rpt mat t1

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Yearly Scheme Of MATHEMATICS

1

1

1. Understand the

concept of whole

numbers.

i. Count, read and write

whole numbers.

ii. Identify place value and

value of each

digit in whole numbers.

iii. Round whole numbers.

Count; read andwrite whole

numbers in

words or

numerals.

Students readand write

whole

numbers while

counting from a

given initial value

to a final value in a

certain specified

interval.

e.g. i. Count on in tens

from 20 to 100.

ii. Count back in

hundreds

from 1200 to 200.

Emphasise the

relationship

between

rounding and

estimation.

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Estimate values,including that of

Real life situations

by rounding.

1

2. Performcomputations

involving addition

and subtraction of

whole numbers to

solve problems.

i. Add whole numbers.

ii. Solve problems involving

addition of

whole numbers.

iii. Subtract whole numbers.

iv. Solve problems involving

subtraction

of whole numbers.

Explore additionand subtraction

using standard

algorithm (rules of

calculations),

estimation, mental

and speed

computation or

penciland-paper.

Use calculators tocompare and

verify answers.

Students pose andsolve problems

Addition and

subtraction

should begin

with

two numbers.

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related to addition

and subtraction

of whole

numbers.

2

3. Perform

computations

involving

multiplication and

division of whole

numbers to solve

problems.

i. Multiply two or more

whole numbers.


multiplication of whole

numbers.

iii. Divide a whole number

by a smaller

whole number.


division of

whole numbers.

Exploremultiplication and

division using

standard algorithm

(rules of

calculations),

estimation, mental

and speed

computation or

penciland- paper.

Use calculators tocompare and

verify answers.

Students explorethe relationship

between

multiplication and

Emphasise that:

The quotient

of a number

divided by

zero is

undefined.

The quotient

of zero

divided by

any number

(except zero)

is zero.

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division.

Students pose andsolve problems

related tomultiplication and

division of whole

numbers.

2


involving combined

operations of

addition,

subtraction,

multiplication and

division of wholenumbers to solve

problems

i. Perform computations

involving any

combination of addition,

subtraction,

multiplication and division of

whole

numbers, including the use

of

brackets.


combined

operations of addition,

subtraction,

operations ofwhole numbers by

using standard

algorithm (rules of

calculations),

estimation,

penciland-

paper or

calculator.

Students usecalculators to

compare and

verify answers.

Emphasise on

the order of

operations and

the use of

brackets.

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whole

numbers, including the use

ofbrackets.

3

1. Recognise and

extend

number patterns

and

sequences formed by

counting on and

counting back in

intervals of any size.

i. Describe the pattern of a

given

number sequence.

ii. Extend number sequences.

iii. Complete missing terms

in given

number sequences.

iv. Construct number

Relate numbersequence to

patterns in real-

life situations.

e.g. Odd numbersare used as

addresses of

houses on one side

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sequences based

on given patterns.

of

the road and even

numbers on the

other.

4

2. Recognise odd

and

even numbers andmake general

statements about

them.

i. Identify and describe odd

and even

numbers.

ii. Make general statements

about odd

and even numbers.

Explore generalstatements about

odd and even

numbers such as:

a. The sum of odd and

even

numbers.

b. The product of odd

and even numbers.

c. The difference between

odd

and even numbers.

4

3. Understand the

characteristics of

prime numbers

i. Identify the characteristics

of prime numbers.

ii. Determine whether a

given

Use calculators orcomputer

programmes to

explore prime

Emphasise that

Number 1 is

not a prime

number.

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number is a prime number.

iii. Determine all the prime

numbers less than 100.

numbers.

Use sieve ofEratosthenes to

generate primenumbers less than

100.

5

4. Understand the

characteristics and

use the knowledge

offactors of whole

numbers.

i. List factors of whole

numbers.


number is a factor of another

whole number.

Determine factorsof whole numbers

by exploring and

investigating.

Emphasise that

1 and the

number

itself are factors

of any number.

5

5. Understand the

characteristics and

use the knowledge

of

i. Identify prime factors from

a list of

factors.

ii. Find prime factor(s) of

Students exploreand investigate to

determine prime

factors of whole

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prime factors of

whole numbers.

whole numbers.

iii. Determine whether a

number is a prime factor of

another whole number.

numbers.

State any givenwhole number as a

product of itsprime factors.

6

6. Understand and

use

the knowledge of

multiples of whole

numbers.

i. List the multiples of whole

numbers.


number is the multiple of

another number.

Students use thedivisibility test of

2, 3, 4, 5, 6, 7, 8, 9,

10, 11 and their

combinations.

e.g. 30 can be

divided by

6.Therefore it can

be divided by 2

and 3 and

vice-versa.

Emphasise that

the list of

multiples of a

number is also

a number

sequence.

Use small

numbers to

develop the

concept.

6

7. Understand the

characteristics and

use the knowledge

of

common multiples

i. Find the common multiples

of two

or three whole numbers.


number is the common

Students findcommon multiples

and LCM by listing

down the multiples

of each given

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7

and Lowest

Common Multiple

(LCM) of whole

numbers.

multiple of two or

three given numbers.

iii. Determine the LCM of

two or three given numbers.

number.e.g.

Multiples of 4 : 4,

8, 12, . Multiples

of 6 : 6, 12,.. Common Multiples

of

4 and 6:12, 24,

36, 48,.which are

the multiples of

12.

Use the method ofprime

factorisation to

find common

multiples and

LCM.

e.g.

4 = 2 x 2

6 = 2 x 3

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Therefore the LCM of 4

and 6 is

2 x 2 x 3 = 12.

Use algorithm tofind the LCM.

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7

8

8. Understand and

use

the knowledge of

common factors and

Highest Common

Factors (HCF) of

whole numbers.

i. Find common factors of

two or three whole numbers.ii. Determine whether a

number is a common factor

of two or three given whole

numbers.

iii. Determine the HCF of two

or three given numbers.

Students list downall the factors ofeach given number

and identify the

same factors for

each number.

Students explore,identify and

determine

common factors of

whole number.

Students find theHCF by listing

down all the

factors of each

given number.

Explore, identifyand determine the

HCF of whole

Common

FactorHighest

Common

Factor (HCF)

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numbers.

Use the method ofprime

factorisations to findthe

common prime factors

and

hence HCF.

e.g.

12 = 2 x 2 x 3

18 = 2 x 3 x 3

Common Prime Factors:

2 and 3

The HCF: 2 x 3 = 6

Use algorithm tofind HCF.

8

1. Understand and

use

the knowledge of

i. Read fractions.

ii. Describe fractions as parts

of awhole.

Use concretematerials and

drawings to

4 read as:

Four over five

22

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fractions as part of a

whole.

iii. Represent fractions with

diagrams.

iv. Write fractions for given

diagrams.

demonstrate the

concept of

fractions such as:

a. Folding a ribbon tofind

one third of its length.

b. The number of girls as

compared to the whole

class.

c. Folding papers.

15 read as:

Fifteen

over twenty two

Use the termsnumerator and

denominator.

9

2. Understand and

use

the knowledge of

equivalent fractions.

i. Find equivalent fractions

for a given fraction.

ii. Determine whether two

given fractions are

equivalent.

iii. Compare the values of

two given fractions.

iv. Arrange fractions in

order.

v. Simplify fractions to the


drawings to

demonstrate the

concept of

equivalent

fractions.

Use paper foldingto explain and

explore.

Use number

lines,

concrete

materials or

the concept of

equivalent

fractions

to compare

fractions.

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lowest terms. Compare thevalues of two

fractions by

converting them tofractions with the

same denominator

or the same

numerator.

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9

3. Understand the

concept of mixed

numbers and their

representations

i. Recognise mixed numbers.

ii. Represent mixed numberswith diagrams.

iii. Write mixed numbers

based on given diagrams.

iv. Compare and order mixed

numbers on number lines.

Use concretematerials,drawings and

number lines to

represent mixed

numbers.

10

4. Understand the

concept of proper

fractions and

improper fractions.

i. Recognise proper and

improper fractions from

given fractions.

ii. Change mixed numbers

into improper fractions.

iii. Change improper

fractions into mixed

numbers.

Use calculators toexplore the

relationship

between mixed

numbers and

improper fractions.

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10

5. Understand the

concept of addition

and subtraction offractions to solve

problems.

i. Perform addition involving:

a. Fractions with common

denominators.

b. Fractions with differentdenominators.

c. Whole numbers and

fractions.

d. Fractions and mixed

numbers.

e. Mixed numbers.

ii. Perform subtractioninvolving:

a. Fractions with common

denominators.

b. Fractions with different

denominators.

c. Whole numbers and

fractions.

d. Fractions and mixed

numbers.

e. Mixed numbers.

Add and subtractfractions by

writing the

fractions in theirequivalent forms

with common

denominators

including the use

of LCM.

Perform additionand subtraction ofmixed numbers by:

i) Adding and

subtracting whole

numbers and fractions

separately.

ii) Writing mixed

numbers in the form of

improper fractions.

Addition and

subtraction

involving

not more thanthree

numbers.

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iii. Solve problems involving

combined operations of

addition and subtraction of

fractions.

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11

6. Understand the

concept ofmultiplication and

division of fractions

to solve problems.

i. Multiply:

a. A whole number by afraction or mixed number.

b. A fraction by a whole

number.

c. A fraction by a fraction

(include mixed numbers).


multiplication of fractions.iii. Divide:

a. A fraction by a whole

number.

b. A fraction by a fraction.

c. A whole number by a

fraction.

d. A mixed number by a

mixed number.


division of fractions.

Examples of:

a. A whole number times

a fraction.

b. A whole number times

a mixed number.

Division

involving notmore than three

numbers

including

whole numbers,

fractions and

mixed

numbers.

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11


involving combined

operations of

addition,

subtraction,

multiplication and

division of fractionsto solve problems.

7. Perform computations

involving

to solve problems.


diagrams todemonstrate

computations.

Limit the

operations to

three numbersincluding

whole

numbers and

mixed numbers.

Emphasise the

order of

operations,including the

use of brackets.

12

1. Understand the

relationship

between

decimals and

fractions.

i. Represent fractions 10 1

and 100 1 as

decimals and vice-versa.

ii. Represent fractions with

denominators 10,100 and

1000 asdecimals.

iii. Read and write decimals

Use concretematerials,

drawings,

calculators and

symbols to explain

the relationship

between decimals

0.3 read as:

zero

point three

0.05 read as:

zero point zero

five

3.29 read as:

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to thousandths.

iv. Change fractions to

decimals and vice-versa.

and fractions. three point two

nine.

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12

2. Understand the

concept

of place value and

value of each digit

in

decimals.

i. State the place value and

value of each digit indecimals.

ii. Compare the values of two

given decimals.

iii. Arrange decimals in

order.

iv. Round decimals to the

nearest wholenumber or up to three

decimal places.

Use number linesto compare andorder decimals.

Emphasise the

relationshipbetween

rounding and

estimation.

13

3. Understand the

concept

of addition and

subtraction of

decimals to solve

problems.

i. Add decimals.


addition of decimals.

iii. Subtract decimals.


subtraction of decimals.

Use calculators orcomputers to

verify answers.

Include whole

numbers.

Addition and

subtraction

should begin

with

two decimals.

Limit to three

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decimal places.

14

4. Understand the

concept

of multiplication

and

division of decimals

to

solve problems.

i. Multiply two or moredecimals.


multiplications of decimals

iii. Divide:

a. A decimal by a whole

number.

b. A decimal by a decimal.c. A decimal by a fraction.


division of

decimals.

Use appropriatecalculation

methods such as

pencil-and -paper,

calculators and

computers.

Formultiplication

and division,

include whole

numbers.

Begin with one

digit whole

number

15

5. Perform

computations

involving combined

operation of

i. Perform computations

involving combined

operations of addition,

subtraction, multiplication

Use calculators orcomputers to

verify answers.

Emphasise the

order of

operations

including the

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addition,

subtraction,

multiplication and

division of decimalsto

solve problems.

and division

of decimals, including the

use of

brackets.ii. Solve problems involving

combined operations of

addition, subtraction,


decimals, including the use

of brackets.

use

of brackets.

17

18

1. Understand the

concept of

percentages and the

relationship

between

percentages and

fractions or

decimals.

i. Express percentages as the

number of parts in every

100.

ii. Change fractions and

decimals to percentages and

vice-versa.


drawings to

demonstrate

percentages.

Use the symbol

% to represent

percent.

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19

20

2. Perform

computations and

solve problems

involving

percentages.

i. Find the percentage of a

quantity.ii. Find the percentage one

number is of another.

iii. Find a number given the

percentage.

iv. Find the percentage of

increase or decrease.

v. Solve problems involvingpercentages.

Use concretematerials anddrawings to

demonstrate

percentages.

21

1. Understand and

use

the knowledge of

integers.

i. Read and write integers.

ii. Represent integers on

number lines.

iii. Compare the values of

two integers.

iv. Arrange integers in order.

v. Write positive or negative

numbers to

32 read as: negative

thirty-two.

5 is less than2

15 is greater than25

The number 0 isneither positive

nor negative.

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represent word descriptions.

22

23

2. Perform

computations

involving addition

and subtraction of

integers to solve

problems.

i. Add integers.

ii. Solve problems involvingaddition of integers.

iii. Subtract integers.


subtraction of integers.

Use number linesto add and subtractintegers.

Use concretematerials,

drawings, and

symbols (e.g.

coloured chips) to

demonstrateaddition and

subtraction of

integers.

Use brackets todifferentiate

between

operations and thesigns

of numbers.

8(7) read

asnegative eight

minus negative

seven.

42 read as

negative four

minus

two.Addition should

include like and

unlike signs.

e.g

Like signs:

9+5,7+ (8)

Unlike signs:3 + (4),

(9) + 5

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1. Understand the

concept ofunknowns.

i. Use letters to represent

unknown numbers.

ii. Identify unknowns in

given situations.

Give a list of termsand students select

algebraic terms

with oneunknown.

An algebraic

term is written

as 3xnot x3

A number, e.g 8is also a term.

2 xis a term.

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25

RELATION

-SHIP

2. Understand the

concept of algebraic

terms.

. Identify algebraic terms

with one unknown.. Identify coefficients in

given algebraic

terms with one unknown.

. Identify like and unlike

algebraic terms with one

unknown.

. State like terms for a giventerm.

Give a list of termsand students selectalgebraic terms

with one

unknown.

p:

The coefficientof

p is 7.

26

3. Understand the

concept of algebraic

expressions.

i. Recognise algebraic

expressions.

ii. Determine the number of

terms in given algebraic

expressions.

iii. Simplify algebraicexpressions by combining

the like terms.

Use concretematerials to

demonstrate the

concept of

combining like and

unlike terms.e.g.

i. 4s+ 8s= 12s

ii. 5r2r = 3r

4p=p+p+p+

p

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iii. 7g+ 6hcannot be

simplified

because they

are notlike terms.

iv. 3k+ 4 + 6k3

= 3k+ 6k+ 43

= 9k+ 1

27

1. Understand the

concept of length to

solve problems.

i. Measure the length of

objects.

ii. Convert one metric unit toanother.

(mm, cm, m and km)

iii. Estimate lengths of objects

in appropriate units.

iv. Use the four operations to

solve problems involving

length.

Emphasise the

importance of

using standardmeasurement.

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2. Understand the

concept of mass tosolve problems.

i. Measure the mass of

objects.

ii. Convert one metric unit to

another.(mg, g, kg, tonne).

iii. Estimate masses of objects

in appropriate units.


solve problems involving

mass.

Emphasise the

importance of

using standard

measurement.

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30

3. Understand the

concept of time inseconds, minutes,

hours, days, weeks,

months and years.

i. Determine the appropriate

measurement of time forcertain events.

ii. Convert measurement of

time in different units

(seconds, minutes, hours,

days, weeks, months and

years).

iii. Estimate the time intervalsof events.


solve

problems involving time.

Use calendars,clocks orstopwatches to

discuss the

measurement of

time for events.

Suggest a unit toestimate or

measure:i. The time it will take to

eat

lunch.

ii. Your age.

iii. How long it takes for

water to boil?

iv. How long it takes torun 100 metres?

1 millennium

= 1000 years1 century

= 100 years

1 year

= 12 months

= 52 weeks

= 365 days

1 week= 7 days

1 day

= 24 hours

1 hour

= 60 minutes

1 minute

= 60 seconds

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4. Understand and

use

times in the

twelvehourand twenty-four

hour system to solve

problems.

i. Read and write times in

twelve-hour system.

ii. Read and write times in

twenty-fourhour system.iii. Convert time in twelve-

hour system to

twenty-four hour system and

vice-versa.

iv. Determine the interval

between two given times.

v. Solve problems involvingtime.

Use digital andanalogue clocks.

Read times fromtrain or busschedules.

Relate events toeveryday

situations.

7.30 read as

seven thirty;

half past seven;

thirty minutespast seven and

thirty minutes

to eight.

Introduce a.m.

and p.m.

0350 read as

three fifty hour3.50 a.m. read

as three fifty

a.m. or three

fifty in the

morning.

1900 read as

nineteenhundred hours.

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32

1. Understand the

concept of angles.

i. Recognise angles.

ii. Denote and label angles.iii. Measure angles using

protractors.

iv. Draw angles using

protractors.

v. Recognise, compare and

classify angles as acute, right,

obtuse and reflex.vi. Draw acute, right, obtuse

and reflex angles using

protractors.

vii. Determine angles on

straight lines equal 180.

viii. Determine one whole

turn is 360.

Students identifyangles in theclassroom. (e.g.

corners of tables,

blackboards,

windows, clock

hands, and opened

doors).

Studentsdemonstrate the

different types of

angles with their

arms.

Guide students onhow to use

protractors tomeasure angles.

An angle is

formedby two straight

lines that meet

at a point called

the vertex.

Angles can be

named as BAC

or Aor BA C.

Use degre ( )

as the unit of

measurement of

angles.

One whole turn

is360.

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33

2. Understand the

concept of parallel

and

perpendicular lines.

i. Determine parallel lines.

ii. Determine perpendicular

lines.

iii. State that the anglesformed by perpendicular

lines is 90.

Students identifyperpendicular and

parallel lines in the

classroom (e.gedges of books,

windows and

doors).

Two lines are

parallel if they

never intersect.

Aperpendicular

line is a line

that

makes a 90

with

another line.

34

3. Understand and

use properties of

angles associated

with intersecting

lines to solveproblems.

i. Identify intersecting lines.

ii. Determine the properties

of vertical, complementary

and supplementary angles.

iii. Determine the value of an

angle on a line, given the

adjacent angle.iv. Solve problems involving

angles formed by intersecting

lines.

Studentsinvestigate the

properties of

angles formed by

intersecting lines.

Sum of adjacent

angles on a

straight line is

180

(a + b =180)

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35

1. Understand the

concept of polygons.

2. Understand the

concept of symmetry

i. Recognise polygons.

ii. Name polygons (triangle,quadrilateral, pentagon,

hexagon, heptagon and

octagon).

iii. Determine the number of

sides, vertices and diagonals

of given polygons.

iv. Sketch polygons.

i. Determine and draw the

line(s) of symmetry of shapes.

ii. Complete shapes given

part of the shapes and the

line of symmetry.

iii. Draw designs using theconcept of symmetry.

Use concretematerials such asprotractors, rulers,

grid papers, geo-

boards and

computer software

to explore the

concept of

polygons. Students explore

the relationship

between the sides,

diagonals and

vertices of

polygons.

Students exploresymmetry by using

mirrors, pattern

blocks, folding

Use capital

lettersTo name

vertices.

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papers or making

inkblot designs.

students explorethe importance ofsymmetry in

everyday situations

(e.g. pattern on

buildings and

tiles).

36

3. Identify and use

the

geometric properties

of triangles to solve

problems.

i. Determine and draw

symmetry line(s)

of given triangles.

ii. Draw triangles using

protractors and rulers.

iii. State the geometric

properties of the different

types of triangles and name

the triangles.

iv. Determine that the sum of

the angles of a triangle is

180.

Investigate therelationship

between angles

and sides of all

types of triangles.

Isosceles

triangle

Equilateral

triangle

Scalene

triangle

Acute triangle

Right-angled

triangle

Obtuse

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v. Solve problems involving

triangles.

Triangle

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37

4. Identify and use

the

geometric properties

ofquadrilaterals to

solve

problems.

i. Determine and draw

symmetry line(s)

of given quadrilaterals.ii. Draw a quadrilateral

using protractor and ruler.

iii. State the geometric

properties of the

different types of

quadrilaterals and

name quadrilaterals.iv. Determine that the sum of

the angles of a quadrilateral

is 360.

v. Solve problems involving

quadrilaterals.

Investigate therelationship

between angles,sides and diagonals

of all types of

quadrilateral.

Square Rectangle

Rhombus

Parallelogram

Trapezium

38 1. Understand the i. Identify the perimeter of a Use square chips, Shapes enclosed

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concept

of perimeter to solve

problems.

2. Understand the

concept

of area of rectangles

to

solve problems.

region.

ii. Find the perimeter of a

region enclosed by straight

lines.iii. Solve problems involving

perimeters.

i. Estimate the area of a

shape.

ii. Find the area of a

rectangle.iii. Solve problems involving

areas.

tessellation grids,

geo-boards, grid-

papers or

computer softwareto explore the

concept of

perimeter.

Investigate anddevelop formula to

find the perimeter

of a rectangle. Use unit squares,

tessellation grids,

geo-boards, grid-

papers or

computer software

to explore the

concept of area. Investigate and

develop formula to

find the area of a

by straight lines

and curves.

cm2 read as

square cm.

The area of a

unit square is 1

square unit

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39

rectangle.

Use unit squarechips or tiles to

investigate, exploreand make

generalisations

about the:

a. Perimeters of

rectangles having the

same area.

b. Areas of rectangleshaving the same

perimeter.

39 3. Understand the i. Identify the heights and Solve problems

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concept of area of

triangles,

parallelograms and

trapezium to solveproblems.

bases of triangles,

parallelograms and

trapeziums.

ii. Find the areas of triangles,parallelograms and

trapeziums.

iii. Find the areas of figures

made up of triangles,

rectangles, parallelograms

or trapeziums.

iv. Solve problems involvingthe areas of triangles,

rectangles, parallelograms

and trapeziums.

such as finding the

height or base of a

parallelogram.

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40

1. Understand

geometricproperties of cubes

and cuboids.

i. Identify geometric solids.

ii. State the geometric

properties ofcubes and cuboids.

iii. Draw cubes and cuboids

on:

a. Square grids.

b. Blank papers.

iv. Make models of cubes and

cuboids by:a. Combining given faces.

b. Folding given layouts of

solids.

Use concretematerials to

demonstrate theconcepts geometric

solids.

Game: Searchingout Solids. Make

up sets of activity

cards containing

descriptions ofsolids such as:

a. Exactly two faces that

are the same shape and

size.

b. All edges have the

same length.

Use concretematerials (opened

boxes) to draw the

layout of cubes

Geometric

solids

includeCubes

Cuboids

Cylinders

Pyramids

Cones

Spheres

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and cuboids.

SHAPES

AND

SPACE

2. Understand the

concept of volume

of

cuboids to solve

problems

i. Estimate the volume of

cuboids.

ii. Find the volume ofcuboids.

Use unit cubes orother concrete

materials to letstudents explore

the concept of

volumes.

cm3 read as

cubic cm.

The volume of aunit cube is 1

cubic unit

41

2. Understand the

concept of volume

of

cuboids to solveproblems

iii. Solve problems involving

volume of cuboids.

Investigate anddevelop formula to

find the volume of

cuboids.

Prepared by : Checked by

___________________________ _______________

(

Mathematics Teacher Form 1 Head of Science andSMK Abaka Tawau Mathematics Department

SMK Abaka Tawau

rpt mat t1

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