MATEMATIK: 11/21/10

Matematik Tahun 5

RANCANGAN PENGAJARAN TAHUNAN MATEMATIK TAHUN 5 ( 2010 )

YEARLY SCHEME OF WORK YEAR 5 ( 2009 )

SEMESTER 1

WEEK

TOPIC

LEARNING AREA

LEARNING OBJECTIVES

Pupils will be taught to:

LEARNING OUTCOMES

Pupils will be able to :

SUGGESTED TEACHING AND LEARNING ACTIVITIES

1 – 2

1. WHOLE NUMBER

1. NUMBER TO

1 000 000

1. Develop number sense up to

1 000 000

(i) Name and write numbers up to

1000 000

(ii) Determine the place value of the digits in any whole number up to 1000 000

(iii) Compare value of numbers up to

1 000 000.

(iv) Round off numbers to the nearest tens, hundreds, thousands, ten thousands and hundred thousands

J Teacher pose number in numerals, pupils name the respective numbers and write the number word.

J Teacher says the number names and pupils show the number using the calculator of abacus, then pupils write the numerals.

J Provide suitable number line scales and ask pupils to mark the positions that represent a set of given numbers.

J Given a set of numerals, pupils represent each number using the number base block or the place value of every digit of the given number.

J Given a set of numerals, pupils compare and arrange the numbers in ascending then descending order.

3 - 4

1. WHOLE NUMBER

2. ADDITION WITH THE HIGHEST TOTAL OF

1 000 000

2. Add numbers to

the total of

1 000 000

(i) Add any two to four numbers to 1 000 000

J Pupils practice addition using the four-step algorithm of:

Estimate the Total
Arrange the numbers involved according to place values.
Perform the operation
Check the reasonableness of the answer.

J Pupils create stories from given addition number sentence.

J Teacher Pose problems verbally, i.e. in the numerical form or simple sentences.

J Teacher guides pupils to solve problems following Polya’s four step mode of:

Understand the problem
Devising a plan
Implementing the plan
Looking back.

5 - 6

1. WHOLE NUMBER

3. SUBTRACTION WITHIN THE RANGE OF

1 000 000

3.Subtract numbers from a numbers less than 1000 000

(i) Subtract one number from a bigger number less than

1 000 000

(ii) Subtract successively from a bigger number less than

1 000 000

(iii) Solve subtraction problems

J Pupils create stories from given subtraction number sentence.

J Pupils practice subtraction using the four-step algorithm of :

Estimate the sum.
Arrange the numbers involved according to place values.
Perform the operation.
Check the reasonableness of the answer.

J Pupils Subtract successively by writing the number sentence in the

a) horizontal form

b) vertical form

J Teacher pose problems verbally i.e.., in the numerical form or simple sentences.

J Teacher guides pupil to solve problems following Polya’s four-step model of :

Understand the problem
Devising a plan
Implementing the plan
Looking back

7 - 8

WHOLE NUMBER

4. MULTIPLICATION WITH THE HIGHEST PRODUCT OF

1 000 000

4.Multiply any to numbers with the highest product of 1 000 000

(i) Multiply up to five digit numbers with

a) a one-digit number

b) a two- digit number

c) 10, 100 and 1000.

(ii) Solve problems involving multiplication.

J Pupils create stories from given multiplication number sentences

e.g. 40 500 x 7 = 283 500

“A factory produces 40 500 batteries per day. 283 500 batteries are produced in 7 days”

J Pupils practice multiplication using the four-step algorithm of:

Estimate the product.
Arrange the numbers involved according to place values.
Perform the operation.
Check the reasonableness of the answer.

J Teacher pose problems verbally i.e., in the numerical form or simple sentence

J Teacher guides pupils to solve problems following Polya’s four-step model of :

Understanding the problem
Devising a plan
Implementing the plan
Looking back

( Apply some of the common strategies in very problem Solving step )

9,10

WHOLE NUMBERS

5. DIVISION WITH THE HIGHEST DIVIIDEND OF

1 000 000

5.Divide a number less than 1 000 000 by a two-digit number

(i) Divide numbers up to six digits by

a) one-digit number

b) 10, 100 and 1000

c) two-digit number

(ii) Solve problems involving division

J Pupils create stories from given division number sentences.

J Pupils practice division using the four-step algorithm of:

Estimate the product.
Arrange the numbers involved according to place values.
Perform the operation.
Check the reasonableness of the answer.

J Teacher pose problems verbally, i.e., in the numerical form or simple sentences.

J Teacher guides pupils to solve problems following Polya’s four-step model of :

Understanding the problem
Devising a plan
Implementing the plan
Looking back

( Apply some of the common strategies in very problem Solving step )

1. WHOLE NUMBER

6. MIXED OPERATIONS

6.Perform mixed operations involving multiplication and division

(i) Calculate mixed operation on whole numbers involving multiplication and division

(ii) Solve problems involving mixed operations of division and multiplication.

J Pupils create stories from given number sentence involving mixed operations of division and multiplication.

J Pupils practice calculation involving mixed operation using the four-step algorithm of :

Estimate the quotient
Arrange the numbers involved according to place values.
Perform the operation
Check the reasonableness of the answer.

J Teacher guides pupils to solve problems following Polya’s four-step model of :

Understanding the problem
Devising a plan
Implementing the plan
Looking back

( Apply some of the common strategies in very problem Solving step )

2. FRACTIONS

1. IMPROPER FRACTIONS

1. Understand improper fractions

(i) Name and write improper fractions with denominators up to 10

(ii) Compare the value of the two improper fractions.

J Demonstrate improper fractions using concrete objects such as paper cut-outs, fraction charts and number lines.

J Pupils perform activities such as paper folding or cutting, and marking value on number lines to represent improper fractions.

2. FRACTIONS

3. MIXED NUMBERS

1. Understand mixed numbers

(i) Name and write mixed numbers with denominators up to 10.

(ii) Convert improper fractions to mixed numbers and vice versa

J Teacher demonstrate mixed numbers by partitioning real objects or manipulative.

J Pupils perform activities such as

a) Paper folding and shading

b) Pouring liquids into containers.

c) marking number lines

14-15

2. FRACTIONS

3. ADDITION OF FRACTIONS

1. Add two mixed numbers

(i) Add two mixed numbers with the same denominators up to 10.

(ii) Add two mixed numbers with different denominators up to 10.

(iii) Solve problems involving addition of mixed numbers.

J Demonstrate addition of mixed numbers through

a) paper folding activities

b) fraction charts

c) diagrams

d) number lines

J Create stories from given number sentences involving mixed numbers.

15-16

2. FRACTIONS

4. SUBTRACTION OF FRACTIONS

1. Subtract mixed numbers

(i) Subtract two mixed numbers with the same denominator up to 10.

(ii) Subtract two mixed numbers with different denominators up to 10.

(iii) Solve problems involving subtraction of mixed numbers.

J Demonstrate subtraction of mixed numbers through

a) paper folding activities

b) fraction charts

c) diagrams

d) number lines

e) Multiplication table.

J Pupils create stories from given numbers sentences involving mixed numbers.

2. FRACTIONS

5. MULTI-PLICATION OF FRACTIONS

1. Multiply any proper tractions with a whole number up to

1 000

(i) Multiply whole numbers with proper tractions

(ii) Solve problems involving multiplication of fractions

J Use groups of concrete materials, picture and number lines to demonstrate fraction as equal share of a whole set.

J Provide activities of comparing equal portions of two groups objects.

e.g.

1 x 6 = 6 = 3

2 2

6 x 1/2 or six halves.

6 x 1 =

1/2 of an orange is ……

^{1/3+1/3+1/3+1/3+1/3+1/3 = 3}oranges.

J Create stories from given number sentences

DECIMALS

1. DECIMAL NUMBER

1. Understand and use the vocabulary related to decimals

(i) Name and write decimal numbers to three decimal places

(ii) Recognized the place value of thousandths

(iii) Convert fractions of thousandths to decimal numbers and vice versa.

(iv) Round off decimal numbers to the nearest

a) tenths

b) hundredths

J Teacher models the concept of decimal number using number lines.

e.g.

8 parts out of 1 000 equals 0.008

23 parts out of 1 000 is equal to 0.023

100 parts out of 1 000 is 0.100

J Compare decimal numbers using thousand square and number line

J Pupils find examples that use decimals in daily situation

3.DECIMALS

2. ADDITION OF DECIMAL NUMBERS

1. Add decimal number up to three decimal places

(i) Add any two to four decimal numbers up to three decimal places involving

a) decimal numbers and decimal numbers

b) Whole numbers and decimal numbers

(ii) Solve problems involving addition of

decimal numbers.

J Pupils practice adding decimals using the four- step algorithm of :

Estimate the total
Arrange the numbers involved according to place values
Perform the operation
Check the reasonableness of the answer.

J Pupils create stories from given number sentences.

20-21

PKSR SEMESTER 1

Semester 2

WEEK

TOPIC

LEARNING AREA

LEARNING OBJECTIVES

Pupils will be taught to:

LEARNING OUTCOMES

Pupils will be able to :

SUGGESTED TEACHING AND LEARNING ACTIVITIES

3. DECIMALS

4. SUBTRACTION OF DECIMAL NUMBERS

1. Subtract Decimal Numbers up to three decimal places

(i) SSubtract a decimal number from another decimal up to three decimal places.

(ii) Subtract successively any two decimal numbers up to three decimal places

(iii) Solve problems involving subtraction of decimal numbers

J Pupils subtract decimal numbers, given the number sentence in the horizontal and vertical from.

J Pupils practice subtracting decimals using the four-step algorithm of :

Estimate the total
Arrange the numbers involved according to place values
Perform the operation
Check the reasonableness of the answer.

J Pupils make stories from given number sentences.

3. DECIMALS

4. MULTIPLICATION OF DECIMAL NUMBERS

(i) Multiply decimal numbers up to three decimal places with a whole number

(i) Multiply any decimal numbers up to three decimal places with

a) a one-digit number

b) a two-digit number

c) 10, 100 and 1000.

(ii) Solve problems involving multiplication of decimal numbers.

J Multiply decimal numbers with a number using horizontal and vertical from.

J Pupils practice adding decimals using the four- step algorithm of :

Estimate the total
Arrange the numbers involved according to place values
Perform the operation
Check the reasonableness of the answer.

J Pupils create stories from given number sentences.

3 .DECIMALS

5. DIVISION OF DECIMAL NUMBERS

1. Divide decimal numbers up to three decimal places by a whole number.

(i) Divide a whole number by

a) 10

b) 100

c) 1000

(ii) Divide a whole number by

a) a one-digit number

b) a two-digit whole number.

(iii) Divide a decimal number of three decimal places by

a) a one-digit number

b) a two-digit whole number

c) 10

d) 100

(iv) Solve problem involving division of decimal numbers

J Pupils practice adding decimals using the four- step algorithm of :

Estimate the total
Arrange the numbers involved according to place values
Perform the operation
Check the reasonableness of the answer.

J Pupils create stories from given number sentences.

4.PERCENTAGE

1. PERCENTENGE

1. Understand and use percentage

(i) Name and write the symbol for percentage

(ii) State fraction of hundredths in percentage

(iii) Convert fraction of hundredths to percentage and vice versa.

J Pupils represent percentage with hundred squares.

J Shade parts of the hundred square

J Name and write the fraction of the shaded parts to the shaded parts to percentage.

4. PERCENTAGE

2. CONVERT FRACTION AND DECIMALS TO PERCENTAGE

1. Relate fraction and decimals to percentage

(i) Convert proper fractions of tenths to percentage.

(ii) Convert proper fractions with the denominators of 2, 4, 5, 20, 25 and 50 to percentage.

(iii) Convert percentage to fraction in its simplest from.

(iv) Convert percentage to decimal number and vice versa

J Identity the proper fractions with the denominators given.

MONEY

1. MONEY TO

RM 1 00 000

1. Understand and use vocabulary related to money

(i) Read and write the value of money in ringgit and sen up to RM 100 000.

J Pupils show different combination of notes and coins to represent a given amount of money.

5. MONEY

1. MONEY TO

RM 1 00 000

1. Use and apply mathematics concepts when dealing with money up to RM 100 000.

(i) Add money in ringgit and sen up to RM 100 000.

(ii) Subtract money in ringgit and sen within the range of RM 100 000.

(iii) Multiply money in ringgit and sen with a whole number, fraction or decimal RM 100 000.

(iv) Divide money in ringgit and sen with the divisor up to RM 100 000.

(v) Perform mixed operation of multiplication and vision involving money in ringgit and sen up to RM 100 000.

(vi) Solve problems in real context involving money in ringgit and sen up to RM 100 000.

J Pupils perform basic and mixed operation involving money by writing numbers sentences in the horizontal and vertical form.

J Pupils create stories from given number sentences involving money in real context, for example,

a) Profit and loss in trade

b) Banking transaction

c) Accounting

d) Budgeting and finance management

J Pupils solve problems following Polya’s four-step algorithm and using some of the common problem solving strategies.

TIME

1. READING AND WRITING TIME

1. Understand the vocabulary related time

(i) Read and write time in the 24-hour system.

(ii) Relate the time in the 24-hour system to the 12-hour system

(iii) Convert time from the 24-hour system to the 12-hour system and vice-versa

J Pupils tell the time from the digital clock display.

J Design an analogue clock face showing time in the 24-hour system

J Pupils convert time by using

the clock face

23 13

22 14

21 15

20 16

19 17

6. TIME

2. BASIC OPERATIONS INVOLVING TIME

2.Understand the relationship between units of time

(i) Convert time in fractions and decimals of a minute to seconds

(i) Convert time in fractions and decimals of an hour to minutes and to seconds.

(ii) Convert time in fractions and decimals of a day to seconds.

(iii) Convert units of time from

a. Century to years and vice versa.

b. Century to decades and vice versa.

J Pupils convert from one unit of time.

J Pupils explore the relationship between centuries, decades and years by constructing a time conversion table.

6. TIME

3. DURATION

3.Add, subtract, multiply and divide units of time.

(i) Add time in hours, minutes and seconds.

(ii) Subtract time in hours, minutes and seconds.

(iii) Multiply time in hours, minutes and seconds.

(iv) Divide time in hours minutes and seconds.

J Pupils add, subtract, multiply and divide units of time by writing numbers sentences in the horizontal and vertical from.

e.g.

5 hr 20 min 30 s

+ 2 hr 25 min 43 s

4 hr 45 min 12 s

- 2 hr 30 min 52 s

2 hr 15 min 9 s

X 7

6.TIME

3. DURATION

4.Use and apply knowledge of time to find the duration.

(i) Identify the start and end times of are event.

(ii) Calculate the duration of an event, involving

a. Hours, minutes and seconds.

b. Days and hours

(iii) Determine the start or end time of an event from a given duration of time.

(iv) Solve problems involving time duration in fractions and/or decimals of hours, minutes and seconds.

J Pupils read and state information from schedules such as :

a) class time-table

b) fixtures in a tournament

c) Public transport, etc

J Pupils find the duration the start and end time from a given situation

7.LENGTH

1. MEASURING LENGTH

1. Measure and compare distances.

(i) Describe by comparison the distance of one kilometer.

(ii) Measure using scales for distance between places.

J Teacher provides experiences to introduce the idea of a kilometer.

e.g.

Walk a hundred-meter track and explain to pupils that kilometer is ten times the distance.

J Use a simple a simple map to measure the distances to one place to another.

e.g.

a) school

b) village

c) town

7.LENGTH

2.RELATIONSHIP BETWEEN UNITS OF LENGTH

2.Understand the relation between units of length

(i) Relate meter and kilometer

(ii) Convert meter to kilometer and vice versa

J Compare the length of a meter string and a 100-cm stick, then write the relationship between the units. Pupils then visualize how far the length would be if 1000 such sticks were to be arrange end to end.

J Pupils use the conversion table for units of length to convert length from km to m and vice versa.

7.LENGTH

3. BASIC OPERATION INVOLVING LENGTH

3.Add, subtract, multiply and divide units of length

(i) Add and subtract units of length involving conversion of units in

a) kilometers.

b) kilometers and meters.

(ii) kilometer and divide units of length in kilometers involving conversion of units with.

a) a one-digit number.

b) 10, 100, 1000

(iii) Solve problems involving basic operations on length.

J Pupils demonstrate addition and subtraction involving units of length using number sentences in the usual conventional manner.

e.g.

a) 2 km + 465 = _______ m

b) 3.5 km + 615 = ________ km

c) 12. 5 km – 625 m = _______ m

J Pupils multiply and divide involving units of length.

e.g.

a) 7. 215 m x 1 000 = _______ km

b) 2. 24 km 3 = ________ m

Create stories from given number sentence.

8.MASS

1. COMPARING MASS

1. Compare mass of objects.

(i) Measure and record masses of objects in kilogram and grams.

(ii) Compare the masses of two objects using kilogram and gram, stating the comparison in multiples or fractions.

(iii) Estimate the masses of objects in kilograms and grams.

J Pupils measure, read and record masses of objects in kilograms and using the weighing scale and determine how many times the mass of an objects as compared to another.

2.Understand the relationship between units of mass.

(i) Convert units of mass from fractions and decimals of a kilogram to grams and vice versa.

(ii) Solve problems involving conversion of mass units in fraction and / or decimals.

J Pupils make stories for a given measurement of mass.

e.g.

Aminah bought 4 kg of cabbages and 500 g celery. Altogether, she bought a total of 4.5 kg vegetables.

9.VOLUME OF LIQUID

1. COMPARING VOLUME

1. Measure and compare volumes of liquid using standard units

(i) Measure and record the volumes of liquid in a smaller metric in fractions and / or decimals of a larger unit.

(ii) Estimate the volumes of liquid involving fractions and decimals in liters and milliliters.

(iii) Compare the volumes of liquid involving fractions and decimals using liters and milliliters.

J Pupils measure, read and record volume of liquid in liter and milliliters using beaker measuring cylinder, etc.

J Pupils measure and compare volume of liquid stating the comparison in multiples or factors.

9. VOLUME OF LIQUID

2.RELATIONSHIP BETWEEN UNITS OF VOLUME

1. Understand the relationship between units of volume of liquid

(i) Convert units of volumes involving fraction and decimals in liter and vice-versa.

(ii) Solve problem involving volume of liquid

J Engage pupils in activities that will create an awareness of relationship.

J Pupils make stories from a given number sentence involving volume of liquid.

9.VOLUME OF LIQUID

3.OPERATIONS ON VOLUME OF LIQUID

1. Add and subtract units of volume

(i) Add units of volume involving mixed decimals in

a) liters

b) milliliters

c) liters and milliliters

(ii) Subtract units of volume involving mixed decimals in

a) liters

b) milliliters

c) liters and milliliters

J Pupils carry out addition up to 3 numbers involving mixed d

9.VOLUME OF LIQUID

1. Multiply and divide units of volume

(i) Multiply units of volume involving mixed number using :

(ii) Divide units of volume using

a) up to 2 digit number,

b) 10, 100, 1000 involving mixed decimals.

(iii) Divide unit of volume using.

a) a one-digit number.

b) 10, 100, 1000.

Involving conversion of units.

(iv) Solve problems involving computations for volumes of liquids.

J Pupils demonstrate division for units of volume in the conventional manner.

J Pupils construct stories about volume of liquids from given number sentences.

10.SHAPE AND SPACE

1. COMPOSITE TWO DIMENSIONAL SHAPES

1. Find the perimeter of composite 2-D shapes.

(i) Measure the perimeter of the following composite 2-D shapes

a) square and square

b) rectangle and rectangle

c) triangle and triangle

d) square and triangle

e) square and triangle

f) rectangle and triangle

(ii) Calculate the perimeter of the following composite 2-D shapes a) square and square.

a) rectangle and rectangle.

b) triangle and triangle

c) square and rectangle

d) square and triangle

e) rectangle and triangle.

(iii) Solve problems involving perimeters of composite 2-D shapes.

J Use measuring tapes, rules or string to measure the perimeter of event composite shapes

10.SHAPE AND SPACE

2.COMPOSITE THREE DEMENSIONAL SHAPES

1. Find the area of composite 2-D shapes

(i) Measure the area of the following composite 2-D shapes

a) square and square

b) rectangle and rectangle

c) square and rectangle

(ii) Calculate the area of the following composite 2-D shapes square and square.

a) rectangle and rectangle

b) square and rectangle

(iii) Solve problems involving areas of composite 2-D shapes.

J Pupils count the unit squares to find the area of composite 2-D shapes on the grid paper.

10.SHAPE AND SPACE

1. Find the volume of composite 3-D shapes

(i) Measure the volume of the following composite 3-D shapes

a) cube and cube

b) cuboid and cuboid

c) cube and cuboid

(ii) Calculate the volume of the composite 3-D shapes following

a) cube and cube

b) cuboid and cuboid

c) cube and cuboid

(iii) Solve problems involving volume of composite 3-D shapes

J Use any combination of 3-D shapes to find the surface area and volume.

11.DATA HANDLING

1. AVERAGE

1. Understand and use the vocabulary to average

(i) Describe the meaning of average.

(ii) State the average of two or three quantities.

(iii) Determine the formul for average

J Prepare two containers of the same size with different volumes of liquid.

J Equal the volume of liquid from the two containers.

J Relate the examples given to determine the average using the formula

11.DATA HANDLING

2.ORGANISING AND INTERPRETING DATA

1. Use and apply knowledge of average

(i) Calculate the average using formula

(ii) Solve problem inreal life situation.

J Calculate the average of two numbers

J Calculate the average of three numbers

J Pose problems involving real life situation.

11.DATA HANDLING

1. Understand the vocabulary relating to data organization in graphs.

1. Organize and interpret data from tables and charts.

(i) Recognize frequency mode, range, maximum and minimum value from bar graphs

(ii) Construct a bar graph from a given set of data.

(iii) Determine the frequency mode, range, average, maximum and minimum value from a given graph.

(i) Discuss a bar graph showing the frequency, mode, range, maximum and minimum value.

J Pupils transform data tables to bar graphs.

Name	Reading test score	Mental Arithmetic test score
Adam	10	8
Davin	7	10
May	9	8

ULANGKAJI

PKSR 2

MAJLIS ANUGERAH CEMERLANG

Disediakan oleh : Hayati bt Edama / SK Tambirat / 2010

MATEMATIK

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