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In chapter 1, we have seven sections which are:

All about numbers up to 100 000. The addition of numbers with totals up to 100 000. The subtraction of numbers with totals of less than 100 000. The multiplication of numbers with products up to 100 000. The division of numbers with dividend up to 100 000. The mixed operation with the basics process (addition, subtraction,

multiplication and division). The solving problem involving the basic process and the mixed operations.

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In this section, the students will learn all about numbers. The students will know howto write numbers in words and numerals. The students also know how to determinetheir place values. Moreover, the students can compare the values of the numbersand round-off the numbers to the nearest place values.

At the end of this chapter, you should be able to:

1. Identify numbers by writing in numerals or in words.

2. Determine of the place value of numbers that have five digits such as

ten thousands, thousands, hundreds, tens and ones.

3. Compare the values of numbers, larger or smaller between two 5-digits

numbers.

4. Round-off numbers to a certain place value by using the steps that are

given and by using the number line.

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Naming and writing skills of the numbers

The whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.

The whole numbers can be written either in words or in numerals.

Determination of place values

In a whole number, the entire number can be partitioned into digits. Each digithas their place values and digit values.

The place values of a number that has five digits:

For example:

So that, the number is 52 341.3

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Comparing the values of numbers.

You can compare two digits numbers by comparing the five digits in theirplace values. First, the comparison must start at the highest place value (tenthousands). If the digits are the same, then move to second highest place

value (thousands), and so on.

We have two methods that can be use to compare the two 5-digits numbers:

Rounding-off numbers

The rounding-off of a whole number is to get the nearest place value for thatnumber. There are two methods to round-off a whole numbers. One is byusing the number line by as shown below.

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We have two methods that can be use to compare the two 5-digits numbers:

Steps for rounding off of a whole number:

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In this section, the students will learn about the addition of numbers with totals up to100 000. The addition is a process to determine the total of two or more numbers.We can use words like total, sum, add or plus to show an addition.


1. Determine the value of numbers after doing the addition of numbers.

2. Know how to add numbers in vertical form with regrouping and verticalform without regrouping and also in horizontal form.

The addition can be expressed in two forms which are vertical or horizontal.The vertical form is divided into two types which are vertical with regroupingand vertical without regrouping. We can use the steps below to add the wholenumbers.

1. First, we align the numbers that we want to add in vertical form. All thedigits must be placed according to their place values.

For example :

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2. Then, add the numbers from the right side to the left side.

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In this section, the students will learn about the subtraction of numbers with totals ofless than 100 000. Subtraction is a process to determine the difference between twoor more numbers. We can use words such as subtract, minus or difference to showsthe subtraction.

Determine the value of numbers after the subtraction is done.

1. Determine the value of numbers after the subtraction is done.

2. Know how to subtract numbers in vertical form with regrouping and

vertical form without regrouping and also subtraction in the horizontal

form.

Subtraction is the inverse of the addition. Subtraction can be expressed in twoforms which are vertical or horizontal. In vertical form there are vertical withregrouping and vertical without regrouping. We can use the steps below tosubtract numbers.

1. First, we align the numbers involved in the subtraction in the vertical form.All the digits must be placed according to their place values.

2. Then, subtracted the numbers from the right side to the left side.

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For example :

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In this section, the students will learn about the multiplication of numbers with productup to 100 000. The multiplication is a process of repeating of the addition of two ormore numbers. Product is a result of the multiplication process. We can use wordslike multiply or times to show the multiplication.


1. Determine the value of numbers after the multiplication is done.2. Know how to multiply the digits starting from ones, tens, hundreds,

thousands and so on.

3. Know how to solve the multiplication problems.

The multiplication is a commutative operation, which means that the product isnot affected by changing the order of the numbers. For example: 4 x 2 = 2 x 4= 8.

We must add one, two or three zero after the number when we multiply

numbers with 10, 100 or 1 000.

For example:

578 x 10 =

We can use the steps below to multiply numbers.

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The product of any number when multiply by zero is zero. For any numberwhen multiply by one, the product is the original number.

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In this section, the students will learn about the division of numbers with dividend upto 100 000. Division is a process where numbers will be shared or grouped equally.The quotient is the result of the division process. While, the dividend is the numberthat will be divided with divisor to get the quotient.

For example :

If the division has a leftover, its called the remainder. This implies that the numbercannot be divided exactly.

At the end of this section, the students should be able to:

1. Determine the value of numbers after the division is done.

2. Know the meaning of dividend, divisor, quotient and remainder.

3. Know how to solve the division problems.

The division process is starts from the left to the right of the number. It isdifferent from the process of addition, subtraction and multiplication. Thedivision also is the inverse of the multiplication. We can check the answer of adivision by multiplying the quotient with the divisor.

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For example:

When a number with zero as the last digit is divided by 10, then the result isthe same number without the last zero digits. This rule is also applied tonumbers having two or more zero as the end digits when being divide by 100or 1 000 respectively.

For example:

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In this section, the students will learn about the mixed operation with the basicprocesses such as addition, subtraction, multiplication and division. The mixedoperation is a process which involved more than one operation.

At the end of this section, you should be able to:

1. Know how to solve the mixed operations and basic processes problems.2. Use the four steps that will be given. By using the steps, students will get the

correct answer.

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In this section, the students will learn on solving problems involving the basicprocesses and the mixed operations. The problems are involved with mixedoperations and the basic processes such as addition, subtraction, multiplication anddivision.


1. Know how to solve the mixed operations and basic processes problems.

2. Use the four steps that will be given. By using these steps, the students will

get the correct answer.

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We have some steps to solve the problem in our daily situations. The steps are:

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In chapter 2, we have four sections which are:

The Proper fractions. The Equivalent Fractions. The Addition of Fractions. The Subtraction of Fractions.

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In section 2.1, the students will learn all about the proper fractions. The students will

know how to write the proper fraction in words and numerals and compare the valueof two proper fractions.


Identify the proper fraction by name and writing and also know to draw thefigure with shaded part of figure to show the fraction of numbers.

Compare the values of the fraction whether larger or smaller. If the numerator

is same, the largest fraction is shows the value of denominator smaller. If thedenominator is same, the largest fraction is shows the value of numerator islarger and for vice versa.

A fraction is a part of a whole. The fraction will be presented by numbers. Forexample, the figure above shows the triangle. The shaded part of triangleshows that is out of the triangle. We can write as or one over two or onehalf of triangle. The table below shows the name of fraction. We can seeclearly about fractions and easy to determine the fractions of any part or any

numbers.

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There are two numbers in fraction. The top number in fraction callednumerator and the bottom number is called the denominator.

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In proper fraction, the numerator is smaller than the denominator.

For example:

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The comparison the values of two fractions

The values of two fractions are compared when the denominator of twofractions is same. The fraction with the larger values of numerator is thelargest fractions.

The values of two fractions also are compared when the numerator of twofractions is same. So, the fraction with the smaller values of denominator is

the largest fractions.

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In section 2.2, the students will learn about the equivalent fractions. The students willknow how to express and write equivalent fractions.


Identify the equivalent fractions and know how to express and write theequivalent fractions.

Know how to determine the equivalent fractions and express equivalent

fractions in the simplest form.

Compare the values of the two fractions

The equivalent fractions are the fractions which have the same value offractions and the same size. However, the equivalent fractions have a differentnumerator and denominator.

For example:

The shaded part in the figure above shows the same value and the same size.

The equivalent fractions also can show by using a number line.

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For example:

We also can get the equivalent fractions by using multiplication. The value of afraction will not change when both the numerator and denominator aremultiplied by the same number.

For example:

The equivalent fractions can give value in simplest form. A fration in thesimplest form is a fraction with its numerator and denominator not divisible byany number except 1. The numerator and denominator must be divide bysame number.

For example:

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In section 2.3, the students will learn all about the addition of fractions. The studentswill know how to add two proper fractions with different denominators up to 10 to its

simplest form and solve problems involving addition of proper fractions.


Know how to add two proper fractions with same denominator and differentdenominator.

Solve problem involving addition of proper fractions.

The addition of fractions is a process of adding two fractions. Students have toadd two proper fractions with the same denominator and with differentdenominators up to 10 its simplest form.

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The addition of fraction with same denominator.

The addition of fraction with different denominator.

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We have some steps in determination of addition of fractions with the differentdenominator. The steps are:

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Solve problems involving addition of proper fractions.

In order to solve the problems by using the additions of fractions, we need touse Polyas four steps algorithm. The steps are:

The total of fractions can be shows in its simplest form.

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In section 2.4, the student will learn subtraction of proper fractions with denominators

up to 10. The student will know how to determine the subtraction p of fractions withsame denominator and different denominator. The students also will learn to solveproblems involving subtraction of proper fractions.


Know how to determine the subtraction of fractions with same denominatorand different denominator.

Solve the problems involving subtraction of proper fractions. Scientific

The subtraction of fractions is a process of finding the differences between twofractions. We have two processes to subtract two proper fractions with thesame denominator and with different denominators up to 10 to its simplestform.

The subtraction of fraction with same denominator.We have some steps in determination of subtraction of fractions with the samedenominator. The steps are:

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The subtraction of fraction with different denominator.

We have some steps in determination of subtraction of fractions with thedifferent denominator. The steps are:

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The problems solving by using the subtraction of fractions.

Solve the problems involving subtraction of proper fractions. Polyas four stepalgorithms are:

The differences of fractions can be shows in its simplest form.

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At the end of this section, students should be able to:

1. Identify the decimal numbers by writing in words and numerals, and also know

to draw the figure with shaded part to show the fraction numbers.

2. Change the fraction to the decimal numbers and change the decimal numbers

to the fractions.

Decimals numbers are shown the fractions with the denominators such as 10, 100, and so on.

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Decimals numbers have a dot which mean as decimal point.

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The decimals point is the separation of whole number and fractions.

The mixed decimals involve the whole number and a fraction.

The determination of place values and digit values ofdecimal numbers

Every digit in decimal has its own of place values and digit values.

The number of decimal places is the number of digits after the decimal point.

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The conversion of fraction to decimal and vice versa

You can change the denominator of fraction like 10 or 100 to a decimal.

The decimal numbers can be changed to fractions.

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1. Know how to determine the addition of two or more decimals numbers.

We can express the decimals in form such as:

i. Figure

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ii. Mathematics sentence

iii. Vertical form

The digits in decimal numbers are aligning according to their place values. Add zeros as place holder for easier calculations. Start to add the digits from the right side to the left side.

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1. Know how to determine the subtraction of two or more decimal numbers.

The subtraction of decimal numbers is a process of determine the differencesof two or more decimals. We must align the digits vertically according to theirplace values and start to subtract the digits from the right side to the left side.The decimal point must in vertical line. You can add zeros as place holder foreasier calculations.

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1. Know how to determine the multiplication of two or more decimal numbers.

2. Know the quickest way to get answer if the decimals multiply with 10, 100 or 1

000.

The multiplication of decimals is the determination the product of themultiplicand and the multiplier. The multiplication of decimals involvingrepeated of whole number in addition of decimals.

We have some steps to multiply decimals:

We must start from the right to the left to multiply decimal numbers. We need to find the total number of decimal places of the multiplicand

because it can be as decimal places of the product. Then, we put the decimalpoint at the product according to the total number of decimal places.

We can move the decimal point 1, 2 or 3 places to the right side to multiply adecimal with 10, 100 or 1 000. This is the quickest way to get the answer.

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1. Know how to determine the division of two or more decimal numbers.

2. Know the quickest way to get answer if the decimals divide with 10.

The division of decimal numbers is the determination the quotient of the sum.The division of decimal numbers also mean as dividing the decimals withwhole numbers equally. We need to arrange the place of decimal point of thequotient exactly above the decimal point of the dividend and then do thedivision as usual.

We can move the decimal point 1 place to the left side respectively to divide adecimal with 10. This is the quick way to get answer.

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1. Solve the problems by using the addition, subtraction, multiplication and

division.

2. Know the addition is the inverse of subtraction and vice versa. The subtraction

is the inverse of division and vice versa.

In order to solve the problems by using the addition, subtraction, multiplicationand division of decimals, we have to follows the steps below for easydetermination. The steps are:

a) Understanding the problem that is given.

b) Create a strategy of solving the problems.

c) Work out the strategy.

d) Always check the results.

The problems are related with daily life such as lengths, volumes of liquids,masses and money.

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In Chapter 4, five sections are covered:

Money up to RM10, 000 Money in basic operations Money in mixed operations Rounding off money Solving problems on money

In section 4.1, students will learn all about money. Students will know how towrite the value of money in words and numerals up to RM10, 000.

In section 4.2, students will learn about basic operations using money Thebasic operations are addition, subtraction, multiplication and division.

In section 4.3, students will learn about money in mixed operations involvingthe addition and subtraction of money up to RM10 000.

In section 4.4, students will learn about the rounding off of the value of moneyto the nearest ringgit. This is for easier calculation.

In section 4.5, students will learn to solve problems involving the value ofmoney up to RM10 000.

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1. Identify the values of money by writing them in numerals or in words up toRM10 000.

Naming and writing skills on money up to RM10 000

The Malaysian currency uses ringgit (RM) in the note form and sen in coinsrespectively.

The values of money are the following:

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a) Notes: RM1, RM5, RM10, RM50 and RM100

b) Coins: 1 sen, 5 sen, 10 sen, 20 sen and 50 sen

We can write the value of money in numerals and in words.

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Questions:

Write the following values of money in words.

a) RM45.80

b) RM5 785.28

Questions:

Write the following values of money in numerals.

a) Thirty-five ringgit and ninety sen

b) Six hundred ninety-seven ringgit and seventy-five sen

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1. Know to use basic operations with money, for example, addition, subtraction,multiplication and division.

Addition of money up to RM10 000

The addition of money up to RM10 000 is conducted the same way as with theaddition of decimal numbers. The addition can be expressed in vertical form.We must separate the ringgit (RM) and sen values by using the decimal pointsin a vertical line. We can use the steps below to add money.

1. First, we line up the values of money in the vertical form. All the digits

must be placed according to their place values.

2. Then, the values must be added from the right side to the left side.

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Questions:

What is the total of each of the following:

a) RM9 589 + RM635.50 = ?

b) RM1 145 + RM5.35 = ?

Subtraction of money up to RM10 000

The subtraction of money up to RM10 000 is conducted in the same way asthe subtraction of decimal numbers. Subtraction is also the inverse of addition.Subtraction can be expressed in the vertical form. We can use the steps belowto subtract numbers.

1. 1. First, we line up the values of money involved in the subtraction in the verticalform. All the digits must be placed according to their place values. The values of

the ringgit and sen will be separated by using decimal points.

2. Then subtract the values from the right side to the left side.

3. Always subtract the larger amounts before the smaller amounts.

. 4. Solve the first two values before proceeding to other values of the money.

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Multiplying money up to RM10 000

Multiplying values of money up to RM10 000 is the same as multiplying withdecimal numbers. The product is bigger than the factors.

We can use the steps below to divide the values of money:

1. We can use the steps below to multiply numbers.

2. Arrange the value of money in the vertical form. All the values must be

placed according to their place values and ringgit and sen are

separated by decimal points.

3. Then start multiplying numbers from the right side to the left side.

4. For ease of calculation, the values with more digits are placed above

when we multiply the values of money.

In multiplication, when any value of money is multiplied with zero, the productis zero. For any value of money multiplied with one, the product will remain thesame value.

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Questions:

Determine the product:

a) RM5 712 x 4

b) RM800 x 25

Division of money less than RM10 000

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The division of money of not more than RM10 000 is the same as the divisionof decimal numbers. The division of money is a process where numbers willbe shared or grouped equally. The quotient is the result of the divisionprocess. The dividend is the number that will be divided with the divisor to getthe quotient.

We can use the steps below to divide the values of money:

1. Arrange the values of money according to their place values and ringgit and sen

are separated by the decimal point at the quotient.

2. Then start the division of money from the left side to the right side.

Questions:

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a) RM9 528 6

b) RM2 127.75 5

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1. Know to use the mixed operation with the value of money involving additionsand subtractions of money up to RM10 000.

The mixed operations of money, therefore, involve the addition andsubtraction of money. We can perform the mixed operations from the left sideto the right side.

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Questions:

Solve the following:

a) RM5 689.55 + RM305.60 RM45 = ?

b) RM569.25 RM35.55 + RM1 565.55 = ?

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1. Know how to round off the values of money for easier calculation.

In our daily life, the estimation or rounding off of the values of money is veryimportant. This is for easier and quick calculation.

We can use some steps to round off the value of money in ringgit and sen tothe nearest ringgit:

1. 1. First, look at the value of the sen.

2. If the value is equal or more than 50 sen, you must add 1 to the ringgit value and

ignore the value after the decimal point.

3. If the value in the sen is less than 50 sen, you just retain the value of the ringgit

and ignore the value after the decimal point.

A number line can also be used to round off the values of money to thenearest ringgit.

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Questions:

Round off the following values of money to the nearest ringgit.

a) RM8 976.35

b) RM235.60

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1. Know how to solve problems involving mixed and basic operations.

2. Use the four steps that are given. By using these steps, students will succeed ingetting correct answers.

We have some steps to solve any problem involving money in our dailysituations.

The steps are:

1. First, we must understand the problem.

2. Then, create a strategy for the problem.

3. Work out the strategy.

4. Lastly, check the result of the strategy.

Questions:

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Mrs. Tan has bought a sofa set for RM3 285 and a set of furniture for RM4500. How much money has Mrs. Tan spent on both sets?

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In this chapter, we have five sections:

All about time.

Time schedules and calendars. Relationships between Units of time. Basic operations with time. The duration of time.

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In section 5.1, the students will learn all about time. The students will know how towrite the value of time in words and numerals.


Identify the value of time by writing in numerals or in words. Tell the time in minutes and hours.

Naming and writing skills of time

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The time is a particular period of a day. Time is express in 12-hours system. Ina day, time is divided into two phases:

a) Phase 1 = between 12 midnight until 12 noonb) Phase 2 = between 12 noon until 12 midnight

We can state the time in a day according to 12-hours system such as:

a) Morningd) Eveningb) Noone) Nightc) Afternoonf) Midnight

We have two types for abbreviation :

We also have two types of clocks:

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In section 5.2, the students will learn about the time schedules and calendars.


Plan and manage activities by using a simple time schedules. Know about year, months, weeks and days.

Time schedules

A time schedule is time planned for certain activities. It is in table form. Wecan put a lot of information in table as a simple schedule.

We have examples of simple schedules such as personal schedules, schoolschedules, bus schedules and etc.

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Zianas Weekend Schedule

From the table, we can obtain some information:

Ziana does her homework from 9.30 a.m. in the morning till 12.30 p.m. in theafternoon.

Ziana take a rest from 1.30 p.m. until 3.30 p.m. in the afternoon. Ziana goes to bed at 10.30 p.m.

Calendars

A calendar is a time schedule showing the dates and the numbers of days,weeks and months throughout a year.

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There are 7 days in a week.

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In section 5.3, the students will learn about units of time. We have units of time suchas second, minute, hour, day, week, month, year, and decade and so on.


Know all about units of time such as second, minute, hour, day, week, month,

year, and decade and so on. Convert the units of time.

The units of time are second, minute, hour, day, week, month, year, anddecade and so on. The relationships units of time are:

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In section 5.4, the students will learn about the basic operations of time. The basicoperations are addition, subtraction, multiplication and division.


Calculate the basic operations such as addition, subtraction, multiplication anddivision of time.

Convert the compound unit of time into single unit for easier calculations.

The basic operations are addition, subtraction, multiplication and division. Thebasic operations of time are the same with the basic operations with whole

numbers. We need to convert a compound of units of time into a single unit foreasier calculations.

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Addition of Time

Subtraction of Time

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Multiplication of Time

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Division of Time

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Duration of Time

Duration time is a period of time when we are given two times for an event. In

an event, it has a starting time and the ending time. So, duration time is aperiod between the starting and ending time.

The duration of time for an event, journey, activities and so on can determineby using the timeline.

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In chapter 6, we have four sections:

All about Length Relationships between Units of Length Basic operations with Length Solving Problems with Length

Section 6.1

The students will learn all about length. The students will know how to write

the value of length in words and numerals and also measure the lengths.

Section 6.2

The students will learn about units of length and the relationship between theunits. We have units of length such as millimeter (mm), centimeter (cm) andmeter (m).

Section 6.3

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The students will learn about the basic operations of lengths. The basicoperations are addition, subtraction, multiplication and division.

Section 6.4

The students will learn all about the problem solving of lengths. The studentswill know how to determine the problem solving of lengths involving addition,subtraction, multiplication and division.


1. Identify the value of length by writing in numerals or in words

2. Measure the unit of length such as millimeter (mm), centimeter (cm) and meter

(m).

Naming and writing skills of length

Length is a distance between two points in a line. The height and the depth

are the example of the length.

For example

Write the time for each following. The units of length are millimeter (mm),centimeter (cm) and meter (m). We measure the object starting from 0 markof the ruler.

For example :

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1. Know all about units of length millimeter (mm), centimeter (cm) and meter (m).

2. Convert the units of length.

The units of time are millimeter (mm), centimeter (cm) and meter (m).Therelationships units of length are:

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Conversion the units of length

We can convert units of length involving millimeter (mm), centimeter (cm) and

meter (m).

To convert a larger unit to a smaller unit, we must multiply (x).

For example :

To convert a smaller unit to a larger unit, we must divide ().

For example :

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1. Calculate the basic operations such as addition, subtraction, multiplication and

division of lengths.

2. Convert the compound unit of length into single unit for easier calculations.

The basic operations are addition, subtraction, multiplication and division. Thebasic operations of lengths are the same with the basic operations with wholenumbers. We need to convert a compound of units of lengths into a single unitfor easier calculations.

Addition of length

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Subtraction of time

Multiplication of time

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Division of time

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In order to solve the problems by using the addition, subtraction, multiplication anddivision of lengths, we have to follows the steps below for easy determination. The

steps are:


b). Create a strategy of solving the problems.


d). Always check the results.

In order to solve the problems by using the addition, subtraction, multiplicationand division of lengths, we have to follows the steps below for easy

determination. The steps are:


b). Create a strategy of solving the problems.


d). Always check the results.

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Measure the Mass Relationships between Units of Mass.

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Basic operations with Mass. Solving Problems with Mass.

In section 7.1, the students will learn the measurement of the mass. Thestudents will know how to read the value and also measure and estimate themasses.

In section 7.2, the students will learn about units of mass and the relationshipbetween the units. We have units of mass such as gram (g) and kilogram (kg).

In section 7.3, the students will learn about the basic operations of mass. Thebasic operations are addition, subtraction, multiplication and division.

In section 7.4, the students will learn all about the problem solving of mass.The students will know how to determine the problem solving of massinvolving addition, subtraction, multiplication and division.


1. Identify the value of mass.2. Measure the unit of mass such as kilogram (kg) and gram (g).

Measuring and estimating skills of mass

Mass is the amount of matter in an object. The mass of the object can bemeasured by used weighing scales.

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The standard units of mass are gram (g) and kilogram (kg). Usually, thesmall object has a small mass. The unit of mass, gram (g) will be use for

expressed the small object.

For the larger object, the unit of mass, kilogram (kg) will be use for expressedit. Always remember that, before measuring the object, the pointer of theweighing scale points at the 0.

We also can estimate the mass of an object by comparing an object withanother object of a known object. The weight of an object is similar with themass of an object.

Write the masses of the following.

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1. Know all about units of mass such as gram (g) and kilogram (kg).

2. Convert the units of mass.

The units of of mass such as gram (g) and kilogram (kg).The relationshipsunits of mass are:

Conversion the units of mass

We can convert units of length involving gram (g) and kilogram (kg).



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Convert each of the following.

a. 2 kg to g

b. 5.8 kg to g

c. 429 g to kg

d. 3 kg 380 g to g

e. 8 kg 255 g to kg

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Addition of mass

Calculate

2.78 kg + 8.11 kg = ________ kg

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Subtraction of mass

Determine

5.18 kg - 3.41 kg = ________ kg

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Multiplication of mass

Division of mass

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1. Solve the problems of mass by using the addition, subtraction, multiplication

and division.

2. Know the addition is the inverse of subtraction and vise versa. The subtraction

is the inverse of division and vise versa.

In order to solve the problems by using the addition, subtraction, multiplicationand division of mass, we have to follows the steps below for easydetermination. The steps are:


b) Create a strategy of solving the problems.


d) Always check the results.

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Hassan weighs 78.5 kg. Adam is 2.05 kg heavier than Hassan. Find the massof Adam, in kg.

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Measure the volume of liquid Relationships between The units of volume of liquid Basic operations with the volume of liquid Solving Problems with the volume of liquid

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In section 8.1, the students will learn the measurement of the volume of liquid.Students will know how to read the value and also measure and estimate the volumeof liquid.


1. Identify the value of volume of liquid.

2. Measure the units of the volume of liquid such as milliliter (m ) and liter( ).

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Measuring and estimating skills of the volumes ofliquid

Volume of liquid is the amount of liquid in a container of which it can hold.Thestandard units of volume of liquid are milliliter (m) and liter ().Usually, lowvolumes of liquid is measured in milliliter (m) and high volume of liquid ismeasured in liter (). The volume of liquid can be measured by using a beakeror a measuring cylinder.

The reading of the volume of a liquid should be taken from the bottom of the

meniscus which is in line with the scale.For example:

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In section 8.2, the students will learn about units of volumes for liquid and therelationship between the units. The units for the volume of liquid are milliliter(m) andliter().


1. Know all about units of volumes of liquid such as milliliter (m ) and liter ( ).2. Convert the units of volumes of liquid.

The units of volumes of liquid such as milliliter(m) and liter().Therelationships units of;

Converting the units of volume of liquid

We can convert units of volume of liquid from milliliter(m) to liter() and viceversa.


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For example:


For example:

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In section 8.3, students will learn the basic operations involving volumes of liquid.The basic operations are addition, subtraction, multiplication and division.


1. Calculate basic operations such as addition, subtraction, multiplication and divisionof volume of liquid.

2. Convert the compound units into a single unit for easier calculations.

The basic operations are addition, subtraction, multiplication and division. Thebasic operations of mass are the same with the basic operations with wholenumbers. We need to convert a compound of units of volume of liquid into asingle unit for easier calculations.

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Addition of volumes

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Subtraction of the volumes of liquid

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Multiplication of the volumes of liquid

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Division of the volumes of liquid

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In section 8.4, students will learn all about solving problems involving volumes ofliquid. Students will know how to solve the problems of the volumes of liquid

concerning addition, subtraction, multiplication and division methods.


1. Solve the problems of volume of liquid by using the addition, subtraction,multiplication and division methods.

2. Know the addition is the inverse of subtraction and vise versa. The subtraction is

the inverse of division and vice versa.

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In order to solve problems using the addition, subtraction, multiplication anddivision method, we have to follow the steps below. The steps are:

Understanding the problem that is given. Create a strategy of solving the problems.

Work out the strategy.

Always check the results.

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Chapter 9 comprises two sections:

Two-dimensional Shapes Three-dimensional Shapes

In section 9.1, students will learn how to measure and identify the shape and space.Students will be exposed on how to read and identify the shapes and also, how to

measure two-dimensional shapes.

n section 9.2, students will learn how to measure and identify shapes andspaces. Students will also know how to read and identify the shape and howto measure three-dimensional shapes.

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Identifying Two-dimensional Shapes

In two-dimensional shapes, there are three common shapes.

Square

Has four straight sides All the sides are in equal lengths. For example:

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Rectangle

Has four straight sides The opposite sides have the same lengths. For example:

Triangle

Has three straight sides Has alternate versions The three sides can be equal OR different in length. For example:

How many sides do the following shapes have?

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Identifying the Dimensions of a Square and aRectangle

The dimensions of a square and a rectangle are their length and breadth. In asquare, all four sides are equals, so, the length and the breadth are the same.

For example:

In a rectangle, the side nearer to us is the length and the other side is thebreadth.

For example:

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Measuring Perimeters of Two-dimensional Shapes

The perimeter of a two-dimensional shape is the total distance or the totallength around a closed shape.

The perimeter of a square, a rectangle and a triangle can be calculated byusing the formula.

Calculate the perimeters of the following shapes.

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Measuring Areas of Two-dimensional Shapes

Area of a shape is the amount of surface that it covers. We can find the areasof 2-dimensional shapes by counting the numbers of unit squares it covers ona grid paper. Unit2 is a square unit.

For example:

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We have another way to find the area of shape without counting the unitsquares. can be calculated by using the formula:

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Calculating the Area of a Square and a Rectangle

The standard units of area are square centimeter (cm2) and square meter (m2).

Solving Problems Related to Perimeters and Areas ofTwo-dimensional Shapes

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The diagram shows a stamp. Find the perimeter and the area of the stamp.

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a) To build a cube

b. To build a cuboid

Volume of Cubes and Cuboids

The volume of a three-dimensional shape is the amount of its space measured

in cubic units.

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The volume of a cube or a cuboid can be found by calculating the number ofunit cubes that are used in the space.

For example:

The cuboid is made of 1 layer of unit cubes.

The number of unit cubes in the upper layer= 4 x 4 = 16 unit cubes

The total number of cubes in 1 layer= 16 x 1 = 16 unit cubes

The cuboid is made of 16 small unit cubes. So, the volume of the cuboid

Find the volume of each cuboid.

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We can calculate the volume of a cube or a cuboid using the formula.

The standard units for volume are:

Calculate the volume of the cube and the cuboid.

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Solving Problems Related to Perimeters and Areas ofTwo-dimensional Shapes

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The diagram shows a biscuit tin. The tin is 10 cm long, 5 cm wide and 15 cmhigh. Find the volume of tin.

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Chapter 10 comprises two sections:

Section 10.1: Pictograph

Section 10.2: Bar graph

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The Horizontal Pictograph

The Vertical Pictograph

We can extract and interpret a lot of information from the horizontal or verticalpictograph.

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In this section, students will study the bar graph. Students will know how to read anddisplay data from the horizontal and vertical bar graph. The students also know how

to describe, extract and interpret the bar graph.


Read and display data from the horizontal and vertical bar graph. Describe, extract and interpret the bar graph. Construct the bar graph from the given data.

Describing, Extracting and Interpreting the Bar Graph

A bar graph is used to display data graphically. The width of each barrepresents a certain data in a bar graph. The width of the bar is equal to thesize and space equally in horizontal or vertical axis. There are two types of bargraphs.

a) Horizontal bar graphb) Vertical bar graph

In horizontal and vertical bar graphs, we must have three points to representthe bar graph.

a) Title: The title of the bar graph will tells us what the bar graph is about.b) Width: The width of the same size and space equally to represent the data.c) Interval: The interval is to show the number of items each width of barrepresents.

For example:

The bar graph shows the favourite juices of some year 4 pupils in class 4Kejora.

The Vertical Bar Graph

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The Horizontal Bar Graph

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We can extract and interpret a lot of information from the horizontal or verticalbar graph.

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Math 4 (2003)