PRIMARY SCHOOL MATHEMATICS SYLLABUS Grades 4 & 5

ministry of education, sport and culture primary school mathematics syllabus grades 4 – 5 first examination 2008 curricu...

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MINISTRY OF EDUCATION, SPORT AND CULTURE

PRIMARY SCHOOL MATHEMATICS SYLLABUS GRADES 4 – 5 FIRST EXAMINATION 2008 Curriculum Development Unit P. O. Box MP 133 Mount Pleasant HARARE All Rights Reserved 2006

ACKNOWLEDGEMENTS The Ministry of Education, Sport and Culture wishes to acknowledge the following for their valued contribution towards the production of this syllabus: 

The National Primary Mathematics Syllabus Panel for their professional and technical support;



The Curriculum Development Unit for the finalisation of this syllabus;



The support staff at Education Services Centre for providing essential services.

1

CONTENT TOPIC

PAGE

Acknowledgement

1

Preamble

3

Aims

3

Assessment objectives

4

Scheme of Assessment

4

Methodology and Time Allocation

5

Presentation of the Syllabus

5

Scope and Sequence Chart

6

Grade 4: Topics

8-20

Grade 5: Topics

21-34

2

1.0

PREAMBLE The syllabus is designed to cover the fourth and fifth years Mathematics which culminates in the grade seven examination. It provides a basic foundation for mathematics to be used in everyday life, secondary school and further studies. The syllabus also provides a grade by grade progression in each study area. Although the objectives are organised on a grade by grade basis, no rigid treatment is intended. There should be no attempt to rush the class for the sake of completing all the listed objectives for the grade. The pace should be determined by the needs of the class, assuming that all the pupils in the class are being encouraged to work as hard as possible. It should not be assumed that all the pupils understand all the work previously taught. It is important to check that pupils have the necessary prerequisites for any work before proceeding by using national diagnostic tests, (1998) copies which are in each school.

2.0

AIMS The syllabus aims to help pupils to:

2.1

be literate and numerate;

2.2

understand, use and communicate mathematical information;

2.3

acquire mathematical concepts and skills for use as tools in study, work, leisure and everyday transactions;

2.4

develop sound mathematical skills that will enable them to interact more meaningfully with their environment;

2.5

develop a positive attitude towards Mathematics;

2.6

think and express themselves clearly and logically;

2.7

develop attributes of co-operation, confidence, honesty, neatness, self-reliance and perseverance through appropriately challenging mathematically related tasks;

2.8

develop an inquiring mind through experimentation;

2.9

prepare for present and further studies in Mathematics and related subjects; and

2.10

grow intellectually.

3

3.0

ASSESSMENT OBJECTIVES Pupils will be assessed on their ability to:

3.1 3.2 3.3 3.4 3.5 3.6 3.7

recall, recognise and use mathematical symbols, terms and definitions; carry out calculations accurately, checking the correctness of the solution; estimate, approximate and use appropriate degrees of accuracy; read, interpret and use tables, charts and graphs; solve mathematical problems showing steps and necessary information; choose and use appropriate formulae and/or algorithms to solve problem and interpret and apply Mathematics in life situations

4.0

SCHEME OF ASSESSMENT Primary School Mathematics will be examined at Grade 7 in two papers as follows: PAPER 1 2

4.1

DESCRIPTION 50 Multiple Choice Questions Structured Questions

DURATION 2 hours 2 hours

MARKS 50 40

PAPER WEIGHTING 60% 40%

PAPER 1:

(2 hours) will consist of 50 multiple choice questions all of which must be answered by the candidate.

PAPER 2:

(2 hours) will consist of two sections: Section A and Section B. Section A will consist of approximately 10 structured questions. Candidates must answer all questions. The total for section A is 25 marks. Section B will consist of 5 structured questions each worth 5 marks. Candidates must choose and answer 3 questions. The total for this/the section is 15 marks.

SKILLS WEIGHTING The weighting of the skills to be assessed will be as follows:    

Knowledge Routine manipulation Understanding and application Problem solving

16% 38% 36% 10%

4

5.0

METHODOLOGY AND TIME ALLOCATION

Teaching methods which build interest and confidence in tackling problems are recommended. The following are some of the methods that may be used: -

discovery; group work; discussion; project work; problem solving; question and answer; Demonstration;

It is recommended that mathematics be allocated 2½ hours for grades 1 to 2 and 3 hours for grades 3 to 7 per week.

6.0

PRESENTATION OF THE SYLLABUS

6.1

The Primary Mathematics Syllabus is presented in three separate documents:   

Grade 1, 2 and 3 Grade 4 and 5 Grade 6 and 7

6.2

Each of the documents has the same Introductory Section and a Scope and Sequence Chart.

6.3

There are four topics, namely:    

Number; Operations; Measures; Relationships (Grades 3-7)

5

7.0

SCOPE AND SEQUENCE CHART

TOPIC NUMBER

OPERATIONS

GRADE 1 Whole numbers (0 to 50) Ordinal numbers from first to tenth Number line (0 to 50) Numerical order Approximations and estimations

GRADE 2 Whole numbers (0 to 100) Ordinal numbers from 1st to 20th

Addition Subtraction

Addition (0 to 100) Subtraction Multiplication (with products less than or equal to 100) Division (where the dividend is 50 or less)

Fractions Proper fractions (denominators 2 and 4)

GRADE 3 Whole numbers (0 to 1000). Ordinal numbers from first to thirtieth. Quantitativeness of number (cardinal numbers), 0 to 1000. Proper fractions (denominators 2, 4, 5 and 10).

GRADE 4 Whole numbers (0 to 10 000) Place value of digits Comparison and approximation. Place value of any digit.. Numeration systems (Arabic and Roman) Proper fractions (denominators 2, 10, 20, 50 and 100). Mixed numbers (with denominators 2 to 10, 20, 50 and 100) Decimals Percentages

GRADE 5 Whole numbers (0 to 100 000) place value of digits Proper fractions (where denominators are 2 to 10, 20, 50 and 100) Mixed numbers Numeration systems (Arabic and Roman) Decimals (up to 3 places) Percentages

Addition of whole numbers (0 to 1000) whose sum is less that or equal to 1 000 Subtraction of whole numbers (0 to 1 000) Addition of proper fractions (fractions with the same denominators 2, 4, 5 and 10) Subtraction of proper fractions (two fractions with the same denominators( 2, 4, 5 and 10) Multiplication of whole numbers (up to 10 x 10) Division of whole numbers (0 to 1000 by single digits) Multiplication of fractions (with

Addition of whole numbers (0 to 10 000) Multiplication of whole numbers (0 to 10 000) Division of whole numbers (by one digit numbers (0 to 10 000) Addition of proper fractions (where denominators are the same and no more than 3 terms are involved) Subtraction of proper fractions Multiplication of proper fractions (with denominators from 2 to 10 inclusive and 100 as improper fraction and vice versa) Addition of decimals (up to two places) Subtraction of decimals (up to two places)

Addition of whole numbers (involving carrying in 4 places within the range 0 to 100 000) Subtraction of whole numbers (0 to 100 000) Multiplication of whole numbers (where the multipliers are two digit numbers made of 0, 1, 2,3,4 and 5, multiples of 100 up to 1000 within the range 0 to 100 000) Division of whole numbers (to include long division by two digit numbers and multiples of 10 and 100 up to 1000 within the range 0 to 100 000) Addition and subtraction of decimals (up to 2 decimal places) Multiplication and division of decimals (by one and two digit whole

6

GRADE 6 Whole numbers (0 to 1 000 000) place value of digits Decimals (with up to 6 digits including up to 3 decimal places) Proper fractions (where denominators are 2 to 10 and multiples of 5 up to 100 inclusive) Mixed numbers (where denominators are 2 to 10 and multiples of 5 up to 100 inclusive) Percentages Numeration systems (Roman numerals from 1 to 50 then 100, 500 and 1000) Addition and subtraction of whole numbers, fractions and decimals (addition and subtraction in the range 0 to 100 000 for whole numbers and for fractions and mixed numbers) Multiplication and division of whole numbers, decimals and fractions Combined operations Ratio and scale

GRADE 7 Whole numbers (0 to 10 000 000) Place value of digits Roman numerals (0 to 1 000) Decimals (with up to 8 digit including up to 3 decimal places) Proper fractions (where denominators are 2 to 10 and multiples of 5 up to 1 000 inclusive) Mixed numbers (where denominators are 2 to 10 and multiples of 5 up to 100 inclusive.) Percentages

Revision of addition and subtraction of whole numbers, decimals and fractions (within the range 0 to 10 000 000) Multiplication and division of whole numbers, fractions and decimals. Processes of finding discount, commission, interest, percentage, hire purchase, sales tax, V.A.T. and proportion Combined operations Ratio and scale Value added tax (V.A.T.)

TOPIC

GRADE 1

GRADE 2

GRADE 3 denominators 2, 4, 5 and 10.)

GRADE 4

GRADE 5 numbers). Addition and subtraction of fractions (where no more than three terms are involved. Multiplication of fractions (by whole numbers not exceeding 10 and the use of percentages).

GRADE 6

GRADE 7

MEASURES

Money (up to 50 cents) Time Mass Length Rate Volume and capacity Shapes

Money (up to $1.00) Time Mass Length Rate Area Volume and capacity Shapes

Money (up to $10,00) Time Mass Length (up to 100m) Rate Area Volume and capacity Direction, angle and lines Shapes

Money (up to $100,00) Time Mass Length (0 to 30cm), (1m to 10m) Rate Area Volume and capacity Direction, angles and lines Shapes

Money Time Mass (quantities up to 5kg) Length Rate Area Volume and capacity Direction, lines and angles Shapes

Money Buying, invoicing and change Time (second to a century) Mass (units from a gram up to a tonne) Length Rate Area (of rectangles and triangles) Volume and capacity Directions, angles and lines -cardinal points -angles on horizontal, vertical and perpendicular lines -geometrical properties of a circle -symmetry, Shapes

Money Mass (units from gram up to a tonne) Length (Standard units up to a km) Time (12 and 24 hour notation) Rate Area (involving square metres and hectares,) area of rectangles, triangles Volume and capacity Direction angles and lines Cardinal points Angles on horizontal and vertical and perpendicular lines Properties of circles, triangles and rectangles Symmetry,

Data handling

Data handling

Data handling

Data handling

Data handling

RELATIONSHIPS

7

GRADE 4 SYLLABUS

GRADE 4

GRADE 4 / TOPIC: NUMBER CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Abacuses, number cards, number square.

Pupils will be able to: Whole numbers (0 to 10 000)



say, read and write numbers in numerals and words in the given range;



Saying, reading and writing any number in numerals or words.



use the abacus to represent given numbers;



Representing numbers on abacuses.



use zero as a place holder;





write given whole numbers in expanded notation.

Using zero as a place holder and relating the value of a digit to its position.



Reading and writing numbers in expanded notation.



Comparing any two numbers or objects/quantities using less than, greater than and equal signs.



Ordering numbers in ascending and descending order.



Approximating quantities by rounding off numbers to the nearest ten, hundred and thousand.



Estimating with reasonable accuracy the number of given objects and cross checking by counting.

Place value of any digit

Whole numbers



compare any two numbers using and = signs;



arrange numbers in order of size;



approximate by rounding off to nearest ten, hundred, thousand;



estimate quantities of given objects.

(Comparison and approximation)

Other forms of numeration systems.



read and write numbers in Arabic and Roman numerals;



Converting Arabic into Roman numeral and vice-versa.



convert numbers from Arabic to Roman numerals and vice-versa.



Matching game using number cards.

(Arabic and Roman)

9

maize cobs, maize plants, plantation trees, school enrolment records counters

Abacuses, clock face with Roman numerals, clock face with Arabic numerals, number cards in Roman numerals. number cards of Arabic and Roman numerals.

GRADE 4

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

regular shapes that can be divided, number lines, fraction charts, fraction strips

Pupils will be able to: Proper fractions (with denominators 2 to 10, 20, 50 and 100.)



read and write fractions in numerals;





interpret diagrams representing fractions;

Saying, reading and writing fractions in numerals.



Interpreting and using diagrammatic representations of fractions.

draw, name and shade fractions on diagrams;



Drawing, naming and shading fractions on diagrams.



compare fractions using and = signs;

Matching and sorting fractions by size using number strips



Drawing charts showing equivalence in fractions.

arrange fractions in ascending or descending order.



Arranging fractions in order.



Comparing fractions using < ,> and = signs.









use fractions and number strips to find equivalent fractions;

Mixed numbers



identify parts of a mixed number;



Describing parts of a mixed number.

(with denominators 2 to 10, 20, 50 and 100)



say, read and write numerals from diagrams and vice versa;





compare mixed numbers using and = signs;

Saying, reading and writing in numerals diagrammatic representations of mixed numbers.



arrange mixed numbers in ascending or descending order.

Comparing mixed numbers using diagrams.



Arranging mixed numbers in ascending and descending order.



10

number lines, regular diagrams of various figures

GRADE 4

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



Discussing decimal notation, (what decimals are and giving examples).



Relating decimals to proper fractions with denominators 10 and 100.

Abacuses number lines, fraction charts 100 square grids



Identifying place value of digits represented on the abacus.



Writing decimal numbers in expanded notation such as 1,23 = 1+ 0,2 + 0,03



Comparing any two decimals using and = signs.



Arranging decimals in order of size.



Rounding off to units and tenths.



Reading and writing fractions with denominator 100.



Drawing diagrams representing percentages.



Using diagrams to represent percentages



Expressing halves, quarters, fifths and tenths as percentages.



Using fractional charts and a 100 square to show fractions, then express as percentages.

Pupils will be able to: Decimals



say, read and write in numerals any given decimals up to two decimal places;



relate fractions with denominators 10 and 100 to decimals;



identify the place value of any digit in decimals;



compare decimals using and = signs;



write decimals in expanded form;



arrange decimals in ascending or descending order;



round off numbers to units or tenths.



read and write fractions with denominator hundred;



illustrate percentages diagrammatically;



use 100 square to express fractions as percentages.

- up to two decimal places

Percentages

11

fraction charts diagrammatic representations 100 square grids

GRADE 4

GRADE 4 / TOPIC : OPERATIONS CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Addition of whole numbers

Pupils will be able to:  recall basic addition facts;



(0 to 10 000)



Recalling addition facts involving two whole numbers with a sum of up to 20, for example, 9+7, 8+5.



Adding two or three whole numbers involving up to 3- carries

Abacuses, flash cards, money, clock faces, abacus diagrams, counters



Adding given known measures, for example, money, length, time, volume.



Recalling subtraction bonds involving two whole numbers.



Subtracting any two numbers in the range up including borrowing up to three times.



Subtracting measures for example, money, length, time, mass and volume.

Subtraction of whole numbers

Multiplication of whole numbers

add within the range including carrying up to three times.



recall basic subtraction facts;



subtract where borrowing is involved;



subtract measures.



recall basic multiplication facts;



Recalling basic multiplication facts.



complete given multiplication task;



Filling in blanks on multiplication charts such as



multiply where carrying is involved;



multiply known measures by numbers;



find factors.

Rulers, clocks, jars, scales, counters

394 X 3 18 

12

Abacuses flash cards on basic facts, clock faces, counters

Multiplying whole numbers by 1 digit numbers including carrying up to three times

GRADE 4

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Pupils will be able to: 

Multiplying number including carrying For example x

1186 8 _______ _______



Multiplying measures for example money, time mass and volume.



Identifying factors of given numbers.



Writing numbers as products of factors.

Division of whole numbers



recall basic division facts;



Recalling basic division facts mentally.

(by one digit number)



divide whole number by long division with or without remainder;



Carrying out long division without a remainder.



divide measures by whole numbers.



Carrying out long division with one-digit remainders.



Dividing measures by numbers.

Addition of proper fractions



add three proper fractions with the same denominator.



Adding proper fractions.

Number lines, fraction charts, fraction diagrams



subtract proper fractions with the same denominators.



Subtracting fractions with the same denominators, for example, 7-5 =2 8 8 8

Number lines, fraction charts, diagrams

(where denominators are the same and no more than 3 terms are involved.) Subtraction of proper fractions

Money, number lines rulers

13

GRADE 4

CONCEPT Multiplication of proper fractions and conversion of mixed numbers (with denominators from 2 to 10 inclusive and 100)

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Pupils will be able to:  multiply fractions by whole numbers;



change mixed numbers to improper fractions and vice versa;

Changing improper fractions to mixed numbers.

Number lines fraction chart percentage square grid



express fractions with denominators 100 as percentages.

Changing mixed numbers to improper fractions.



Expressing fractions with denominator 100 as a percentage such as 30 = 30% 100



Multiplying fractions by whole numbers.



Finding fractions of numbers and measures such as ¾ of $12



Revising place values in decimals.



Adding decimal numbers such as 324,45 + 128,38



Subtracting decimals such as 725,68 - 316,79

 

Addition of decimals



add decimals.

(up to two places)

Subtraction of decimals



subtract decimals.

(with up to the two decimal places.)

14

Abacuses number lines work cards counters

Abacuses Number lines work cards counters

GRADE 4

GRADE 4 / TOPIC : MEASURES OBJECTIVES Pupils will be able to:

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Money



express money in decimal form;



Real coins and bank notes

(Money up to $100,00)



write money in expanded form;

Identifying all Zimbabwean coins and bank notes.



Listing all Zimbabwean bank notes and coins.



Discussing characteristics of each coin and bank note.



Converting dollars to cents and viceversa.



Breaking down bank notes and coins into smaller units.



Writing amounts of money in expanded notation for example $3,83 = $3 + 80c + 3c.



Writing amounts of money as expanded fraction for example $9,74 = $ (9+70 + 4 100 100

CONCEPT



convert cents to dollars and vice versa.

15

Plastic or card representations of money

GRADE 4

CONCEPT

Time

OBJECTIVES Pupils will be able to:

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



use units of time;



Giving times when events occurred.



convert time from one unit to another;





Giving the duration of an event.

tell time to the nearest 5 minutes ; 

Converting units of time from one form to another for example. 60min = 1hr 14 days = 2 weeks = fortnight

Calendars Watches sun dials conversion charts clock-faces with Arabic or Roman numerals. Clocks



Telling and using number of days in each month.



Reading time on clock faces to the nearest 5 mins.



Indicating time on clock faces and stating the given time.



Using a.m. p.m. noon and midnight to tell time.



Mass

use a.m. and p.m., noon and midnight to tell time.



convert kilograms to grams and vice versa;



Expressing kilograms as grams and vice versa.



find the mass of different objects by weighing.



Finding and comparing masses of objects.

16

Scales, balances, beam balances, containers

GRADE 4

CONCEPT

Length (up to 100m.)

Rate

Area

OBJECTIVES Pupils will be able to:

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



measure lengths to the nearest mm, cm or m;





estimate lengths using spans and paces.

Strings, Rulers, tape measures, click wheels, trundle wheels





compare two quantities.

find areas of rectangles using the formula Area of rectangle = L x W.

Stating and using the conversions: 10mm 100cm 1000mm

= 1cm = 1m = 1m



Estimating lengths



Finding lengths of objects.



Comparing lengths.



Linking two measures correctly to express rate for example kilometres per hour (km/h)



Using non-standard units to estimate lengths and widths.

Distance tables, clock faces. Square and rectangular shapes, rubber bands (assorted colours),



Estimating area of squares and rectangles by using spans or paces.



Marking square grids in given rectangles.



Counting and tabulating the number of squares along the length, width and the total to establish that L x W = Area of rectangle.

string

Using formula to find area of rectangles.

17

GRADE 4

CONCEPT

Volume and capacity

OBJECTIVES Pupils will be able to:

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS





Graduated containers,



convert millilitres to litres and vice versa; measure volumes and capacities.

 

Measuring capacity or volume in millilitres and litres. Measuring liquids in litres, ½ litres, ¼ litres and millilitres. Converting millilitres to litres and viceversa using 1 litre = 1000 millilitres.

water

1 - litre containers ½ - litre containers ¼ - litre containers

Directions, angles and lines



indicate North, South, East and West;



Indicating N, S, E, W.



recognise 1, 2, 3 or 4 right angles.



Drawing a compass and labelling cardinal points.



Identifying and telling the number of right angles on the compass.



Drawing diagrams with right angles.



Identifying and naming right angles on the compass and drawing diagrams with right angles.



Identifying use of right angles in real life situations.



Identifying directions of places in relation to the school.

18

Compass, maps card strips, diagrams, rectangular cards, rulers

GRADE 4

CONCEPT

Shapes

OBJECTIVES Pupils will be able to:

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



identify different solid and plane shapes;





identifying various shapes in given patterns.

Identifying, naming and drawing representations of cylinders, cubes, rectangular prisms, squares, rectangles, right-angled triangles, circles and spheres.

Shapes, scissors, paper, paint or crayons brushes



Drawing and colouring shapes to produce various patterns.



Exploring the environment and identifying the shapes and patterns.

19

GRADE 4

GRADE 4 / TOPIC: RELATIONSHIPS CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



Collecting various forms of data, for example, number of trees in an orchard and pupils’ modes of travelling to and from school.



Reading information from calendars and bus time tables.

Calendars, timetables, charts, bar graphs and column graphs, ready reckoners



Classifying data.



Using information to draw bar graphs.



Reading and interpreting information on bar and straight line graphs.

Pupils should be able to: Data handling



explain statistical data accurately;



use data to draw bar graphs and column graphs;



read and interpret information from given tables and graphs;



collect and record data.

/im

20

GRADE 4

GRADE 5 SYLLABUS

21

G

GRADE 5 / TOPIC : NUMBER CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



Saying, reading and writing in numerals and words numbers in the range.



Abacuses flash cards charts counters

Counting forwards and backwards in tens and hundreds.



Identifying values of given digits in any number such as 6375;3 is hundreds.



Comparing numbers using and = signs,



Arranging numbers in order of size.



Designing number sequences.



Rounding off numbers to the nearest ten, hundred, thousand and ten thousand.



Estimating numbers of given objects and checking by counting.



Writing numbers in expanded form 8327 = 8000 + 300 + 20 +7.

Pupils will be able to: Whole numbers



count forwards and backwards;

Range (0 to 100 000)



say, read and write numbers in the range;

Place value of any digit



give values of digits in a given number;



arrange numbers in order of size;



write sequences;



round off to a given degree of accuracy;



write numbers in expanded notation/form.

22

G

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Fraction charts work cards flash cards

Pupils will be able to: 

say, write and read fractions with denominators in the given range;



Breaking down wholes into equal parts and relating them to the whole.



compare fractions;





write fractions in their equivalent forms as well as their lowest terms;

Comparing fractions using and = signs.



Writing fractions in their equivalent forms and reducing them to their lowest terms.



Arranging a set of fractions in ascending or descending order.



Using the terms numerator and denominator.



Forming mixed numbers by putting together wholes and fractions of wholes for example.

Proper fractions (where the denominators are 2 to 10, 20, 50 and 100)



Mixed numbers

differentiate between numerator and denominator.



identify mixed numbers;



solve problems involving mixed numbers;



convert mixed numbers to improper fractions and vice-versa;

2 and



use and = signs correctly when comparing mixed numbers.

2

23

Fraction charts, Diagrams Regular objects

3 4

3 4



Reading, interpreting and writing mixed numbers.



Using diagrammatic representations of mixed numbers.



Converting mixed numbers into improper fractions and vice-versa.

G

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Pupils will be able to:

Numeration systems (Arabic and roman numerals)

Decimals (up to 3 places)



Comparing two mixed numbers using signs and = signs.



say, read and write Roman numerals;





convert Roman numerals to Arabic numerals and vice versa.

Familiarising pupils with Roman numerals from 1 to 50 and 100.



Writing numbers 1 to 20 in Roman numerals.



Showing how the Roman numeration system is built from basic numerals for 1,5, 10 and 50.

Conversion charts



say, read and write in numerals, decimals with 1, 2 or 3 decimal places;



Saying, reading and writing in numerals up to 3 decimal places.



determine place value of a digit in a given decimal;





interpret diagrammatic representations of decimals;

Giving values of digits in numbers up to 3 decimals places with no more than 5 digits.



round off to the nearest unit, tenth and hundredth;

Interpreting diagrammatic representation of decimals.



compare decimals using the , and = signs.

Comparing decimals using the and = signs.



Rounding off decimals to the nearest unit, tenth and hundredth.

 

24

Number cards

Abacuses Diagrams of fractions, decimal fraction charts

G

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

100 square grid, charts

Pupils will be able to: Percentages



express fractions as percentages and vice versa;



Expressing percentages as fractions and vice versa.



express one quantity /amount as a percentage of another;



Expressing one quantity /amount as percentages of another.



compare percentages using the and = signs.



Comparing percentages using the and = signs.



Finding percentages equivalent to

1 1 1 1 , , and 2 4 5 10

25

G

GRADE 5 / TOPIC: OPERATIONS CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Addition of whole numbers

Pupils should be able to:  recall basics addition facts;



Recalling basic addition facts, such as, 8+7=15 9+6=15.



Adding with carrying.

Abacuses flash cards work cards counters



Adding measures where whole numbers are involved.



Deducing and generalising the associative and commutative laws.



Recalling basic subtraction facts.

Abacuses



Subtracting measures where whole numbers are involved.



Subtracting by decomposition and equal additions up to 4 places.

flash cards. work cards counters



Recalling basic multiplication facts up to 10x10 including product values of 0.

Multiplication chart



Multiplying by one digit numbers for example 1 275 x 9 =

counters



Multiplying by 2 digit number for example 756 x 24 =



Multiplying by multiples of 10 for example 948 x 80



Multiplying by multiples of 100 for example 72 x 300 =

(involving carrying in 4 places within the range 0 to 100 000.)

Subtraction of whole numbers (0 to 100 000.)



add with carrying involved;



add measures;



use the associative law.



recall basic subtraction facts;



subtract by decompositional equal additions;



subtract measures.

Multiplication of whole numbers (where the multipliers are two digit numbers made of 0;1; 2;3;4 and 5, multiples of 10 and multiples of 100 up 1000 within the range 0 to 100 000.)



recall basic multiplication facts;



multiply by one digit number;



multiply by two digit numbers;



multiply by multiples of 10 and 100;



deduce and generalise multiplication processes;



multiply measures.

26

dial for multiplication

G

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Pupils should be able to:

Division of whole numbers (to include long division by two digit numbers and multiples of 10 and 100 up to 1000 within the range 0 to 100 000)

Multiplication and division decimals

Multiplying measures where whole numbers are involved.



Deducing and generalising on multiplication of numbers for example 2x3=3x2, (2x3)x4=2x(3x4)



recall basic division facts;



Recalling basic division facts.

Charts and



carry out long division by one/two digit number divisors, with or without remainders;



Dividing by one digit numbers using long division.

tables



Dividing by two digit numbers using long division.



Dividing by multiples of 10 and 100.



Addition and subtraction of decimals (up to 2 decimal places.)



divide numbers involving measures where whole numbers are involved.



add and subtract decimals;





convert fractions to percentages and vice versa.

Identifying decimals and place values.



Adding and subtracting decimals.



Adding and subtracting decimal measures.



Recalling multiplication and division facts.



Multiplying and dividing by multiples of ten, single digit whole numbers and two digit whole numbers.



Converting fractions to decimals and vice versa.



identify place value;



multiply and divide decimals.

27

counters

Abacuses flash cards work cards

Abacuses flash cards work cards

G

CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



Identifying numerators and denominators.

Equivalent fraction Charts.



Adding and subtracting fractions with the same denominators.

rods and blocks



Finding common denominators.



Finding equivalent fractions.



Adding and subtracting proper fractions with different denominators.



Recalling basic multiplication facts.



Multiplying whole numbers by proper fractions and vice versa.



Changing fractions to percentages and vice versa.



Using the word "of " such as

Pupils should be able to: Addition and subtraction of fractions (Where no more than three terms are involved)



identify and use numerators and denominators appropriately;



add and subtract proper fractions with same denominators;



add and subtract proper fractions with different denominators.

Multiplication of fractions



multiply proper fractions by whole numbers;

(by whole numbers not exceeding 10 and the use of percentages.)



change fractions to percentages and vice versa;



represent ratio in three ways;



use "of" to mean multiply.

Number lines, diagrams on ratio

3 4

of 12, 25% of 50.

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Writing ratio in 3 ways.



Finding part of a whole by multiplying by a fraction.

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CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

Combined operations

Pupils should be able to:  work out exercises which combine addition and subtraction.



Addition and subtraction

SUGGESTED MATERIALS

Adding and subtracting whole numbers by first adding before subtracting such as 7-9+4

= 7+4 -9 = 11 - 9 = 2



Adding and subtracting fractions by first adding before subtracting such as

1 3 4 + 5 5 5

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=

1 4 3 + 5 5 5

=

5 3 5 5

=

2 5

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CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

Multiplication and division

Pupils should be able to:  work out exercises which combine multiplication and division of whole numbers;



Dividing whole numbers by multiplying with the inverse of the divisor such as 12 ÷ 4 =

12 1 x = 3 and 1 4

6 ÷ 3x2 =



work out problems which combine multiplication and division of fractions.

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SUGGESTED MATERIALS

6 1 2 x x =4 1 3 1

Dividing fractions by multiplying with the inverse of the divisor such as:

1 4

1 1 2 1 = x = and 2 4 1 2

1 8

3 6 1 x = x 8 8 8

8 6 1 x = 3 8 4

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GRADE 5 / TOPIC: MEASURES CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

give relationships between coins and bank notes



Shop articles

Calculate change.



Applying knowledge of money for example in shopping, selling and paying bills.



Showing relationships of Zimbabwean currency denominations, for example expressing notes in terms of other denominations.



Relating duration of events in everyday life in terms of seconds, minutes, hours and days.



Measuring time intervals of less than one minute, such as a duration of (i) a clap of hands (ii)a blink of an eye (iii)a jump



Telling time to the nearest minute, using a.m and p.m.



Estimating time from shadows and from the position of the sun.

Pupils will be able to: Money



Identifying all the denominations of the Zimbabwean Currency.

Zimbabwean coins and bank notes. Bills and statements.



Time



read and use time.

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Watches Clock-faces Sun-dials Sand bottle/Egg Timer Calendars Digital watches

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CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Pupils will be able to:  -

Mass (quantities up to 5kg)



find masses of quantities/objects;



estimate masses up to 5kg.

Converting units of time such as 1 minute = 60 seconds 2 weeks = fortnight 1 year = 365 days 2 weeks = 14 days 1 leap year = 366 days.



Saying and using the number of days in each month.



Using Standard International (SI) units for time.



Writing the date in S.I units, year, month and day.



Establishing that 1000grammes = 1 kilograme. Measuring the masses of quantities up to 5 kilograms to the nearest 50grams.



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Estimating masses of quantities from 0 to 5 kilograms and checking the degree of accuracy by weighing.

Beam balance 5g counters standard masses stones, books, shoes, bags. scales 50g weights objects to be weighed

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CONCEPT

OBJECTIVES

SUGGESTED ACTIVITIES

SUGGESTED MATERIALS

Length

Pupils will be able to:  estimate and measure length using standard and non-standard units;



Measuring distances up to 1km using non-standard units.





Finding the perimeter using the fact that it is the total distance around a figure.



Drawing rectangles and squares of different sizes to establish the perimeter of the rectangle as that of a square as P=2(LxW) P = 4S

30cm rulers Metre rules tape measures rope or string conversion table rectangular shapes square shapes



Linking two measures correctly to express rate, for example kilometres per hour (km/h), cents per litre.

Rate



find the perimeter of a figure using formulae.

relate two quantities as rate.

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Work cards, charts

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GRADE 5 / TOPIC : RELATIONSHIPS CONCEPT Data handling

OBJECTIVES Pupils will be able to:  collect data and use it to draw graphs; 

discuss methods of collecting and organising data;



read and interpret information;



make observations and report.;



construct their own time tables.

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SUGGESTED ACTIVITIES

SUGGESTED MATERIALS



Collecting data in groups and presenting it on a graph and table.

Charts Graphs Time tables



Interpreting data for example marks for different classes.



Reading and extracting information from given diagrams/time tables.



Drawing line graphs and interpreting them.



Drawing conclusions on observations.

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