National curriculum for grades 7 to 9: mathematics · MINISTRY OF EDUCATION NATIONAL CURRICULUM FOR...

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REPUBLIC OF LIBERIA

MINISTRY OF EDUCATION

NATIONAL CURRICULUM FOR GRADES 7 TO 9

MATHEMATICS

February 2011

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MESSAGE FROM THE MINISTER OF EDUCATION

I wish to extend my thanks and appreciation to ECSEL, UNESCO and all our partners for their immense contribution to this important task of revising and

strengthening of the National Curriculum. Special thanks to USAID through LTTP for their funding and technical support in the harmonization or realignment of

the curriculum. We extend sincere thanks and appreciation to the Bureau of Curriculum Development and Textbook Research, the National Curriculum Taskforce,

and the subject specialists from various institutions for the level of professionalism that went into this exercise.

The revision and strengthening of our National Curriculum comes at a time when our nation is faced with the Herculean task or challenge of education

transformation, national reconstruction, recovery and renewal in the aftermath of a devastating civil war. Hence, critical to this national challenge is the rebuilding

of the education sector as Liberians can not achieve the desired socio-economic progress in the absence of a strong, vibrant and productive education and training

system.

The revised national curriculum has two features which include the regular core subject areas of Mathematics, Science, Language Arts and Social Studies and

emphasis is being given to the global challenge of HIV/AIDS, Peace, Citizenship, Human Rights and Environmental education. Secondly, the new curriculum is

developed in line with international standards especially those practiced and enshrined in the curriculum of our sisterly Republic of Nigeria and Ghana who are also

members of the West African Examinations Council (WAEC) .

We wish to urge all our education partners including students, teachers, principals, proprietors of schools and members of school boards to use this curriculum in

our schools to enhance quality and relevant instruction and to enable our students to be adequately prepared to take the West African Senior Secondary Certificate

Examinations (WASSCE) come 2013 as envisaged by us in the education sector.

May I conclude by once again saying big thank-you to all those who contributed to make this project a success.

Hon. E. Othello Gongar

MINISTER

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INTRODUCTION

Mathematics is an indispensable tool in our modern world. We use the knowledge of mathematics in our everyday activities, and we see that knowledge applied in

practically everything we see around us. It is critical to develop in our students those core skills of computation, translating problems into mathematical language

and be able to solve them, and to apply mathematical concepts to everyday activities. This curriculum on Mathematics has been written precisely to develop these

skills early in Liberian junior high school students.

A student-centred approach is emphasized in this curriculum. This is based on the firm belief that learning becomes more permanent, meaningful, and exciting

when students themselves take ownership of the learning process. Teachers are, therefore, urged to contrive those classroom strategies that would engage

students actively in the teaching/learning process.

AIMS AND OBJECTIVES At the end of this course of study, students will, among other things, be able to:

1. Become successful in the study of the basics of mathematics.

2. Acquire the necessary skills that will allow them to become problem solvers and informed decision makers.

3. Make connections between Mathematics and the world around us.

4. Bring Mathematics to life with many real-life applications.

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SEMESTER: ONE

GRADE: 7

PERIOD: I

UNIT: I

TOPIC: ARITHMETIC SKILLS

SPECIFIC OBJECTIVES:

Upon completion of this topic, students will be able to:

1. Identify, define and give examples of even, odd, prime and composite numbers.

2. Compute factors and prime factorization of positive integers

3. Explain the sieve of Eratosthenes to determine the prime and composite numbers between 1 and 100.

4. Find the LCM, GCF, and LCD of given positive integers.

5. State the divisibility rule for 2, 3, 5 and 9.

6. Give examples of numbers divisible by 2, 3, 5 and 9

7. Find the square and square roots of a given number.

OUTCOMES CONTENTS ACTIVITIES MATERIALS/RESOURCES EVALUATION

Classify even, odd, prime

and composite numbers

using the Sieve of

Eratosthenes.

1. Even, odd, prime and

composite numbers.

2. Factors and factoring

3. Divisibility rule

4. LCM, GCF, LCD

5.Square roots

1. Activities involving defining

and giving examples of even,

odd, prime and composite

numbers.

2. Identifying, defining and

giving examples of divisibility

rules for 2, 3, 5, and 9. 3.

3. Using the sieve of the

Eratosthenes to determine

prime numbers between 1 and

100.

4. Computing factors and prime

factorization of positive

integers from any

5. Population data.

6. Finding LCM, GCF and

A. Primary Text

M.F. Macrae, et al. New General

Mathematics for Junior Secondary

Schools 1 (Pearson/Longman)

B. Secondary Text

Mathematical Association of

Ghana, Mathematics for Junior

High Schools - Pupils’ Book 1

(Pearson/Longman, 2005)

Other Materials/Supplementary

Readings

Wall chart containing definition

of even, odd, prime and

composite numbers.

A chart containing the

Fundamental tasks

students should be able to

do: 1. Distinguish between even,

odd, prime and composite

numbers.

2. Explain and apply the

divisibility rules.

3. Demonstrate the method

of factoring.

Other essential evaluation

tools:

Quizzes

5

LCD of given positive

numbers.

divisibility rules.

Oral question and answer

sessions

Home assignments

Short answer tests

SEMESTER: ONE

GRADE: 7

PERIOD: II

UNIT: II

TOPIC: FRACTION



1. Simplify complex fractions.

2. Find fractional parts of any given number.

3. Apply the solutions of complex fractions to ratio, proportions and fraction of parts.


1. Apply the knowledge of

ratio, proportion and complex

fraction in solving community

problems.

1. Operations on fractions.

2. Fractional parts of

numbers.

3. Combining and

simplifying complex

fractions.

4. Ratio and proportion

written as fractions.

1. Guiding students to

simplify complex fractions.

2. Students solve problems

relating to ratio, proportion

and complex fraction.

A. Primary Text


Mathematics for Junior

Secondary Schools 1

(Pearson/Longman)

B. Secondary Text





Other

Materials/Supplementary

Readings

Fundamental tasks students

should be able to do: 1. Seatwork to:

- simplify complex fraction

- write ratio and proportion as

fraction.

- find fractional parts of

numbers


tools:

Quizzes

6

Wall chart containing

definition of even, odd,

prime and composite

numbers.

A chart containing the

divisibility rules.


sessions

Home assignments

Short answer tests

SEMESTER: ONE

GRADE: 7

PERIOD: III

UNIT : III

TOPIC: DECIMALS, PERCENTS AND FRACTIONS



1. Convert from decimal to percent/fraction and vice versa.

2. Apply decimal and percent to the solution of problems involving commissions, discounts, taxes, interests, profit and loss and royalty.

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Students will use the method

of finding simple interest,

commission, discounts, profit

and loss and royalty in their

business transactions with

others.

1. Conversion of decimal to

percent, fraction and

conversely.

.

2.. Commission and

discounts

a) Simple interest, profit

and loss

b) Taxes and royalty.

1. Converting from decimal to

percent and vice versa.

2. Solving problems

involving commission,

discount, taxes, interest, profit

and loss and royalty.

A. Primary Text

M.F. Macrae, et al. New

General Mathematics for

Junior Secondary Schools 1

(Pearson/Longman)

B. Secondary Text





Other


Readings

Poster sheets containing the

formulas for finding simple

interest, discount, profit and

loss, taxes and royalty.

Scientific calculator.

Computer


should be able to do: Exercises that include :

1. Simple interest

2. Commission

3. Discount

4. Profit and loss

5. Royalty


tools:

Quizzes


sessions

Home assignments

Short answer tests

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SEMESTER: TWO

GRADE: 7

PERIOD: IV

UNIT: IV

TOPIC: BASIC ALGEBRA



1. Add, subtract, multiply and divide signed numbers with emphasis on population concept such as births and mortality.

2. Use the grouping symbols in performing basic operations.

3. Identify, define and give examples of a term, variable, constant, co-efficient, exponent, monomial, binomial and trinomial.

4. Evaluate algebraic expressions and formulas with specific example on computing various population risks such as birth, death, migration, etc….

5. Solve and graph linear open sentences in one variable.


Use the skills of adding,

subtracting, multiplying

and dividing signed

numbers in daily life

situation.

1. Operations of

addition, subtraction,

multiplication and

division on signed

numbers.

2. Positive and negative

integers.

3. Basic algebraic

expressions and

variables:

a. variable

b. constant

c. co-efficient

d. exponents

4. Evaluation of

1. Guide students add,

subtract, multiply and

divide sign numbers.

2. Instruct students to use

the grouping symbols in

performing basic

operations.

3. Let students identify,

define and give examples

of these terms; co-

efficient, exponent,

monomial, binomial and

trinomial.

4. Evaluating algebraic

expressions and formula.

A. Primary Text

A. Primary Text




(Pearson/Longman)

B. Secondary Text


Ghana, Mathematics for

Junior High Schools - Pupils’

Book 1 (Pearson/Longman,

2005)

Other


Readings

Graph sheet

Fundamental tasks students should

be able to do: Solving problems involving:

1. Addition

2. Subtraction

3. Multiplication

4. Division

5. Positive and negative integers

6. Basic algebraic expressions

Other essential evaluation tools:

Quizzes

Oral question and answer sessions

Home assignments

Short answer tests

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algebraic expressions

and formulas.

5. Solving and graphing

linear open sentences in

one variable.

Number line

Calculator

SEMESTER: TWO

GRADE: 7

PERIOD: V

UNIT: V

TOPIC: GEOMETRY



1. Identify and construct simple geometric figures such as line segment and angles.

2. Bisect line segments and angles.

3. Identify and give examples of the kinds and properties of angles and polygons.

4. Find the perimeters and areas of given polygons.

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OUTCOMES CONTENTS ACTIVITIES MATERIALS EVALUATION

Students will use the

construction skills to

construct simple geometric

figures such as line segments

and angles using straight

edge protractor and compass.

1. Construction a. Kinds of polygons

b. Perimeters and

areas of polygons

2. Angles

1. Let students identify and

construct simple geometric

figures such as line segments

and angles.

2. Let students identify and

give examples of the kinds

and properties of angles and

polygons.

3. Let students find the

perimeters and areas of a

given polygon.

A. Primary Text




(Pearson/Longman)

B. Secondary Text



Junior High Schools -

Pupils’ Book 1


Other


Readings

Geometry set

Calculator

Computer

Fundamental tasks


do: Individual activities

involving:

1. Constructing

2. Drawing different kinds

of polygons

3. Finding perimeters and

areas of polygons


tools:

Quizzes


sessions

Home assignments

Short answer tests

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SEMESTER: TWO

GRADE: 7

PERIOD: VI

UNIT: VI

TOPIC: GEOMETRY



1. Find the volume and surface area of figures.

2. Plot points and determine and determine the associated pairs of numbers.

3. Graph open-sentences in one variable.

4. Use open sentences to solve geometry and age problems.


Students will apply the skills

to find volume and surface

area of figures..

1. Solid geometry

a. Surface areas of

polygons.

b. Volume of polygons

2. Co-ordinate geometry;

a. integers, negative and

positive (number line)

b. co-ordinate point

c. graph of open sentences

in one variable

1. Let students find volume

and surface areas of

figures.

2. Let students plot points

and determine the co-

ordinate of integers in the

rectangular co-ordinate

system R².

3. Guide students to graph

open sentences in one

variable.

4. Guide students to apply

one variable sentence to

solve numbers, geometry

and age problems.

A. Primary Text



Junior Secondary Schools

1 (Pearson/Longman)

B. Secondary Text

Mathematical Association

of Ghana, Mathematics for


Pupils’ Book 1


Other


Readings

Graph sheets.

Number line

Computer

Fundamental tasks

students should be able

to do: 1. Solve the following

problems in geometry:

-Areas of polygons

-Volume of polygons

2. Coordinate geometry

-integers (negative and

positive)

- coordinate points

-graph of open sentences

Other essential

evaluation tools:

Quizzes

Oral question and

answer sessions

Home assignments

Short answer tests

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Scientific calculator

SEMESTER: ONE

GRADE: 8

PERIOD: I

UNIT: I

TOPICS: A.OPERATIONS ON RATIONAL NUMBERS;

B. NUMBER THEORY



1. Perform operations on whole numbers and decimals.

2. Perform operations on fractions and integers.

3. Solve equations involving operations of rational numbers.

4. Write prime factorizations of a number.

5. Write numbers in exponential form.


Students will apply knowledge

of operations of rational

numbers to operate small

business.

1. Operations on Rational

numbers:

a. Adding and subtracting

whole numbers,

decimals, fractions and

integers.

b. Multiply and divide

whole numbers,

decimals, fractions and

integers.

2. Problems involving

1. Let students use data on

population pattern to add,

subtract, multiply and divide

whole numbers.

2. Have students find the

fractional part of candidates

votes polled in the 2005

elections.

3. Let students find the

missing measurement to

A. Primary Text




(Pearson/Longman)

B. Secondary Text




Pupils’ Book 2


Fundamental tasks


do: 1. Perform operations on

rational numbers.

2. Solve problems

involving

-prime factorization

-exponentiation.


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operations

- Prime factorization

- Exponents

complete a recipe using

fractions.

4. Have students add birth

rate (positive) and death rate

(negative) as integers.

5. Use exponents to show

how a disease can become

pandemic.

Other


Readings

Graph sheets.

Number line

Computer


Poster on population

census for a community.

tools:

Quizzes

Oral question and

answer sessions

Home assignments

Short answer tests

SEMESTER: ONE

GRADE: 8

PERIOD: II

UNIT: II

TOPIC: BASIC ALGEBRAIC EXPRESSIONS AND FORMULAS



1. Evaluate basic expressions and formulas.

2. Simplify basic algebraic expressions by combining like terms.

3. Solve problems involving basic algebraic expressions and formulas.

4. Multiply and divide monomials.

5. Simplify numerical expressions by following the order of operations.

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1. Students will follow

directions in solving problems

of real – life situations.

1. Order of Operations

2. Algebraic Expressions

3. Using formulas

4. Adding and subtracting

monomials, binomials and

trinomials.

5. Multiplying and dividing

monomials, binomials and

trinomials (Law of indices)

6. Equations involving

7. Inequalities.

8. Solve verbal problems

involving algebraic

expressions.

1. Guide students simplifying

expressions involving order of

operation.

2. Students evaluate algebraic

expressions.

3. Let students use formulas to

solve problems.

4. Guide students in adding

and subtracting like terms.

5. Guide students to multiply

and divide monomials by

using Laws of indices.

A. Primary Text




(Pearson/Longman)

B. Secondary Text





2005)

Other


Readings

Graph sheets.

Number line

Computer





should be able to do: 1. Evaluate basic expressions

and formulas.

2. Simplify basic algebraic

expressions by combining

like terms.

3. Solve problems involving

basic algebraic

expressions and formulas.

4. Multiply and divide

monomials.

5. Simplify numerical

expressions by following

the order of operations.


tools:

Daily seatwork

Quizzes

Take home assignment

Test involving algebraic


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SEMESTER: ONE

GRADE: 8

PERIOD: III

UNIT: III

TOPIC: PERCENT, PROPORTION AND RATES



1. Convert fractions and decimals to percent and vice – versa.

2. Identify the three types of percents.

3. Find rates using proportions.

4. Find simple interest, discount, commission, percent gain or loss, sales tax.

5. Solve word problems involving applications of percent.

6. Solve problems involving ratio and proportion.


Students will apply the concepts

of percent to operate a credit

union, sales, income, etc.

1. Fractions, Decimals

and Percents.

2. The three parts of

percent.

3. Simple interest.

4. Discount and

commission.

5. Percent gain or loss.

6. Rates and unit rates.

7. Word problems

involving percent.

1. Let students relate

fractions, decimals and

percent using graph paper.

2. Let students’ use rates

of goods to determine a

better buy.

3. Students open a mini

business in the class using

“symbol” money to

purchase items on interest,

as loan.

4. Finding the percentage

of votes polled by

candidates in the 2005

general election.

A. Primary Text




(Pearson/Longman)

B. Secondary Text





2005)

Other


Readings

Graph sheets.


should be able to do: Exercises involving solving

problems with:

1. Fractions and decimals.

2. Three types of percent

problems

3. Rates using proportions

4. Interest, discount,

commission, gain and loss,

sale tax


tools:

Daily seatwork

Quizzes

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8. Using proportion to

solve problems

involving scale

drawing (map and

actual distance).

5. Compare telephone

rates.

6. Let students find actual

(ground) distances using

Atlas of Liberia.

Number line

Computer







SEMESTER: TWO

GRADE: 8

PERIOD: IV

UNIT: IV

TOPICS: 1. APPLICATION OF ALGEBRAIC CONCEPTS

2. RELATIONS AND FUNCTIONS



1. Solve problems involving numbers, age, geometry, coins, etc.

2. Find the domain and range of a relation or function.

3. Graph relations and functions.

4. Graph linear inequalities.

5. Add and subtract polynomials.

6. Multiply polynomials by monomials and / or binomials.

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Students will apply concepts

and skills of algebraic

expressions to real life

situations.

1. Number problem

2. Age problem

3. Coin problem

4. Geometry problem

5. Relations and

functions

6. Graphing linear

inequalities

7. Polynomials

a. adding and

subtracting

polynomials

b. multiplying

polynomials by

monomials, binomials.

1. Solve problems in one

variable of coin, age,

geometry, numbers and

population density.

2. Construct graph of order

pairs.

3. Differentiate between a

relation and function.

4. Determine the domain and

the range of a function.

5. Find the product of

Polynomials by

a. monomials

b. binomials

A. Primary Text




(Pearson/Longman)

B. Secondary Text





Other


Readings

Graph sheets.

Number line

Computer





should be able to do: 1. Solve problems involving

numbers, age, geometry,

coins, etc.

2. Find the domain and range

of a relation or function.

3. Graph relations and

functions.

4. Graph linear inequalities.

5. Add and subtract

polynomials.

6. Multiply polynomials by

monomials and / or

binomials.


tools:

Daily seatwork

Quizzes



expressions and formulas

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SEMESTER: TWO

GRADE: 8

PERIOD: V

UNIT: V

TOPIC: GEOMETRY AND MEASUREMENT



1. Identify angle relationship (vertical, adjacent, complementary, and supplementary)

2. Compute the sums of angles in a given polygon

3. Construct angles and triangles by SAS, ASA, SSS

4. Find the area of trapezoid

5. Find the surface areas of prisms

6. Convert selected metric units.


Students will apply the

concepts and skills of

geometry and

measurement in designing

and constructing roads,

buildings, household

furniture, etc.

1. Angle relationship (vertical, adjacent,

complementary and

supplementary).

2. Simple polygons (sum of

interior angles of regular

polygons).

3. Construction of angles

and triangles by using

(SAS, ASA, SSS).

4. Area of trapezoid.

5. Surface area prisms.

6. Conversion of metric

1. Let students name vertical

and adjacent angles.

2. Guide students to find

complementary and

supplementary angles.

3. Find sums of angles in

given regular polygons, using

farmland as an example.

4. Help students to construct

angles and triangles by SAS,

ASA and SSS.

5. Find areas of trapezoid.

6. Let students compute

A. Primary Text



Secondary Schools 2

(Pearson/Longman)

B. Secondary Text





Other


Readings

Graph sheets.


be able to do: 1. Identify angle relationship

(vertical, adjacent, complementary,

and supplementary)

2. Compute the sums of angles in a

given polygon

3. Construct angles and triangles by

SAS, ASA, SSS

4. Find the area of trapezoid

5. Find the surface areas of prisms

6. Convert selected metric units.


Daily seatwork

Quizzes


Tests involving algebraic


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units (selected units). surface areas using a carton.

7. Find metric units

conversion using physical

models.

Number line

Computer


Poster on population census

for a community.

SEMESTER: TWO

GRADE: 8

PERIOD: VI

UNIT: VI

TOPIC: PROBABILITY, STATISTICS AND TRIGONOMETRY



1. Correctly arrange data in descending and ascending order prepare frequency table and construct histogram.

2. Make and interpret double bar graphs, double line graphs and circle graphs.

3. Compute the mode, median, and mean of a set of a population data.

4. Find the range, variance and standard deviation, using population data.

5. Compute the probability of simple, independent and dependent events, using population data.

6. Squares and Square Roots.

7. Solve problems using Pythagoras Theorem.

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skills and concepts of

probability and statistics

in predicting population

pattern and the odds of an

event happening.

1. Frequency tables and

Histograms

2. Measures of variability (range, variance and

standard deviation)

3. Making and

interpreting graphs

(double bar and line, circle)

4. Experiments with games

of chance.

5. Probability of an event (simple, independent,

dependent)

1. Guide students in making and

constructing frequency tables and

histograms.

2. Let students to find range,

variance and standard deviation.

3. Guide students to use

population data.

.4. Guide students in making and

interpreting double bar graphs,

double line graphs and circle

graphs from data collected about

students in the school (family size,

favorite leader).

5. Let students toss a coin, roll a

die or spin the probability spinner

and record events.

A. Primary Text




B. Secondary Text






Readings

Graph sheets.

Number line

Computer


Poster on population census for

a community.


be able to do: 1. Correctly arrange data in

descending and ascending order

prepare frequency table and

construct histogram.

2. Make and interpret double bar

graphs, double line graphs and

circle graphs.

3. Compute the mode, median, and

mean of a set of a population data.

4. Find the range, variance and

standard deviation, using

population data.

5. Compute the probability of simple,

independent and dependent events,

using population data.

6. Squares and Square Roots.

7. Solve problems using Pythagoras

Theorem.


Daily seatwork

Quizzes




Assignments,/ activities including:

1. Constructing frequency table.

2. Finding the mean, mode,

median, range, variance, and

standard deviation of a set of

population data.

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SEMESTER: ONE

GRADE: 9

PERIOD: I

UNIT: I

TOPIC: ARITHMETIC



1. Identify and define rational and irrational numbers.

2. Solve ratio, proportion, variation, speed, average and rate of work problems.

3. Compute simple and compound interests.

4. Using formulas (Geometry).

5. Find a rational number halfway between another.


Students will

appreciate the

knowledge gained

from arithmetic as they

interact with other

members of the

community.

1. Rational and Irrational

numbers.

2. Ratio, proportion and

percent.

3. Variation, speed and rate of

work problems.

4. Simple and compound

interests.

5. Using Geometry formulas.

6. Density and rational numbers

1. Guide Students in identifying and

classifying rational and irrational

numbers using calculators.

2. Add, subtract, multiply and divide

rational numbers using data from

population census as examples.

3. Guide students in identifying the

means and extremes of a proportion.

4. Use ratios and proportions to

compute the shares of partners in a

business, etc.

5. Let students solve problems

involving direct and inverse variation.

A. Primary Text



Secondary Schools 3

(Pearson/Longman)

B. Secondary Text






Readings

Geometric set

Boxes

Cylindrical objects

Liter cups

Medicine droppers


be able to do: 1. Identify and define rational and

irrational numbers.

2. Solve ratio, proportion, variation,

speed, average and rate of work

problems.

3. Compute simple and compound

interests.

4. Using formulas (Geometry).

5. Find a rational number halfway

between another.

6. Constructing frequency tables.

7. Finding the mean, mode, median,

range, variance, and standard

deviation of a set of population data.

Give group activities involving:

8. Defining, identifying and

performing operations from rational

22

Rulers and meter stick

Graph sheets

Coins

Die

Different stoppers

Different color chalks

Poster sheets

and irrational numbers.

9. Solving ratio, proportion, variation

speed, average and rate.

10. Computing simple and compound

interests


Daily seatwork

Quizzes




SEMESTER: ONE

GRADE: 9

PERIOD: II

UNIT: II

TOPIC: BASIC ALGEBRA



1. Use the laws of indices/radicals in multiplying and dividing numbers.

2. Simplify radicals and convert radicals to exponents and vice – versa.

3. Add and subtract Polynomials.

4. Multiply polynomials by monomials and binomials.

5. Divide polynomials by binomials.

6. Find squares of binomials.

7. Factor the differences of two squares (binomials).

23


Students will apply

basic algebraic skills

and concepts in

solving problems in

their daily lives.

1. Law of Indices.

2. Simplifying radicals.

3. Converting radicals to

exponents.

4. Adding and subtracting

polynomials.

5. Multiplying

a. polynomials by monomials

b. binomials by binomials.

6. Dividing polynomials by

binomials.

7. Factoring difference of two

squares.

8. Exponential expressions

and radical expressions

1. Finding sums and differences of

polynomials.

2. Finding the products of

monomials by polynomials.

3. Applying the law of indices in

multiplying and dividing arithmetic

and algebraic expressions.

4. Converting exponential

expressions to radical expression and

conversely.

5. Factor the differences between

two squares using methods as:

x² - y² = x² - xy + xy – y²

= x(x + y) - y(x + y)

= (x + y) (x – y))

A. Primary Text




B. Secondary Text

Mathematical Association of Ghana,

Mathematics for Junior High

Schools - Pupils’ Book 1



Readings

Geometric set

Boxes

Cylindrical objects

Liter cups

Medicine droppers


Graph sheets

Coins

Die

Different stoppers


Poster sheets


should be able to do: 1. Use the laws of

indices/radicals in

multiplying and dividing

numbers.

2. Simplify radicals and

convert radicals to

exponents and vice – versa.

3. Add and subtract

Polynomials.

4. Multiply polynomials by

monomials and binomials.

5. Divide polynomials by

binomials.

6. Find squares of binomials.

7. Factor the differences of two

squares (binomials).


tools:

Daily seatwork

Quizzes




24

SEMESTER: ONE

GRADE: 9

PERIOD: III

UNIT: III

TOPIC: RELATIONS AND FUNCTIONS



1. Define and represent relations and functions.

2. Find the Cartesian product of two relations and determine the domain and range of a given relation.

3. Evaluate linear function in one variable.

4. Determine the slope of a line given its equation and two points and vice – versa.

5. Evaluate linear function in two variables.

6. Graph linear equations in two variables given its slope and point.

7. Solve problems involving linear function by graphing.



skills and concepts of

coordinate graphing to

represent and interpret

their daily lives

1. Cartesian products

2. Relation and Function

3.Domain and Range

4. Linear Function in

one variable (graphs)

5. Slope of a line given two points

6. Solving problems involving linear

function in one variable

7. Linear function in two variables

1. Guide students in finding

Cartesian Products.

2. Have students in determining the

domain and range of a given relation.

3. Guide students in evaluating linear

functions (one and two variables).

4. Let students graph linear

functions.

5Tell students to find the slope of a

line given its equation on a graph.

6. Guide students in determining the

A. Primary Text




(Pearson/Longman)

B. Secondary Text





Other


Readings

Geometric set


should be able to do: 1. Define and represent

relations and functions.

2. Find the Cartesian product

of two relations and

determine the domain and

range of a given relation.

3. Evaluate linear function in

one variable.

4. Determine the slope of a

line given its equation and

two points and vice –

versa.

5. Evaluate linear function in

two variables.

25

8. Equation and graph of a line given

its slope and

y – Intercept.

slope of a line when two points are

given.

7. Involve students in finding the

equation and graph of a line when its

slope and y – intersect are known.

Boxes

Cylindrical objects

Liter cups

Medicine droppers


Graph sheets

Coins

Die

Different stoppers


Poster sheets

6. Graph linear equations in

two variables given its

slope and point.


linear function by

graphing.


tools:

Daily seatwork

Quizzes


SEMESTER: TWO

GRADE: 9

PERIOD: IV

UNIT: IV

TOPIC: GEOMETRY



1. Identify, define and give examples of transversal, parallel lines, perpendicular lines and their properties.

2. Identify and define regular polygons and their properties.

3. Find the sum of interior and exterior angles of regular polygons.

4. Construct triangles using SSS, SAS or ASA.

5. Construct parallelograms.

6. Solve problems involving similar triangles.

7. Identify vertical, adjacent, complementary and supplementary angles.

26


Students will recognize

geometric patterns in

architecture design and

household furniture.

1. Constructing of parallel

lines, perpendicular lines and

transversal and their

properties (corresponding

angles, Alternate interior and

exterior angles, etc.)

2. Construct regular

polygons and their

properties.

3. Construct:

a. Given angles

b. Perpendicular lines.

Perpendicular

Bisector of a segment.

4. Construct:

a. Triangle using

SSS,SAS or ASA

b. Parallelograms

5. Similar triangles.

1. State or list properties of

parallel lines, perpendicular

lines and transversal.

2. Let students state or list

properties or postulates

associated with parallel lines

cut by transversal.

3. Guide students in listing

properties of regular polygons

and using said properties.

4. Guide students in finding the

interior and exterior angles of

regular polygons.

5. Instruct students in listing

and stating properties of similar

triangles.

A. Primary Text




(Pearson/Longman)

B. Secondary Text





2005)

Other


Readings

Geometric set

Boxes

Cylindrical objects

Liter cups

Medicine droppers


Graph sheets

Coins

Die

Different stoppers


Poster sheets


should be able to do: 1. Identify, define and give

examples of transversal,

parallel lines,

perpendicular lines and

their properties.

2. Identify and define regular

polygons and their

properties.

3. Find the sum of interior

and exterior angles of

regular polygons.

4. Construct triangles using

SSS, SAS or ASA.

5. Construct parallelograms.


similar triangles.

7. Identify vertical, adjacent,

complementary and

supplementary angles.


tools:

Daily seatwork

Quizzes

Take home assignments

Exercises for groups in

class to involve:

listing properties of

parallel lines and regular

polygons; stating

properties of similar

triangles

27

SEMESTER: TWO

GRADE: 9

PERIOD: V

UNIT: V

TOPICS: A. TRIGONOMETRY

B. MEASUREMENT



1. Apply the Pythagoras Theorem to compute one side of a right angle triangle when the other two sides are given.

2. Solve problems involving Pythagoras Theorem.

3. Identify, define and compute the trigonometric ratios (functions) of a:

a. Sine of Acute angles

b. Cosine of Acute angles

c. Tangent of Acute angles

4. Find angles of depression and elevation using the sine, cosine and tangent of ratios.

5. Use trigonometry tables (calculators) in finding sine, cosine and tangents of acute angles.

6. Solve problems involving angle of elevation and depression.

7. Convert metric units to customary units and vice versa.


Students will

appreciate the concepts

and skills of

trigonometry as they

apply them in

surveying, shipping, on

air traffic industries.

1. The Pythagorean Theorem.

2. Application of Pythagorean

Theorem

3. Sine, cosine and tangent of

acute angles.

4. Trigonometric tables.

5. Application of sine, cosine

and tangent ratios.

1. Guide students to discover the

relationship amongst the sides of

a triangle.

2. Guide students in using the

Pythagorean Theorem in problem

solving.

3. Let students explain the sine,

cosine and tangent of acute

angles’ relationship in their own

words.

A. Primary Text




(Pearson/Longman)

B. Secondary Text





2005)


be able to do: 1. Apply the Pythagoras Theorem to

compute one side of a right angle

triangle when the other two sides

are given.


Pythagoras Theorem.

3. Identify, define and compute the

trigonometric ratios (functions) of

a:

d. Sine of Acute angles

28

6. Angles of depressions and

elevation.

7. Converting metric and

customary units.

4. Guide students in the

application of sine, cosine and

tangent ratios.

5. Let students use liter cup and

medicine dropper and rulers and

yardstick to ratio of metric and

customary units of length and

capacity.

Other


Readings

Geometric set

Boxes

Cylindrical objects

Liter cups

Medicine droppers


Graph sheets

Coins

Die

Different stoppers


Poster sheets

e. Cosine of Acute angles

f. Tangent of Acute angles

4. Find angles of depression and

elevation using the sine, cosine

and tangent of ratios.

5. Use trigonometry tables

(calculators) in finding sine,

cosine and tangents of acute

angles.

6. Solve problems involving angle of

elevation and depression.

7. Convert metric units to customary

units and vice versa.


Daily seatwork

Quizzes


Exercises for groups in class to

involve:

listing properties of parallel lines

and regular polygons; stating

properties of similar triangles

Activities will involve :

a) Pythagorean Theorem.

b) Computing the trigonometric

ratio and table.

c) Converting metric unit to

customary units.

29

SEMESTER: TWO

GRADE: 9

PERIOD: VI

UNIT: VI

TOPIC: PROBABILITY AND STATISTICS



1. Make frequency tables and histograms from a given data.

2. Find measures of central tendency using population data.

3. Compute the measures of variability (range, variance and standard variation)

4. Read and interpret stem and leaf, box and whiskers and scatter plots.

5. Make stem and leaf plot from a set of class test scores.

6. Use the fundamental counting principle in solving: a. Multiplication b. Venn diagram c. Diagrams with two finite.

7. Find permutation and combination of an event occurrence.


Students will appreciate

the skills and concepts of

probability to interact

with other people.

1. Frequency tables and

Histograms.

2. Measures of Central

tendency

(mode, median and mean).

3. Measure of variability

(range, variance and

standard variation).

4. Stem and leaf plot

5. Box and whisker plot

6. Scatter plot

1. Let students collect data

about test scores and make a

frequency table and histogram

from the data.

2. Have students collect and

present data about favorite

meal on a histogram and find

the central tendency of the

data.

3. Have students make :

a. Stem and leaf plot from

class test scores.

b. Box and whisker plots from

class test score.

A. Primary Text




(Pearson/Longman)

B. Secondary Text





2005)

Other


Readings

Geometric set


should be able to do: 1. Make frequency tables

and histograms from a

given data.

2. Find measures of central

tendency using

population data.

3. Compute the measures of

variability (range,

variance and standard

variation)

4. Read and interpret stem

and leaf, box and

whiskers and scatter

plots.

5. Make stem and leaf plot

30

7. Permutation

8. Combination

4. Pupils list the number of

attires taken from a set of

shirts and trousers.

5. Pupils find the probability

of picking a color shirt and

trouser from a set of attire.

Boxes

Cylindrical objects

Liter cups

Medicine droppers


Graph sheets

Coins

Die

Different stoppers


Poster sheets

from a set of class test

scores.

6. Use the fundamental

counting principle in

solving: a. Multiplication

b. Venn diagram c.

Diagrams with two finite.

7. Find permutation and

combination of an event

occurrence.


tools:

Daily seatwork

Quizzes


Assign groups or

individuals to collect,

organize and interpret

data on :

1. Test score.

2. Population pattern

3. Die, coin

4. Birth rate

5. Death rate

6. Number of persons in

class ( males and

females)

The printing of the National Liberian Curriculum is provided by ECSEL - European Commission Support for Education in Liberia

National curriculum for grades 7 to 9: mathematics · MINISTRY OF EDUCATION NATIONAL CURRICULUM FOR...

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