year 4 math syllabus

8/14/2019 Year 4 Math Syllabus

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LEARNING OBJECTIVES

Pupils will be taught to

SUGGESTED TEACHIN G

AND LEARNING ACTIVITIES

LEARNING OUTCOMES

Pupils will be able to

POINTS TO NOTE VOCABUL ARY

Develop number senseinvolving numbers of up to100 000.

Use the calculator, abacusand/or ruler to explore variousaspects of numbers in thecontext of daily lifeexperiences.

(i) Name and write numbers upto 100 000.

Naming and writing numbers toinclude numbers in extendednotation, for example:

76 051 = 70000 + 6000 + 0 + 50+ 1

76 051 = 76 thousands + 5 tens+ 1 ones

76 051 = 7 ten thousands + 6thousands + 5 tens + 1ones

number

numerals

count

place value

value of the digits

partition

estimate

check

(ii) Determine the place value ofthe digits in any wholenumber up to 100 000.

Estimate quantities up to100 000.

compare

count in

hundreds

ten thousands

Compare numbers with the aidof a ruler to explain why aparticular number has a biggeror smaller value.

(iii) Compare value of numbersto 100 000.

The number line can be used tomodel number cardinality. Thelonger line represents a hghernumber and the shorter lineotherwise.

round off to thenearest

tens

hundreds

thousands

(iv) Round off numbers to thenearest tens, hundreds andthousands.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Add numbers to the total of100 000.

Pupils add any two to fournumbers using

number sentence(horizontal form)

47 325 + 895 =

vertical form

3 3 4 8 31 8 3 7 9

+ 2 8 3 5 1

Expose pupils to quick additionstrategies, such as, pairing often, doubling, estimation, etc.

Pupils practice mental addition

by using the abacus as anaddition model.

(i) Add any two to four numbersto 100 000.

Allow pupils to performestimation either before or afteraddition. Estimating answersbefore adding builds confidenceamong pupils, while estimatingafter adding provides a check onoperation performed.

An example of a quick additionstrategy, i.e. pairing of ten, is asfollows (refer to the additionexample in the SuggestedTeaching and Learning Activitiescolumn):

In the ones place value, add 9and 1 to make 10. Then 10 and 3make 13. Apply this pairs of ten

strategy where appropriate forthe rest of the operation.

number sentences

vertical form

without trading

trading

quick calculation

pairs of ten

double numbers

estimates

range

Pupils create stories from givenaddition number sentences.

Pose to pupils problems in allforms, i.e. numerical, simplesentences, tables and pictures.

(ii) Solve addition problems. The ability to solve additionproblems is to be developed byfirst providing story constructionexercises. Then, provideexercises to transform simplesentences to number sentences,for example:

How many is three added tofive?

= 3 + 5

After pupils are familiar with storyconstruction and transformationactivities, provide word problemsexercises.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Subtract numbers from anumber less than 100 000.

Pupils subtract one or twonumbers from a number usingnumber sentences in thevertical form.

Allow pupils to check answersby performing estimations.

Expose pupils to quick

subtraction strategies, such as,estimation, pairing of ten, counton and count back, etc.

Pupils practice mentalsubtraction by using the abacusas a subtraction model.

(i) Subtract one or two numbersfrom a bigger number lessthan 100 000.

Limit problems to the subtractionof a number from a biggernumber.

Include also subtractingsuccessively two numbers from abigger number.

Provide the experience of

performing subtraction by writingnumber sentences in thehorizontal and vertical form.

Emphasise subtraction as takeaway, difference or inverse ofaddition where appropriate.

Allow pupils to practice mentalcalculation.

number sentence

vertical form

without trading

with trading

quick calculation

pair of tens

count on

estimates

range

Pupils create stories from givensubtraction number sentences.

Pose to pupils problems in allforms, i.e. numerical, simplesentences, tables and pictures.

(ii) Solve subtraction problems. Approach problem solving usingPolyas four-step algorithm of

Understanding the problem

Devising a plan

Implementing the plan

Checking the solution

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Multiply any two numberswith the highest product of100 000.

Pupils multiply by writingnumber sentences in thevertical and horizontal form andmodel multiplication using thenumber line or other aids.

(i) Multiply three-digit numberswith

o 100,

o two-digit numbers.

Multiplication exercises shouldinclude:

without trading (withoutregrouping).

with trading (withregrouping).

times

multiply

multiplied by

multiple of

various

Expose pupils to variousstrategies in multiplication, suchas, multiples of a number,benchmarking of tens,hundreds, and so on.

Introduce to pupils someproperties of multiplication, forexample:

(ii) Multiply four-digit numberswith

o one-digit numbers,

o 10,


Limit products to less than100 000.

Provide regular exercise ofrecalling basic facts ofmultiplication, followed bymultiplication exercises in thevertical form of multiplicationnumber sentences.

commutativeassociative

estimates

commutative property,

90 x 8 = 8 x 90

associative property,

(96 +42) +16 = 96 + (42 + 16)

Pupils practice mentalmultiplication by using theabacus as the multiplicationmodel.

(iii) Multiply two-digit numbers

with 1 000.

Names of multiplication

properties need not beintroduced.

Examples of multiplicationstrategies:

4 385 18

= (4 385 20) (4 385 2)

lattice multiplication.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils create stories from agiven multiplication numbersentence, for example:

6500 x 6 = 39 000

A company printed 6500copies of magazines per week.In 6 weeks 39 000 copies were

printed.

Pose to pupils, problems in theform of tables, words andpictures.

(iv) Solve multiplicationproblems.

Approach problem solving usingPolyas four-step algorithm of


Devising a plan



Make sensible estimations tocheck products of multiplication.

times

multiply

multiplied by

multiple of

commutative

associative

estimates

lattice

multiplication

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Divide a number less than100 000 by a two-digitnumber.

Model division using thenumber line or other aids anddivide using the long divisionmethod.

(i) Divide four-digit numbers by


o 10, 100 and 1000,


Exercises should include:

Division without trading (withoutregrouping).

without remainder,

with remainder.

divide

dividend

quotient

divisor

remainder

Exposed pupils to various

strategies in division such as,divisibility of a number, divideby 10, 100 and 1000, etc.

Pupils practice mental divisionby using the abacus as adivision model.

(ii) Divide five-digit numbers by


o 10, 100 and 1000,


Division with trading (with

regrouping). without remainder,

with remainder.

Provide regular exercise ofrecalling basic facts of division,followed by the long divisionexercise.

factors

long division

Pupils create stories from given

division number sentences.Pose daily problems in the formof words, tables and pictorials.

(iii) Solve division problems. Approach problem solving using

Polyas four-step algorithm of Understanding the problem

Devising a plan



Make sensible estimations tocheck quotients.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Perform mixed operationinvolving addition andsubtraction.

Perform mixed operation in theform of number sentences(vertical and horizontal) andmodel the operation using thenumber line or other aids.

Pupils practice mentalcomputations by using the

abacus as a computationmodel.

(i) Perform mixed operationsinvolving addition andsubtraction with numbersless than

o 100,

o 1 000,

o 10 000.

For mixed operation numericalproblems involving addition andsubtraction calculate from left toright.

Examples of mixed operationnumerical problems

48 + 62 93 =

597 128 + 473 =

4825 3215 + 1600 =

Avoid problems such as

2 4 + 8 = ?

mixed operation

Pupils create stories from givenmixed operations number

sentences.Pose to pupils, daily problemsin the form of words, tables andpictorials.

(ii) Solve mixed operationproblems.


Understanding the problem Devising a plan



Make sensible estimations tocheck solutions.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Name and write properfractions with denominatorsup to 10.

Partition concrete objects ormanipulative materials intoequal parts and compare partsto the whole to introduce properfractions, for example:

Paper

Partition paper equally byfolding.

(i) Name and write properfractions with denominatorsup to 10.

Emphasise fraction as:

equal size portions of awhole,

equal shares of a whole set.

The shaded portion of the wholefigure is one part out of five. It is

written in the fraction form as51 .

We say it as one over five orone fifth.

proper fraction

numerator

denominator

equivalent

one over two

half

one half

two halves

quarter

portions

compare

Fraction chart/strips andCuisenaire rods

(ii) Compare the value of two

proper fractions with

o the same denominators,

o the numerator of 1 anddifferent denominatorsup to 10.

Relate fractions to quantities

such as volume, length andmass.

Compare the values of two

proper fractions with fractionstrips and Cuisenaire rods.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Express equivalent fractionsfor proper fractions.

Express equivalent fractionswith the aid of fraction charts orstrips, strings, number lines andgraphics using conventionaltechnology or ICT.

(i) Express and write equivalentfractions for proper fractions.

Two fractions of differentnumerator and denominator butwith the same value areequivalent fractions. Theexamples below illustrate theidea.

a)

2

1 4

2

b) 02

1 1

0 61

62

63

64

65

1

c)6

2

2

2

3

1=

The value of a fraction will notchange when both the numeratorand denominator are multiplied

or divided by the same number.

proper fraction

equivalent

fraction

number line

Use number lines, fraction chartor strips, suitable graphics andICT to express equivalentfractions in its simplest form.

(ii) Express equivalent fractionsto its simplest form.

A fraction in the simplest form isa fraction with its numerator anddenominator not divisible by anynumber except 1.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Add two proper fractionswith denominators up to 10.

Demonstrate addition of properfractions through paper foldingactivity or use fraction charts,diagrams and number lines.

(i) Add two proper fractions withthe same denominator up to10 to its simplest form

o with 1 as the numeratorfor both fractions,

o with differentnumerators.

Limit exercises so that the sumof the two proper fractions is lessthan or equal to 1, for example

a)3

1

3

1+

b)4

3

4

1+

simplest form

multiples

fraction chart

diagram

number line

solve problem

Pupils add two proper fractionsby converting one of thefractions or both to theirequivalent form.

(ii) Add two proper fractions withdifferent denominators up to10 to its simplest form



Examples of addition usingequivalent fractions are asfollows:-

8

3

8

21

8

2

8

1

4

1

8

1

4

1

8

1

2

2

=

=

+=

+=

+

+

Pupils create stories from givennumber sentences involvingfractions.

Pose to pupils, daily problems

in the form of words, tables andpictorials.

(iii) Solve problems involvingaddition of proper fractions.



Devising a plan



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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Subtract proper fractionswith denominators up to 10.

Demonstrate subtraction ofproper fractions through paperfolding activities or use charts,diagrams and number lines.

(i) Subtract two proper fractionswith the same denominatorup to 10 to its simplest form



Examples of subtraction ofproper fraction are as follows

a)5

2

5

13

5

1

5

3==

21

6

3

6

25

62

6

5

3

1

6

5

31

6

5

3

3

22

=

=

=

=

=

simplest form

multiply

fraction chart

diagram

number line

solve problem

(ii) Subtract two proper fractionswith different denominatorsup to 10 to its simplest form



b)

Pupils create stories from givennumber sentences involvingfractions.

Pose to pupils, daily problemsin the form of words, tables andpictorials.

(iii) Solve problems involvingsubtraction of properfractions.



Devising a plan



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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Understand decimalnumbers.

Teacher introduces the conceptof decimals using Dienesblocks, hundred squares, placevalue chart and number line.

Pupils find and presentquantities that use decimals indaily situations, example

capacity of milk, water, weightof sugar/flour/biscuits, oil, andmoney.

(i) Name and write decimalswith

o one decimal place,

o two decimal places.

Using decimals is another way ofrepresenting values less than 1.

Decimals are fractions of tenth,hundredth and so on.

Dienes block representing 0.3,three parts out of 10.

0.3 is read as three tenths butcommonly said nominally aszero point three.

7.81 is seven and eighty-onehundredth.

43.69 is forty-three and sixty-nine hundredth.

Hundre square r pr ting0.09, nine parts out of 100.

d s e esen

Types of decimals:

decimal fraction, e.g. 0.4

mixed decimals, e.g. 3.7

State zero before a decimalpoint where relevant.

decimals

place-value chart

tenth

hundredth

hundred squares

decimal point

decimal placedecimal fraction

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils write digits of givendecimal numbers in the placevalue chart.

(ii) Recognise the place value of

o tenths,

o hundredths,

o tenths and hundredths.

The place value chart showing0.3.

Tens Ones Tenths

3

mixed decimal

convert

tenths

hundredths

(iii) Convert fraction to decimalsof

o tenths,

o hundredths,

o tenths and hundredths,

and vice versa

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Add decimals up to twodecimal places.

Pupils perform addition ofdecimals through numbersentences and use numberlines to model addition of anytwo to four decimal numbers.

(i) Add any two to four decimalsof one decimal placeinvolving

o decimals only,

o whole numbers anddecimals,

o mixed decimals.

Note the place values after adecimal point.

vertical

mixed decimals

place value

decimal point

estimates

range

(ii) Add any two to four decimalsof two decimal placesinvolving

o decimals only,

o whole numbers anddecimals,

o mixed decimals.

Pupils create stories from givennumber sentences.


(iii) Solve problems involvingaddition of decimal numbers.



Devising a plan




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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils model subtraction ofdecimals using number linesand subtract decimal numbersthrough number sentences inthe vertical form.

(i) Subtract one to two decimalsfrom a decimal of onedecimal place involving

o decimals only,

o mixed decimals,

o whole numbers anddecimals (mixed

decimals).

Subtract decimals up to twodecimal places.


vertical

mixed decimals

place value

decimal point

estimates

range

(ii) Subtract one to two decimalsof one or two decimal places.



(iii) Solve problems involvingsubtraction of decimals.



Devising a plan

Implementing the plan Checking the solution


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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Multiply decimals up to twodecimal places with a wholenumber.

Pupils model multiplication ofdecimals using number linesand multiply decimal numbersusing number sentences in thevertical form.

(i) Multiply any decimal of onedecimal place with

o one-digit number,

o 10, 100 and 1000.

Provide pupils with exercises ofperforming multiplication ofdecimals by writing in the verticalform.


vertical form

decimal point

estimates

range

decimal place

(ii) Multiply any decimals of two

decimal places witho one-digit number,

o 10, 100 and 1000.



(iii) Solve problems involvingmultiplication of decimals.



Devising a plan



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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Divide decimals up to twodecimal places by a wholenumber.

Pupils model division ofdecimals using number linesand divide decimal numbers bythe long division method.

(i) Divide decimals of onedecimal place by

o one-digit number,

o 10.

Limit exercises with dividends ofup to two decimal places only,for example:

3 2 = 1.5

1.4 4 = 0.35

value

long division

divide

dividends

quotient

(ii) Divide decimals of two

decimal places by one-digitnumber.

division

remainderfactor

(iii) Divide decimals by a wholenumber with the dividendvalue of up to two decimalplaces.



(iv) Solve problems involvingdivision of decimals.


Understanding the problem Devising a plan




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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Understand and use thevocabulary related tomoney.

Show different combinations ofnotes and coins to represent agiven amount of money.

(i) Read and write the value ofmoney up to RM10 000.

RM

sen

note

2. Use and applyknowledge of money in reallife situation.

Perform basic operationsinvolving money by writingnumber sentences in thevertical and horizontal form.

(i) Add money up to RM10 000. Perform addition and subtractionof money by writing numbersentences in the vertical form.

coin

value

total

(ii) Subtract money from up toRM10 000.

Limit,

a) addition to the highest totalof RM10 000, and

b) subtraction within the rangeof RM10 000.

balance

amount

buy

sell

(iii) Multiply money to the highestproduct of RM10 000.

(iv) Divide money with dividendnot more than RM10 000.

Exclude division withremainders.

Pupils perform mixedoperations involving money bywriting number sentences in thevertical and horizontal.

(v) Perform mixed operationinvolving addition andsubtraction involving moneyup to RM10 000.

(vi) Round off money to thenearest ringgit.

Pupils create stories from given

number sentences.


(vii) Solve problems involving

money of up to RM10 000

Approach problem solving using

Polyas four-step algorithm of


Devising a plan




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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Understand, read and writetime in hours and minutes.

Teacher introduce how to readand write time in hours andminutes using analog clock anddigital clock.

(i) Read time in hours andminutes according to the 12-hours system.

The proper way of reading andwriting time.

Say, Nine oclock in themorning and write, 9:00 a.m..

ante meridiem

post meridiem

(ii) Write time in hours andminutes according to the 12-hours system.

Say, Nine fifteen in the eveningor, A quarter past nine in theevening, and write, 9:15 p.m..

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Construct a simpleschedule.

Pupils gather information toconstruct a simple schedule, forexample:

Time Activities

7:45 1:00 p.m school

1:00 2:00 p.m lunch

2:00 3:30 p.m extra class

3:30 4:30 p.m homework

5:00 6:30 p.m games/sport

6:30 8:00 p.m dinner

8:00 9:30 p.m watch tv

9:30 p.m go to bed

(i) Construct, read and extractinformation from a simpleschedule.

Ante meridiem (a.m.) refers tothe time 12:01 in the morning to11:59 in the morning.

Post meridiem (p.m.) refers tothe time 12:00 noon onwards till11:59 at night.

Provide experiences of

constructing time-tables involvingdaily activities of pupils.

schedule

activity

daily

construct

gather information

extract information

2. Read a calendar. Pupils explore the calendar tolook for names of the months ina year.

Pupils arrange in sequence, themonths of a year.

(i) Extract information from acalendar.

Emphasise to pupils that acalendar contains the followinginformation;

days in a given month,

weeks in a given month,

day in a given year,

holidays in a given month,

festivals in a month.

There are different types ofcalendars such as, the Roman,Hijrah, Lunar (Chinese) andAandu (Tamil) calendars.

leap year

January

February

March

April

May

June

July

August

September

October

(ii) Solve simple real lifeproblems involving readingthe calendar.

November

December

Holiday

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Add, subtract, multiply anddivide units of time.

Pupils add, subtract, multiplyand divide time and convertunits of time. Units of timeinvolve minutes, hours, months,years, and decades.

(i) Add time involvingconversion of units withanswers in compound unitsof :

o hours and minutes,

o years and months,

o decades and years.

Practice mental calculation.Show calculation throughnumber sentence in the verticalform.

Examples of addition andsubtraction activities:

30 minutes + 45 minutes

= 75 minutes

= 1 hour 15 minutes.

hour

minute

add

plus

total

sum

subtractminus

(ii) Subtract time involvingconversion of units withanswers in compound unitsof :


o years and months,


15 hours + 17 hours

= 32 hours

= 1 day 8 hours.

22 months 4 months

= 18 months

= 1 year 6 months. 27 years + 2 years

= 29 years

= 2 decades 9 years.

take away

difference

altogether

(iii) Multiply time involvingconversion of units withanswers in compound units

of :


o years and months,


Practice mental multiplicationand division.

Limit multiplicand and divisor to asingle digit and excluderemainders.

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(iv) Divide time involvingconversion of units withanswers in compound unitsfor time duration of :


o years and months,


Examples of multiplication anddivision activities:

20 minutes 4

= 80 mins

= 1 hr 20 mins

45

2255 years

45 yrs = 4 decades 5 yrs.

Pupils create stories about timefrom given number sentences


(v) Solve problems involvingbasic operations of time:


o years and months,




Devising a plan



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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Use and apply knowledgeof time to find the duration.

Pupils extract information fromschedules, such as class time-table, prayer schedule, busschedule, etc.

(i) Read and state the start andend of an event from aschedule.

Expose pupils to a variety ofschedules.

clock

analog

digital display

Pupils model time on a numberline to determine the duration ofan event, for example

1230 to 200 pm: lunchstart end

1230 100 200

(ii) Calculate the duration of anevent from a schedule in

o minutes,

o hours,o hours and minutes within

a day and twoconsecutive live days.

a.m.

p.m.

duration

schedule

event

program

start

end

1 hr 30 min

Duration for lunch is 1 hour 30

mins.

(iii) Calculate the start or the endof an event from a givenduration of time and read thestart or end of an event.

Period

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Measure lengths usingstandard units.

Pupils measure, read andrecord lengths of objects. Thefollowing tools are used tomeasure lengths:

(i) Read measurement of lengthusing units of milimetre.

Depth and height are examplesof length.

read

scale

measure

metre ruler,

small ruler,

measuring tape.

(ii) Write measurement of lengthto the nearest scales of tenthdivision for:

o centimetre,o metre.

Emphasise that measuringshould start from the 0 mark ofthe rule.

Remind pupils that the symbolsfor the units of length are:

m for metre,

cm for centimetre,

mm for milimetre.

measuring tape

divisions

length

width

height

depth

compare

measurement

(iii) Measure and record lengthsof objects using units of

o millimetre,o centimetre and

milimetre,

o metre and centimetre.

Measurements are made to thenearest metre, centimetre andmilimetre.

Include compound units.

record

compound

(iv) Estimate the lengths ofobjects in

o millimetre,

o metre and millimetre,

o centimetre andmillimetre.

Encourage pupils to check forreasonableness of estimations.

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LEARNING OBJECTIVES


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LEARNING OUTCOMES



Understand the relationshipbetween units of length.

Pupils construct tables ofrelationship between units oflength.

(i) State the relationshipbetween centimetre andmilimetre.

Emphasise these units of lengthrelationships:

1 m = 100 cm

1 cm = 10 mm

measurement

relationship

Pupils use conversion tables toconvert from one unit of lengthto another.

(ii) Convert units of length from:

o milimetres to centimetresand vice versa,

o compound units to asingle unit.

Examples of conversionexercises for units of length:

200 cm = 2 m

2 m = 200 cm

5 cm = 50 mm

50 mm = 5 cm

1 m 50 cm = 150 cm

= 1.5 m

5 m 30 cm = 530 cm

= 5.3 m

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Add and subtract length. Pupils demonstrate additionand subtraction of lengths usingnumber sentences in theconventional manner.

(i) Add units of length, involvingconversion of units in;

o millimetre,

o metre and centimetre,

o centimetre andmillimetre.

Give answers in mixed decimalsto 2 decimal places.

add

plus

total

subtract

minus

difference

(ii) Subtract units of length,involving conversion of unitsin;

o millimetre,

o metre and centimetre

o centimetre andmillimetre

altogetherconvert

mixed decimal

multiply

product

divide

divisor

2. Multiply and dividelength. Pupils demonstratemultiplication and division usingnumber sentences in theconventional manner.

(i)Multiply units of length,involving conversion of units,by;

o a one-digit number,

o 10, 100, 1000.

multiplicandestimate

estimation

(ii) Divide units of length,involving conversion of units,by;

o a one-digit number;

o 10, 100, 1000.

Limit division exercises toquotients without remainders.

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Pupils construct problems froma given number sentenceinvolving measurement oflength, for example,

How many 25 cm ribbons canyou cut from a strip of 2 metresin length?

= 2 metres 25 centimetres

(iii) Solve problems involvingbasic operations on length.

Apply the four step approachwhen solving problems.

Practice mental calculations andestimations when solvingproblems involving length.

Make sensible estimation tocheck answers.

25 cm

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SUGGESTED TEACHIN G


LEARNING OUTCOMES



Measure mass usingstandard units.

Pupils measure, read andrecord masses of objects inkilograms and grams usingweighing scale.

(i) Measure of masses using inunits of kilogram and gram.

Emphasise that measuringshould start from the 0 mark ofthe weighing scale.

read

weighing scale

divisions

(ii) Read measurement ofmasses to the nearest scalesdivision of kilograms andgrams.

weight

weigh

compare

record

(iii) Estimate the masses ofobjects using kilograms andgrams.

Encourage pupils to check foraccuracy of estimations.

Compound

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Understand the relationshipbetween units of mass.

Pupils construct tables ofrelationship between units ofmass.

Pupils use conversion tables toconvert from one unit of massto another.

(i) Convert units of mass from

o kilograms to grams,

o kilograms and grams tograms,

o kilograms and grams tokilograms.

Provide conversion exercises toemphasise the relationship

1 kg = 1000 g

Practice mental calculations andlimit answers to problems inmixed decimals up to twodecimal places, for example

3 kg 200 g = 3.2 kg, 1 kg 450 g = 1.45 kg.

measurement

relationship

decimal point

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Add and subtractinvolving units of mass.

Pupils write number sentencesin the horizontal or verticalform to represent calculationsinvolving mass, for example

3kg 450 g + 2 kg 310 g = ?

(i) Add mass involving units ofmass in;

o kilograms,

o grams,

o kilograms and grams.

Request answers to calculationinvolving mass in mixeddecimals to two decimal places.

convert

mixed decimals

total

subtract

minus

3 kg 450 g

+ 2 kg 310 g5 kg 760 g

5 kg 760 g = 5.76 kg

3 450 g 3.45 kg

+ 2 310 g + 2.31 kg

5 760 g 5.76 kg

(ii) Subtract mass involving unitsof mass in;

o kilograms,

o grams,

o kilograms and grams.

Have pupils to practice mentalcalculations and verify answersby calculating in the conventionalmanner.

altogether

sumdifference

heavy

total weight

weighs

2. Multiply and divide unitsof mass.

3 kg 450 g

x 3

9 kg 1350 g

10 kg 350 g

10 kg 350 g = 10.35 kg

(iii) Multiply mass involvingconversion of units, with


o 10, 100, 1000.

multiply

product

multiplicand

Pupils divide using the long

division technique.

(iv) Divide mass involving

conversion of units :

o one-digit number,

o 10, 100, 1000.

Limit division exercises involving

mass with quotients withoutremainders.

Make sensible estimations ofquotients before dividing.

divide

divisor

remainders

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils pose problems from agiven number sentenceinvolving mass, for example

= 2 kg 400 gram packets

How many 400 gram packetsof sugar can be made from 2 kgof sugar?

(v) Solve problems involvingbasic operations with mass.


Practice mental calculations andestimations when solvingproblems involving mass.


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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Measure and comparevolume of liquid usingstandard units.

Pupils measure, read andrecord volume of liquid in litresand mililitres using beakers,measuring cylinders, etc.

(i) Read measurement ofvolume of liquid in litres andmililitres.

Capacity is the amount ofsubtance a container can hold.

Emphasise that the correctreading for the measurement ofvolume of liquid using ameasuring cylinder is where thescale is in line with the bottom ofthe meniscus.

read

meniscus

record

capacity

measuring

cylinder

water levelbeaker

(ii) Write measurement ofvolume of liquid to thenearest scales of tenthdivision for

o litre,

o mililitre.

measuring jug

divisions

(iii) Measure and record thevolume of liquid in litres andmililitres.

Estimate volume of liquid byhalving or doubling techniques.

(iv) Estimate the volume of liquidin litres and mililitres.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Understand the relationshipbetween units of volume ofliquid.

Pupils construct tables ofrelationship between units ofvolume of liquid.

Pupils use conversion tables toconvert from one unit of volumeto another.

(i) Convert units of volume,from

o litres to mililitres,

o mililitres to litres,

o litres and mililitres tolitres,

o litres and mililitres to

milillitres.

Emphasise relationships.

1 = 1 000m

Practice mental calculations.

Emphasise answers in mixeddecimals up to two decimalplaces, for example

5.8 = 5 800 m

2 500 m = 2.5

3 520 m = 3.52

4 250 m = 4250 m

measurement

relationship

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Add and subtract units ofvolume.

Pupils write number sentencesin the horizontal or verticalform to represent calculationsinvolving volume of liquid, forexample:

3 450 m + 2 310 m = 5.76

(i) Add volume of liquidinvolving conversion of unitsin;

o litre,

o mililitre,

o litre and mililitre.

Give answers in mixed decimalsto 2 decimal places.

Practice mental calculations andverify answers by conventionalcalculation.

convert

mixed decimals

total

subtract

minus

altogether

3 450 m+ 2 310 m

5 760 m

5 760 m = 5.76

3 450 m 3.45 m

+ 2 310 m + 2.31 m

5 760 m

5.76 m

(ii) Subtract volume of liquidinvolving conversion of unitsin :

o litre,

o mililitre,

o litre and mililitre.

sum

2. Multiply and divide unitsof volume.

(i) Multiply volume of liquidinvolving conversion of unitsby :


o 10, 100, 1000.

multiply

product

divide

divisor

multiplicand

Pupils demonstrate division ofvolume of liquid in theconventional manner.

(ii) Divide volume of liquidinvolving conversion of unitsby:


o 10, 100, 1000.

Limit division without remainders.

Estimate volume of liquid from agiven situation.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils construct problems forconversion of units from a givenmeasurement of volume, forexample:

There are three empty glassesto be filled with milk, 1.5 litres intotal. How much milk can eachglass hold?

(iii) Solve problems involvingvolume of liquids.


Practice mental calculations andestimations when solvingproblems involving volume ofliquid.


1.5

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Understand the perimeterof a two-dimensional shape.

Pupils draw a square, arectangle and a triangle anddescribe the features of theshapes.

(i) Identify the sides of a:

o square,

o rectangle,

o triangle.

A square and a rectangle, eachhas four sides. A trianle hasthree sides.

length

breadth

perimeter

area

Pupils measure the perimeterof given shapes usingsuggested measuring tools, for

example, a thread or string anda ruler.

(ii) Measure and record theperimeter of a:

o square,

o rectangle,

o triangle.

Verify that the perimeter of theshapes: a square, a rectangle ora triangle is equal to the sum of

the length of its sides.

2. Understand the area of atwo-dimensional shape.

Pupils draw a square and arectangle and label the lengthsand breadths of the shapes.

(i) Identify the dimensions of a:

o square,

o rectangle.

Pupils build various shapeswith equal number of square

tiles.Pupil compare using a gridpaper, for example:

The area of square ABCD is 4square units. The area ofrectangle PQRS is 12 squareunits.

(ii) Compare with unit squaresthe size of a:

o rectangle,o square.

Use a small square tile as a unitsquare. The figures have

different shapes but they havethe same size.

The area of each figure is 6square units.

Verify that the area (the numberof unit squares) for a square orrectangle is the product of itsdimensions.

S R

A

CD

B

P Q

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils use rulers to measurethe dimensions of squares andrectangles.

(iii) Measure and record thedimensions of squares andrectangles.

Tabulate measurements ofdimensions and their product, forexample:

Shape Length

(cm)

Breadth

(cm)

L x B

(squarecm)

A 4 4 16

B 6 5 30

C 3 6 18

3. Find the area andperimeter two-dimensionalshapes.

Pupils calculate area using theformula:

Area = length x breadth

Area of rectangle

= 4 cm x 3 cm

= 12 cm2

(i) Calculate the perimeter ofsquares and rectangles.

(ii) Calculate the area ofsquares and rectangles.

The square centimetre andsquare metre are the units ofarea.

cm2

stands for squarecentimetre.

m2

stands for square metre.Limit shapes to squares andrectangles only.

square centimetre

(cm2

)

square metre (m2)

breadth

3 cm

length

4 cm

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pupils create stories aboutperimeters or areas from givennumber sentences


(iii) Solve problems involvingperimeter and area of two-dimensional shapes.


Practice mental calculations andestimations when solvingproblems involving perimeter andarea.


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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



1. Understand the volumefor cubes and cuboids.

Pupils draw three-dimensionalshapes of cubes and cuboidsfrom given measurements, forexample:

Pupils draw nets of cuboidsfrom a given set ofmeasurements and buildcuboids. Label the dimensions

of the cuboids constructed.

(i) Identify the dimensions ofcubes and cuboids.

Limit three-dimensional shapesto cubes and cuboids only.

The dimensions of cubes orcuboids are length, breadth andheight.

volume

cubic unit

formula

height

Explore volume of cuboidsusing units of small cubes.

Eight small cubes fit into onebig cube, so the volume of thebig cube is 8 cubic units.

(ii) Compare with a unit cube:

o cuboid

o cube

Use small cubes as unit cube.

State volume of a big cube in thetotal numbers of small unitcubes.

Verify that the volume of a cubeor cuboid is the product of itsdimensions.

3 cm

3 cm

3 cm

2 cm

5 cm7 cm

(iii) Measure and record thedimensions of cubes andcuboids.

Tabulate the measurements ofdimensions of cubes andcuboids and find their product.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



2. Find the volume forcubes and cuboids.

Pupils calculate volume usingthe formula:

Volume = length x breadth xheight

(i) Calculate the volume ofcubes and cuboids.

The standard unit for volume isthe cubic metre (m

3). A smaller

unit for volume is the cubiccentimetre (cm

3).

height

breadth

length

volume

Pupils create stories aboutvolume of cubes and cuboidsfrom given number sentences

breadth

height

length


(ii) Solve problems involvingvolume of cubes andcuboids.


Practice mental calculations and

estimations when solvingproblems involving volume ofcubes and cuboids.


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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Use pictographs to readand display data.

Teacher shows a pictographand pupils talk about thepictograph, for example:

Pocket Money Saved byPupils in a Week

(i) Describe a pictographfeaturing

o the picture used torepresent data,

o the title of the graph,

o what the axes represent,

o What one unit of picture

represent.

Allow pupils to create storiesfrom the pictographs shown tothem.

key

quantity

Teacher guides pupils toextract and interpret informationfrom pictographs by posingappropriate questions.

(ii) Extract and interpretinformation from pictographs. Involve counting activities toshow numbers or quantities,making comparison and findingthe total quantity.

Siti Lee Rani

Represents RM1.00

Teacher provides information intabular form, pupils transformthe information intopictographs.

(iii) Construct pictographs toillustrate given information.

Use these steps whenconstructing pictographs.

Determine what thehorizontal axis and verticalaxis represent.

Use one number or the samesymbol to represent one unitor more.

Write heading of thepictograph.

Ensure that a key is present.

Limit to 5 columns or rows.

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LEARNING OBJECTIVES


SUGGESTED TEACHIN G


LEARNING OUTCOMES



Pose to pupils, daily problemsin the form pictographs fromsources such as magazines,newspapers, etc.

(iv) Solve a given problem byorganising and interpretingnumerical data inpictographs.

Emphasise five aspects inhandling data:

specifying the problem;

planning the data to becollected and the analysis tobe carried out;

collecting the data in a

variety of ways, for examplethrough surveys or usingprepared sources of data;

processing and representingthe data;

interpreting and discussingthe results.

Many children collect information

and draw graphs without theunderstanding of the purpose.Provide children withopportunities to:

formulate and clarifyquestions,

interpret a range of graphsand charts, especially thosefrom secondary sources, e.g.

magazines, newspapers, etc;

interpret and analyse data inways that foster speculation

justify interpretations,analyses and conclusions.

Keep a balance across the fiveaspects of data handling.

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LEARNIN G OBJECTI VES SUGGESTED TEACHIN G LEARNIN G OUTCOMES POINTS TO NOTE

Pupils will be taught toAND LEARNING ACTIVITIES


VOCABULARY

Use bar graphs to read anddisplay data.

Teacher shows a bar graph andpupils talk about the bar graph,for example:

(i) Describe a bar graphfeaturing

o the title of the graph,

o what the axes represent,

Allow pupils to create storiesfrom the bar graphs shown tothem.

bar graph

axis

horizontal axisBars representing data aresometimes presentedhorizontally, hence is called thehorizontal bar graph.

Wait ing T ime at Cempaka Cl in ic vertical axis

Teacher guides pupils toextract and interpret informationfrom bar graphs by posingappropriate questions.

(ii) Extract and interpretinformation from bar graphs.

Involve counting activities toshow numbers or quantities,making comparison and findingthe total quantity.

Teacher provides information intabular form, pupils transformthe information into bar graphs.

(iii) Construct bar graphs toillustrate given information.

Use these steps whenconstructing bar graphs.

Determine what thehorizontal axis and verticalaxis represent.

Write title of the graph.

Limit to 5 columns or rows.

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LEARNIN G OBJECTI VES SUGGESTED TEACHIN G LEARNIN G OUTCOMES POINTS TO NOTE

Pupils will be taught toAND LEARNING ACTIVITIES


VOCABULARY

Pose to pupils, daily problemsin the form bar graphs fromsources such as magazines,newspapers, etc.

(iv) Solve a given problem byorganising and interpretingnumerical data in bar graphs.

Emphasise five aspects inhandling data:

specifying the problem;

planning the data to becollected and the analysis tobe carried out;

collecting the data in a

variety of ways, for examplethrough surveys or usingprepared sources of data;

processing and representingthe data;

interpreting and discussingthe results.

Keep a balance across the five

aspects of data handling.

45

year 4 math syllabus

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