PRIMARY SCHOOL MATHEMATICS SYLLABUS ... OF EDUCATION, SPORT AND CULTURE PRIMARY SCHOOL MATHEMATICS SYLLABUS GRADES 6 – 7 FIRST EXAMINATION 2008 Curriculum Development Unit P. O

MINISTRY OF EDUCATION, SPORT AND CULTURE

PRIMARY SCHOOL MATHEMATICS SYLLABUS

GRADES 6 – 7

FIRST EXAMINATION 2008

Curriculum Development Unit P. O. Box MP 133 Mount Pleasant HARARE

All Rights Reserved 2006

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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.

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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 6: Topics 9-23 Grade 5: Topics 24-41

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1.0 PREAMBLE

The syllabus is designed to cover the last two years of primary school Mathematics which culminates in the grade seven public 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 that 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.

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3.0 ASSESSMENT OBJECTIVES

Pupils will be assessed on their ability to: 3.1 recall, recognise and use mathematical symbols, terms and definitions; 3.2 carry out calculations accurately, checking the correctness of the solution; 3.3 estimate, approximate and use appropriate degrees of accuracy; 3.4 read, interpret and use tables, charts and graphs; 3.5 solve mathematical problems showing steps and necessary information; 3.6 choose and use appropriate formulae and/or algorithms to solve problem and 3.7 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 DESCRIPTION DURATION MARKS PAPER WEIGHTING

1 50 Multiple Choice Questions 2 hours 50 60%

2 Structured Questions 2 hours 40 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.

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

Knowledge 16%

Routine manipulation 38%

Understanding and application 36%

Problem solving 10%

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5.0 METHODOLOGY AND TIME ALLOCATION Teaching methods that 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)

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7.0 SCOPE AND SEQUENCE CHART

TOPIC GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7

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

Whole numbers (0 to 100) Ordinal numbers from 1

st to 20

th

Fractions - Proper

fractions (denominators 2 and 4)

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).

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

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

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)

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

OPERATIONS Addition Subtraction

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

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

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

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

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

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

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whole numbers (up to 10 x 10) Division of whole numbers (0 to 1000 by single digits) Multiplication of fractions (with denominators 2, 4, 5 and 10.)

and vice versa) Addition of decimals (up to two places) Subtraction of decimals (up to two places)

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 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).

Ratio and scale Value added tax (V.A.T.)

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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 Shapes Symmetry

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,

RELATIONSHIPS Data handling Data handling Data handling Data handling Data handling

GRADE 6 9

GRADE 6

SYLLABUS

GRADE 6 10

GRADE 6 / TOPIC: NUMBER

CONCEPT OBJECTIVES

Pupils will be able to:

SUGGESTED ACTIVITIES SUGGESTED MATERIALS

Whole numbers (0 to 1000 000)

say, read, and write any number in the range;

give values of digits of any given number in the range;

approximate numbers;

identify prime numbers in the range 0 - 50;

arrange numbers in order of magnitude;

write numbers in expanded notation.

Saying, reading and writing numbers in numerals or words

Writing numerals in expanded notation to determine place value.

Comparing two numbers by using greater than, less than and equal signs.

Arranging sets of numbers in order of magnitude.

Identifying prime numbers between 0 and 50.

Approximating numbers to the nearest ten, hundred, thousand and ten thousand.

Practising identifying place values, and rounding off.

Abacus, number lines, 50 square grids.

GRADE 6 11

CONCEPT OBJECTIVES



Proper fractions (with denominators 2 to 10 and multiples of

5 up to 100 inclusive)

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

write equivalent forms of fractions;

compare fractions and arrange them in order of size.

Saying, reading and writing fractions in numerals and identifying numerators and denominators.

Recognising, interpreting, and using diagrammatic representation of proper fractions with denominators in the range.

Presenting fractions in an equivalent form, for example

3 = 1 6 2

Comparing two proper fractions using <, > and = signs.

Arranging proper fractions in order of size.

Reading meters showing tenths and hundredths.

fraction charts number cards number lines.

Mixed numbers (with denominators 2 to 10 and multiples of

5 up to 100 inclusive)

identify mixed numbers;

compare mixed numbers;

convert mixed numbers to improper fractions and vice versa.

Saying, reading and writing mixed numbers.

Comparing any two mixed numbers using <, > and = signs.

Changing mixed numbers to improper fractions and vice versa.

Mixed number charts, number lines.

GRADE 6 12

CONCEPT OBJECTIVES



Decimals

(decimals up to 6 digits including up to 3

decimal places)

say, read and write any given decimal number;

tell the value of any digit in a given decimal number;

compare any two decimal numbers using <, >, and = signs;

arrange decimals in order of size;

round off decimals.

Saying, reading and writing any number expressed in decimal form with up to 3 decimal places.

Writing decimals in expanded notation to determine place value.

Comparing any two decimals by using greater than less than and equal to signs.

Arranging sets of decimals in order of magnitude.

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

Number strips, Abacuses, fraction charts, equivalent fraction charts, money.

Percentages

express fractions as a percentage and vice versa.

Reading and writing percentages from diagrammatic representations and numerals.

Converting fractions to percentages and vice versa.

Reading and writing fractions expressed as percentages.

Money, 100 square grid, number lines graduated up to 100, metre rule.

GRADE 6 13

CONCEPT OBJECTIVES



Other numeration systems Roman numerals from I to L then C, D and M (1 – 50, 100, 500 and 1 000).

say, read and write Roman numerals;

convert from Roman to Arabic numerals and vice versa.

Saying, reading and writing Roman numerals in the range.

Working with basic symbols to construct other Roman numerals I - L

Converting from Arabic to Roman numerals and vice versa.

Number cards, conversion charts, clock faces with Roman and Arabic numerals.

GRADE 6 14

GRADE 6 / TOPIC : OPERATIONS

CONCEPT OBJECTIVES



Addition and subtraction of whole numbers, fractions and decimals 0 - 1000 000

give mental answers to addition and subtraction of basic facts;

use the associative and commutative laws;

add and subtract measures;

add and subtract decimals;

add and subtract proper fractions and mixed numbers.

Recalling addition and subtraction basic facts.

Adding and subtracting numbers, and fractions using the commutative and associative laws where applicable, for example 2+3 = 3+2 commutative law 2+(3+4) = (2+3)+4 associative law

Adding and subtracting measures where no more than two units of each measure are involved.

Using decimal notation where applicable.

Filling in one missing element for open sentences involving addition or subtraction.

Illustrating, addition and subtraction operation on a number line.

Adding and subtracting proper fractions and mixed numbers.

Adding and subtracting decimals.

work cards, fraction charts, place value charts, number lines, money,

weights,

balance,

graduated and non graduated,

containers,

metre rules,

rulers.

GRADE 6 15

CONCEPT OBJECTIVES



Multiplication and division

(of whole numbers, fractions and decimals)

recall multiplication basic facts;

multiply and divide using long methods;

multiply decimals by decimals;

multiply and divide proper fractions by whole numbers and vice versa;

calculate fractions, decimals, percentages of numbers and measures;

write numbers in index notation.

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

Recalling division facts where the dividends are no more than 100 and the divisor is a single digit whole number , 10 and multiples of ten.

Multiplying using the long method: numbers and measures within the given range.

Dividing using the long method: numbers and decimal measures up to 3 decimal places.

Multiplying proper fractions and mixed numbers where no more than 3 terms are used and where the denominator is 10 and below.

Dividing fractions by whole numbers and vice versa.

Writing numbers in index notation for example 2

4 = 16.

Finding fractions, decimals and percentages up to 100% of numbers and measures, for example, money and length.

Addition charts

number lines

fraction charts

work cards

100 square grid

abacuses

flash cards

GRADE 6 16

CONCEPT OBJECTIVES



Combined operations

Involving three operations (addition, subtraction and multiplication or division).

work out mathematical exercises involving three operations.

Adding, subtracting and multiplying or dividing whole numbers and/or fractions using the law of precedence/priority.

5-3x2+9

= 5-6+9

= 14-6

= 8

4

3 +

6

1

3

2

8

1

= 4

3 +

6

1 x

2

3

8

1

= 4

3 +

4

1

8

1

= 8

8

8

1

= 8

7

N.B. Multiplication and division are carried out before addition and subtraction.

GRADE 6 17

CONCEPT OBJECTIVES



Ration and scale

say and write ratio in three ways;

express quantities as ratio;

reduce ratio to the lowest terms;

share using ratio;

draw diagrams to scale and interpret scale.

Saying and writing ratio in 3 ways, for

example, 2 to 5, 2:5 and 5

2.

Expressing quantities as ratio: for example 15cm to 1m 20c : $1,50.

Reducing ratio to the lowest terms.

Sharing quantities and measures using ratio.

Converting scale distances into actual measurements and vice versa.

Drawing lines and simple plans to scale.

Diagrams drawn to scale, Rulers, classroom blocks, Money,

click wheels,

tape measures,

strings.

GRADE 6 18

GRADE 6 / TOPIC : MEASURES

CONCEPT OBJECTIVES Pupils will be able to:


Money

prepare invoices correctly;

work out change;

distinguish between buying price and selling price and to calculate profit or loss.

Preparing invoices and calculating change.

Role playing on buying and selling.

Calculating the differences between buying and selling prices and working out profit/loss.

Invoices, corner/class shop, money, selling charts.

Time (second to a century)

read and convert time;

estimate and calculate time taken;

tell and write time in 12 hour and 24 hour notations.

Using the following units of time in meaningful contexts. century, decade, leap year, month, week, day, hour, minute and second.

Telling and using the number of days in each month.

Using the following conversions: 60minutes = 1 hour 24hours = 1 day 7 days = 1 week 365 days = 1 year 366 days = 1 leap year 10years = 1 decade 100years = 1 century

Telling and writing time to the nearest minute.

telling and writing time on the 12 and 24 hour notations.

Estimating time from shadows and from the position of the sun at different times of the day.

Interpreting a calendar and writing in SI notation.

Charts on units of time watches calendars clock faces sun dials.

GRADE 6 19



Mass (mass from a gramme up to a tonne)

convert units of mass;

estimate and measure mass;

find gross and net mass up to a tonne.

Stating and using the conversions: 1000g = 1kg 1000kg = 1 tonne.

Converting masses in smaller units to larger units and vice-versa. Such as 125g=0,125kg.

Estimating and comparing any two masses.

Measuring the mass of quantities up to 5kg to the nearest 50g.

Selecting appropriate units of mass for finding the mass of given quantities.

Estimating and measuring mass to the nearest kilogram in the range 1 kilogram to 5 kilograms.

Determining gross and net mass.

Scales and balances containers for example packets, bottles, bags. soil stones 50g to 1kg weights

Length (standard and non standard)

estimate and measure length using standard and non standard units;

find the perimeter of figures;

draw lines to scale.

Measuring distances up to 1km.

Estimating length by pacing and by using spans to establish that the perimeter is the sum of the lengths of the sides of a figure.

Applying the formula P= 2(L+B) for rectangles and P=4xS for squares.

Discussing meaning and use of scale.

Drawing lines to a given scale.

Rulers, metre rules, metre sticks, tape measures, ropes or strings, conversion table of length, buildings, rectangular shapes.

GRADE 6 20



Rate

link two quantities as rate;

calculate speed.

Linking two quantities as rate such as cents/kilogram, grams/ litre.

Comparing distances covered and time taken.

Deriving the formula of S = D . T

Estimating speeds using standard and non- standard units.

Charts with formulae ready reckoners graphs pendulums

stop watches.

Area

Areas of quadrilaterals and triangles

estimate areas of given figures;

calculate area of quadrilaterals and triangles.

Estimating areas of squares, rectangles and triangles by counting squares.

Deriving the formulae: A= L x W for rectangles A = ½ B x H for triangles

Finding areas of quadrilaterals.

Selecting the appropriate unit for measuring areas of different surfaces up to square metres.

metre rules metre sticks tape measures

figures divided into one centimetre squares.

GRADE 6 21



Volume and capacity determine volume of cubes, cuboids, and rectangular prisms;

find volume of irregular shapes by displacement.;

estimate capacity and calculate volume.

Stating and using the following conversions

1000ml = 1 litre 1000cm

3 = 1 litre

1cm3 = 1ml

Selecting the appropriate unit to measure volume.

Deriving and using the formula V = L x W x H for rectangular prisms and/or cuboid.

Using estimated lengths of sides of regular solids to estimate volume based on the formula.

Finding volume of irregular objects by displacement..

1cm cubes rectangular prisms, cubes, water, fine sand, graduated measuring cylinders, irregular stones,

containers.

Directions, angles and lines

Cardinal points in relation to position of places.

Angles with emphasis on horizontal, vertical and perpendicular lines.

.

identify the 8 cardinal points;

identify the position of a point in relation to another given point ;

illustrate 4

1,

2

1,

4

3and 1 revolution;

identify horizontal, vertical and/or perpendicular lines;

Identifying and illustrating 8 main points of a compass:

Showing 4

1,

2

1,

4

3 and one revolution

in terms of right angles.

Determining whether an angle lies between 0 and 1, 1 and 2, 2 and 3, or 3 and 4 right angles.

Pairs of compasses, diagrams showing direction or compass points, rims of bicycles, tyres, protractors. Newsprint, circles, rectangles, squares, triangles, manila, letters of the alphabet, regular polygons.

GRADE 6 22



Shapes

Parts of a circle.

Symmetry

distinguish 2 dimensional from 3 dimensional shapes;

classify shapes according to their properties;

identify shapes in a composite shape.

Identifying the radius, the diameter, circumference and an area of a circle.

draw and state the number of lines of symmetry for different shapes.

Identifying and drawing representations of cylinders, cubes, rectangular prisms, squares, rectangles, right-angled triangles, isosceles triangles, equilateral triangles, scalene triangles, circles, spheres, triangular prisms and cones and recognizing any four sided plane figure as A quadrilateral.

Listing properties of plane and solid shapes.

Identifying flat surfaces and curved surfaces, edges, corners or vertices and sides of shapes.

Identifying shapes in composite figures and objects.

Identifying the radius, the diameter, circumference and an area of a circle.

illustrating axes of mirror symmetry for squares, triangles; rectangles, circles and relevant combinations

Plane shapes,

solid shapes

Atlas

GRADE 6 23

GRADE 6 / TOPIC : RELATIONSHIPS

CONCEPT OBJECTIVES



Data handling

read and extract information from tables and graphs;

draw and interpret graphs.

Reading and extracting information from tables and graphs.

Collecting, presenting and discussing data.

Drawing graphs such as vertical or horizontal bar graphs and straight line graphs from given information.

Interpreting information on diagrams accurately.

charts timetables distance tables graph paper fare tables.

GRADE 7

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GRADE 7

SYLLABUS

GRADE 7

25

GRADE 7 / TOPIC : NUMBER

CONCEPT OBJECTIVES



Whole numbers

(0 - 10 000 000)

say, read and write numbers in numerals

or words;

give the value of a digit in a given

number;

arrange numbers in order of magnitude;

compare any two numbers using <, > and

= signs;

identify prime numbers;

find prime factors of numbers in the

range;

round off numbers;

estimate quantities;

express numbers in expanded notation.

Saying, reading and writing in numerals

or words any number in the range.

Finding the place value of a digit in a

number.

Identifying place value of digits of

numbers represented on an abacus.

Arranging numbers in ascending or

descending order.

Comparing any two numbers using <, >

and = signs.

List prime numbers in the range.

Factorising numbers in the range.

Expressing numbers to the nearest ten,

hundred, one thousand, ten thousand,

hundred thousand and million.

Estimating number of objects and

checking by counting.

Writing numbers in expanded notation

such as 37642 = (3 x 104) + 7 x 10

3) +

(6 x 102) + (4 x 10

1) + (2 x 10

o).

Abacuses,

number cards,

seeds/counters,

maize cob,

trees in a school plantation,

number lines,

vegetables in the school garden,

100-square grid,

money.

GRADE 7

26

CONCEPT OBJECTIVES

Pupils will be able to: SUGGESTED ACTIVITIES SUGGESTED MATERIALS

Other numeration systems

(Roman numerals to M).

convert numbers from one system to

another.

Matching Roman numerals and Arabic

numerals in the range (I – L).

Working with basic Roman numeral

symbols to construct numerals up to

1000.

Converting from one numeration

system to another.

Clock faces with Roman and Arabic

numerals

number lines,

number cards in Roman and Arabic

numerals.

Proper fractions

(with denominators 2 to 10 and

multiples of 5 up to 100 inclusive)

say, read, and write proper fractions in

numerals;

interpret diagrams representing proper

fractions;

compare and arrange proper fractions in

order of size;

convert proper fractions to decimals;

write proper fractions in equivalent forms

and/or reduce to lowest terms.

Saying, reading and writing proper

fractions in numerals.

Identifying and using diagrammatic

representations of proper fractions.

Comparing any two proper fractions

using <, > and = signs.

Arranging proper fractions in order of

magnitude.

Expressing proper fractions in their

equivalent forms and/or reducing

fractions to lowest terms.

converting proper fractions to decimals

and vice-versa.

Fraction charts,

number lines,

diagrammatic representations,

equivalency charts and conversion

charts

GRADE 7

27

CONCEPT OBJECTIVES


Mixed numbers

with denominators 2 to 10 and

multiples of 5 up to 100 inclusive.

say, read and write mixed numbers in

numerals;

represent mixed numbers on diagrams

and vice versa;

identify the whole number and fraction

parts of a mixed number;

write mixed numbers as improper

fractions;

write mixed numbers as decimals.

Saying, reading and writing mixed

numbers in numerals.

Recognising diagrammatic

representations of mixed numbers.

Identifying whole numbers and fractions

in given mixed numbers.

Converting mixed numbers to improper

fractions and vice - versa.

Converting mixed numbers to decimals

and vice versa.

Number lines,

fraction charts,

conversion charts,

diagrammatic representation charts.

Decimals

With up to 8 digits including up to

3 decimal places.

say, read and write decimals to 3

decimals places;

identify place value of digits in decimals;

write decimals in expanded notation;

compare decimal fractions using <, > and

= signs;

round off decimals.

Saying, reading and writing decimals in

numerals and words.

Giving the value of a digit in any of the

three places after the comma.

Arranging decimals in order of size.

Comparing any two decimal numbers

using <, > and = signs.

Rounding off decimals to the nearest

unit, tenth and hundredth.

Abacuses, decimal number lines,

metre rule,

Odometer readings,

water and electricity meters.

GRADE 7

28

CONCEPT OBJECTIVES


Percentages

say, read and write percentages;

express fractions as percentages and

vice-versa.

Expressing fractions as percentages

and vice versa.

Expressing quantities as percentages of

other quantities.

Fractional charts conversion and

100-square grid.

GRADE 7

29

GRADE 7 / TOPIC : OPERATIONS

CONCEPT OBJECTIVES



Addition and subtraction of whole

numbers, fractions and decimals

within the range 0 to 10 000 000.

recall basic addition and subtraction

facts;

add and subtract decimals and whole

numbers;

add and subtract fractions and mixed

numbers;

add and subtract measures;

interpret invoices and statements of

accounts.

Reciting basic addition and subtraction

facts.

Adding and subtracting whole numbers

and decimals.

Adding proper fractions and mixed

numbers.

Adding and subtracting measures.

Completing addition and subtraction

sentences with missing parts.

Adding 2 or 3 whole numbers to

establish associative and commutative

laws.

Interpreting statements of savings

accounts which contain details of

deposits, withdrawals and balance.

Interpreting statements of shopping

accounts which contain details of

invoices, payments and details of

amounts due.

Applying given postal rates to relevant

situations involving letters, parcels,

postal orders, money orders and

telegrams.

Deposit and withdrawal statements.

statements of accounts,

invoices,

work cards,

savings books/passbook,

receipts,

postal rates tables,

- automatic teller machine (ATM)

cards,

- cheque book.

GRADE 7

30

CONCEPT OBJECTIVES



Multiplication and division of whole

numbers, fractions and decimals

recall basic facts of multiplication and

division;

work out long multiplication of whole

numbers and decimals;

carry out long division of whole numbers

and decimals;

express mixed numbers as improper

fractions and vice versa;

multiply mixed numbers;

divide fractions by whole numbers and

fractions;

express fractions and decimals as

percentages and vice versa;

calculate tax, interest, commission and

discount;

solve problems related to tax, interest,

commission and discount;

solve direct proportion problems;

solve inverse proportion problems;

solve hire purchase problems;

write numbers in index notation.

Reciting basic multiplication and division

facts.

Multiplying whole numbers and

decimals using the long multiplication

method.

Dividing whole numbers and decimals

using long division.

Expressing decimals and fractions as

percentages.

Expressing mixed numbers as improper

fractions and vice versa

Multiplying fractions.

Multiplying mixed numbers.

Dividing fractions by whole numbers.

Dividing fractions by fractions.

Dividing mixed numbers by mixed

numbers.

Calculating discount, commission,

interest, sales tax or Value Added Tax

(V.A.T.)

Solving direct and inverse proportion

problems.

Explaining hire purchase and solving

related problems.

Writing numbers in index notation.

Work cards,

fraction charts,

place value charts,

multiplication dials,

newspaper cuttings of advertisements,


hire purchase agreements,

tax rates tables,

interest rates tables.

GRADE 7

31

CONCEPT OBJECTIVES



Combined operations involving all

four operations

work out mathematical exercises

involving all four operations.

Working out mathematical exercises

Which involve four operations using rule of

precedence/priority

2

1 x 12 +

4

3 ÷

2

1 -

4

13

= 2

1 x 12 +

4

3 x

1

2 -

4

13

= 6 + 2

3 -

4

13

= 2

17 -

4

13

= 4

124

= 4

14

N.B. Multiplication and division are carried

out before addition and subtraction.

Ratio and scale

express one quantity as a ratio of

another;

Relating quantities using ratios.

Simplifying ratios to their lowest terms.

Rulers,

diagrams drawn to scale,

atlases,

GRADE 7

32

CONCEPT OBJECTIVES



share using ratio;

convert scale distances to actual

distances and vice versa.

Sharing using ratio, for example, 1:2:3.

Calculating actual or scale

distances/lengths.

building plans,

money.

GRADE 7

33

GRADE 7 / TOPIC: MEASURES

CONCEPT OBJECTIVES


Money

prepare and interpret invoices;

complete deposit and withdrawal slips;

interpret financial transactions;

calculate postal rates and simple interest.

Preparing and interpreting invoices.

Filling in deposit and withdrawal slips.

Interpreting statements of accounts

which contain details of withdrawals,

deposits interest and balance.

Calculating postal rates of letters,

parcels, postal orders and money

orders.

Calculating simple interest and

balances.

Interpreting statements involving hire

purchase.

Drawing up simple household and

personal budgets.

Invoices,

deposit slips,

withdrawal slips,


money order forms,

postal order forms,

telegram forms,

money,

used stamped envelopes,

hire purchase statements,

newspaper adverts on hire purchase

and ready reckoners on interest.

GRADE 7

34

CONCEPT OBJECTIVES



Mass

From a gram up to a tonne.

convert one unit of mass to another;

determine mass of quantities to the

nearest 50g;

estimate masses and verify their

estimates;

solve problems involving gross and net

mass.

Changing one unit of measurement to

another such as grams, kilogrammes,

tonnes and vice versa.

Measuring the mass of quantities up to

10 kilograms to the nearest 50 grams in

the range 1kg to 10kg.

Selecting appropriate units of mass to

measure given quantities.

Estimating mass to the nearest kilogram

in the range 1 to 10kg.

Estimating mass to the nearest 5

kilograms in the range 11 kilograms to

50kg.

Differentiating the terms net and gross

mass.

Using the terms “net” and “gross mass”

in problem solving.

Weights,

scales,

objects to be weighed,

containers,

balances.

GRADE 7

35

CONCEPT OBJECTIVES



Length

Using standard units up to a

kilometre and non-standard units.

estimate lengths and distances using

spans and paces;

measure length and distance;

measure and/or calculate perimeter of

given figures;

draw lines and simple plans to scale.

Measuring distances up to 1km

Estimating length by pacing and by

using spans.

Applying the formula P=2x(L+B) for

perimeters of rectangles and P= 4xS for

perimeters of squares.

Drawing lines and simple plans to a

given scale.

Interpreting scale to give answer in real

life.

Rulers,

tape measures,

metre sticks,

click wheels,

plane and solid shapes,

strings.

Time

tell and write time in 12-and 24-hour

notation;

add and subtract time units;

write dates in SI notation;

solve problems involving time.

Telling and writing time in 12-hour and

24-hour notation.

Converting time from 12-hour to 24-hour

notation and vice versa.

Adding and subtracting time units.

Solving problems involving time.

Writing dates in SI notation.

12 and 24 hour clock faces,

calendars,

watches,

time conversion charts,

tables time.

GRADE 7

36

CONCEPT OBJECTIVES



Rate

relate distance, speed and time;

state and write rate linking two

quantities;

apply knowledge of rate in problem

solving.

Recording time taken to cover stipulated

distances and using the information to

derive the formula

S = D in km/h or m/s.

T

Using the formula to calculate speed

Using expressions of rate linking two

quantities such as cents per kilogram,

cubic centimeters per litre, expressions

of discount, commission and interest.

Estimating speeds by recalling relevant

experience involving walking, cycling

and vehicle speeds.

Pendulums

watches

click wheels

tape measures

metre sticks

strings

scales

money

Area

Including acres and hectares

calculate area of rectangles and triangles

using various units of measure;

select appropriate units of measure to

find area;

estimate and calculate area using

appropriate formulae.

Converting and using the following units

of area:

100 square metres = 1 are

(100m2 = 1 a)

100 acres = 1 hectare

(100 a = 1ha

10 000 square metres = 1 hectare

(10 000m2 = 1 ha.

Calculating area of various surfaces

using various units of measure.

Applying the formulae:

A = L x W for rectangles

Tape measures,

30cm and metre rules,

ropes,

triangular templates,

rectangular templates,

plane surfaces.

GRADE 7

37

CONCEPT OBJECTIVES



A = ½ b x h for triangles.

Selecting appropriate units from square

centimetres, acres and hectares for

measuring given areas.

Estimating the lengths of given shapes

and calculating their estimated area

using appropriate units.

Volume and capacity

- up to cubic metres

state and use capacity and volume units

of measure;

find volume using the formula

V = L X W X H;

select and use appropriate units to

measure volume;

estimate volume and/or verify by

measuring.

Stating and using the following

conversions.

1000 millilitres = 1 litre

1000cubic centimetres = 1 litre

1000 litres = 1 cubic metre

Measuring capacity and volume of

various containers in millilitres and cubic

centimetres.

Deriving and using the formula

V = L x W x H for rectangular prisms or

=

A x H for shapes with uniform cross

sections.

Using the formula V = L x W x H to

calculate volume of rectangular prisms

and cuboids

Estimating capacity of containers

according to the appropriate units of

measure.

Graduated containers,

Cubes,

rectangular prisms,

various containers,

measuring cylinders or jugs,

conversion tables.

GRADE 7

38

CONCEPT OBJECTIVES



Using estimated lengths of sides to

calculate estimates of volume.

Direction angles, and lines

Including acute, obtuse and reflex

angles, arc and chord of a circle

draw and label compass points;

determine direction of given points from a

reference point;

name angles between given compass

points in right angles;

identify and name horizontal, vertical and

perpendicular lines;

illustrate and name parts of a circle;

calculate missing angles of triangles;

identify and name acute, obtuse and

reflex angles;

identify symmetrical shapes and objects;

identify and draw the lines of symmetry of

plane shapes;

complete symmetrical shapes given lines

of symmetry.

Identifying 8 main points of the

compass.

Determining direction half way between

any two given main points such as NE.

Indicating directions using angle arms.

Dividing a circle into 4 and 8 equals

parts to illustrate compass points and

angles.

Identifying 4

1,

2

1 ,

4

3and 1

revolution in terms of right angles

Determining whether an angle is

between 0 and 1 ; 1 and 2; 2 and 3 or

3 and 4 right angles.

Identifying horizontal, vertical,

perpendicular, oblique and parallel lines.

Drawing horizontal vertical, oblique,

perpendicular and parallel lines.

Identifying and drawing the radius,

diameter, circumference, arc and chord

of a circle.

Compass,

Atlas,

right angled templates/set squares,

clock faces,

circle templates,

pair of compasses,

mirrors,

alphabet figures,

lines,

circles,

pairs of scissors,

regular and irregular plane figures.

GRADE 7

39

CONCEPT OBJECTIVES


Deducing that interior angles of

rectangles add up to 4 right angles and

those of a triangle add up to 2 right

angles.

Dividing a square and a rectangle

diagonally to make right angled

triangles.

Illustrating and writing number of axes

of mirror symmetry for squares,

triangles, rectangles, circles and

relevant combinations of them.

Shapes

use the terms 2- and 3- dimensional

shapes in correct context and name the

shapes;

list properties of 2- and 3- dimensional

shapes;

name, draw and make 3- dimensional

shapes;

name and draw triangles and polygons.

Identifying 2-dimensional and 3-

dimensional shapes.

Identifying flat and curved surfaces,

edges, corners or vertices and sides of

shapes.

Counting edges, corners /vertices and

sides of given shapes.

Listing the properties of 2- and 3-

dimensional shapes.

Identifying and drawing representations

of scalene, isosceles, equilateral and

right angled triangles, quadrilaterals,

squares, rectangles, pentagons,

hexagons, circles, cubes, rectangular

Various 2- and 3- dimensional shapes,

Rulers,

Pencils,

physical structures of plane and solid,

shapes,

models.

GRADE 7

40

and triangular prisms, cylinders,

pyramids on square bases, spheres,

and cones.

Building/making solid shapes.

Identifying a combination of shapes in

physical structures.

GRADE 7

41

GRADE 7 / TOPIC : RELATIONSHIPS

CONCEPT OBJECTIVES



Data handling

read, extract and interpret data from

tables and graphs;

choose suitable scales and draw graphs

from tabulated information;

use graphs in real life situations.

Reading and extracting data from tables

and graphs.

Collecting, classifying and tabulating

data such as heights of pupils, rainfall,

mass and temperatures.

Identifying the most appropriate graph

to represent given information.

Choosing suitable scale for drawing

graphs.

Plotting given points on grid when

drawing graphs.

Interpreting and discussing information

on the graph.

Square paper

tables and diagrams

graphs on statistical data

Documents

PRIMARY SCHOOL MATHEMATICS SYLLABUS ... OF EDUCATION, SPORT AND CULTURE PRIMARY SCHOOL MATHEMATICS SYLLABUS GRADES 6 – 7 FIRST EXAMINATION 2008 Curriculum Development Unit P. O