1.3. Convert verbal expression into
mathematical form. 5.1.4. Define: ·
Polynomial, ·
Degree of polynomial ·
Coefficients of a polynomial 5.2.1 Recognize polynomial in one, two and more
variables 5.2.2 Differentiate between different types of
polynomials 5.2.3 Recognize polynomials of various degrees
e.g. linear, quadratic, cubic and biquadratic polynomials. 5.3.1 Add, subtract and multiply polynomials 5.3.2 Divide a polynomial by a linear
polynomial The students should be able
to: 5.4.1. Recall and verify the formulas: ·
·
·
a2 -b2 =
(a – b)(a + b) ·
4ab = ( a + b)2 -(a - b)2 ·
2(a2 + b2 )=( a + b)2 + (a - b)2 ·
Apply above formula to find any missing element. 5.4.2. Apply them to solve problems like: ·
evaluate (102)2, (1.02)2, (98)2 and
(0.98)2 find |
* * * * * * |
* * * * * * * * |
* * * * * |
Sep 7 To Oct. 10 |
2nd Term
Number of Days: 89
Semester duration: October 11 to March 20
|
6- Factorization and
Algebraic Manipulation 5.1 Factorization 5.2 Algebraic manipulation |
6.1.1Define factorization
as a process of decomposition into factors 6.1.2Factorize expressions
of the following types: ·
ka + kb + kc, ·
ac + ad + bc + bd ·
Middle term breaking method ·
a2 ·
a2 - b2 ·
a2 ·
completing square method 6.2.1
Apply factorization to simplify
algebraic fractions. 6.2.2
Find LCM (Least common multiple)
of different algebraic expression. 6.2.3
Use LCM to simplify different
algebraic fractions with operations( add, subtract , multiply and divide) |
* * |
|
* * * * |
Oct. 11 To Oct 31 |
|
7. Algebraic Equations 7.1
linear equations. 7.2
Quadratic Equations. |
7.1.1 Define Algebraic equations and related terms.
(solution. root and solution set) 7.1.2 Distinguish between linear and quadratic
equation in one variable. 7.1.3 Write the standard form of linear and
quadratic equation in one variable 7.1.3 Solve linear equation for one variable 7.1.4 Solve real life problems related to
linear equations. 7.2.1 Solve quadratic equation (in one variable)
using factorization methods 7.2.2 Solve
real life problems related to quadratic equation. |
* * |
* |
* * * * |
Nov. 1 To Nov. 28 |
|
SIMULTANEOUS LINEAR EQUATIONS 8.1 Solution of
simultaneous linear equations |
The students should be able
to: 8.1.1. Recognize simultaneous linear equations
in two variables and write simultaneous linear equation in standard form. 8.1.2 Solve simultaneous
linear equations using: ·
Method of substitution ·
Method of elimination. 8.1.3 Solve real life problems involving two
simultaneous linear equations in two
variables. 8.1.4 Make the indicated variable as subject. |
* * |
* |
* * * |
Nov. 29 To Dec. 15 |
|
9-FUNDAMENTALS OF GEOMETRY 9.1Lines
and Angles 9.2 Triangles 9.3 Quadrilateral |
The students should be able
to: 9.1.1 Define basic concepts of geometry e.g.
Point, line etc. 9.1.2 Different types of angles. 9.1.3 Apply the following properties 1.
sum of all adjacent lines equal to 180. 2.
sum of all angles at a point equals 360. 9.1.4 Define
parallel lines 9.1.5 Draw a transversal to intersect two parallel
lines and demonstrate corresponding angles, alternate interior angles,
vertically opposite angles and interior angles on the same side of the
transversal. 9.1.6 Describe the following relations
between the pairs of angles when a transversal intersects two parallel lines: ·
pairs of corresponding angles are equal ·
pairs of alternate interior angles are equal ·
pair of interior angles on the same side of transversal is
supplementary and
demonstrate them through figures. 9.2.1 Define triangle and types. 9.2.2 Properties of triangle i.e. interior
sum of triangle, isosceles triangle property, one exterior angle equal to sum
of two opposite interior angles. 9.3.1 Define Quadrilateral and its types. 9.3.2 Demonstrate the properties of
rectangle, square kite, trapezium, rhombus and parallelogram 9.3.3 Solve the questions related to
properties. |
* * * * * |
* * * |
* * * |
Dec. 15 To Feb 16 |
|
|
7-
PRACTICAL GEOMETRY 9.1
Construction of angles and angle bisectors 9.2
construction of lines 9.3Construction
of triangle and Quadrilateral |
The students should be able
to: 9.1.1.
Construct angles using compass the multiples of 15 up to 180 degrees.
9.1.2.
Draw angle bisectors of an angle. 9.2.1
Draw parallel lines 9.2.2
Draw right bisectors of a line segment. 9.2.3
Draw perpendicular at any point P on a line 9.2.4
Draw the perpendicular on a line from a point outside the line. 9.3.1 Draw equilateral triangle and
isosceles triangle (any method and any measurement) 9.3.2Construct Square,
rectangle, parallelogram, rhombus and kite. (by any method) |
|
|
* * * * * * * |
Feb 18 To March 16 |
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