MINISTRY OF EDUCATION, SPORT AND CULTURE PRIMARY SCHOOL MATHEMATICS SYLLABUS GRADES 4 5 FIRST EXAMINATION 2008


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1 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
2 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
3 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 820 Grade 5: Topics
4 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 cooperation, confidence, honesty, neatness, selfreliance 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
5 3.0 ASSESSMENT 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: PAPER 2: (2 hours) will consist of 50 multiple choice questions all of which must be answered by the candidate. (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% 4
6 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 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 37) 5
7 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 Whole numbers (0 to 100) Ordinal numbers from 1 st to 20 th Fractions Whole numbers (0 to 1000). Ordinal numbers from first to thirtieth. Quantitativeness of number (cardinal Whole numbers (0 to ) place value of digits Proper fractions (where denominators are 2 to 10, 20, 50 and 100) Approximations and estimations  Proper fractions (denominators 2 and 4) numbers), 0 to Proper fractions (denominators 2, 4, 5 and 10). Mixed numbers Numeration systems (Arabic and Roman) Decimals (up to 3 places) 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 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 Whole numbers (0 to ) 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 Addition of whole numbers (0 to ) Multiplication of whole numbers (0 to ) Division of whole numbers (by one digit numbers (0 to ) 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) 6 Addition of whole numbers (involving carrying in 4 places within the range 0 to ) Subtraction of whole numbers (0 to ) 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 ) 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 ) Addition and subtraction of decimals (up to 2 decimal places) Multiplication and division of decimals (by one and two digit whole Whole numbers (0 to ) 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 for whole numbers and for fractions and mixed numbers) Multiplication and division of whole numbers, decimals and fractions Combined operations Ratio and scale Whole numbers (0 to ) 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 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 ) 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.)
8 TOPIC GRADE 1 GRADE 2 GRADE 3 GRADE 4 GRADE 5 GRADE 6 GRADE 7 denominators 2, 4, 5 and 10.) 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). 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, RELATIONSHIPS Data handling Data handling Data handling Data handling Data handling 7
9 GRADE 4 SYLLABUS GRADE 4
10 GRADE 4 / TOPIC: NUMBER CONCEPT Whole numbers (0 to ) Place value of any digit Whole numbers (Comparison and approximation) say, read and write numbers in numerals and words in the given range; use the abacus to represent given numbers; use zero as a place holder; write given whole numbers in expanded notation. compare any two numbers using <, > and = signs; arrange numbers in order of size; approximate by rounding off to nearest ten, hundred, thousand; Saying, reading and writing any number in numerals or words. Representing numbers on abacuses. 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. Abacuses, number cards, number square. maize cobs, maize plants, plantation trees, school enrolment records counters estimate quantities of given objects. 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. Other forms of numeration systems. (Arabic and Roman) read and write numbers in Arabic and Roman numerals; convert numbers from Arabic to Roman numerals and viceversa. Converting Arabic into Roman numeral and viceversa. Matching game using number cards. Abacuses, clock face with Roman numerals, clock face with Arabic numerals, number cards in Roman numerals. number cards of Arabic and Roman numerals. 9 GRADE 4
11 CONCEPT Proper fractions (with denominators 2 to 10, 20, 50 and 100.) read and write fractions in numerals; interpret diagrams representing fractions; draw, name and shade fractions on diagrams; use fractions and number strips to find equivalent fractions; compare fractions using <, > and = signs; arrange fractions in ascending or descending order. Saying, reading and writing fractions in numerals. Interpreting and using diagrammatic representations of fractions. Drawing, naming and shading fractions on diagrams. Matching and sorting fractions by size using number strips Drawing charts showing equivalence in fractions. Arranging fractions in order. regular shapes that can be divided, number lines, fraction charts, fraction strips Comparing fractions using <,> and = signs. Mixed numbers (with denominators 2 to 10, 20, 50 and 100) identify parts of a mixed number; say, read and write numerals from diagrams and vice versa; compare mixed numbers using <, > and = signs; arrange mixed numbers in ascending or descending order. Describing parts of a mixed number. Saying, reading and writing in numerals diagrammatic representations of mixed numbers. Comparing mixed numbers using diagrams. Arranging mixed numbers in ascending and descending order. number lines, regular diagrams of various figures 10 GRADE 4
12 CONCEPT Decimals  up to two decimal places say, read and write in numerals any given decimals up to two decimal places; relate fractions with denominators 10 and 100 to decimals; 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 identify the place value of any digit in decimals; Identifying place value of digits represented on the abacus. compare decimals using <, > and = signs; Writing decimal numbers in expanded notation such as 1,23 = 1+ 0,2 + 0,03 write decimals in expanded form; Comparing any two decimals using <, > and = signs. arrange decimals in ascending or descending order; Arranging decimals in order of size. round off numbers to units or tenths. Percentages read and write fractions with denominator hundred; illustrate percentages diagrammatically; use 100 square to express fractions as percentages. Rounding off to units and tenths. Reading and writing fractions with denominator 100. Drawing diagrams representing percentages. Using diagrams to represent percentages fraction charts diagrammatic representations 100 square grids Expressing halves, quarters, fifths and tenths as percentages. Using fractional charts and a 100 square to show fractions, then express as percentages. 11 GRADE 4
13 GRADE 4 / TOPIC : OPERATIONS CONCEPT Addition of whole numbers (0 to ) recall basic addition facts; add within the range including carrying up to three times. 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 Subtraction of whole numbers recall basic subtraction facts; subtract where borrowing is involved; subtract measures. 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. Abacuses flash cards on basic facts, clock faces, counters Multiplication of whole numbers recall basic multiplication facts; complete given multiplication task; multiply where carrying is involved; multiply known measures by numbers; Subtracting measures for example, money, length, time, mass and volume. Recalling basic multiplication facts. Filling in blanks on multiplication charts such as X Rulers, clocks, jars, scales, counters find factors. Multiplying whole numbers by 1 digit numbers including carrying up to three times 12 GRADE 4
14 CONCEPT Multiplying number including carrying For example 1186 x 8 Multiplying measures for example money, time mass and volume. Identifying factors of given numbers. Division of whole numbers (by one digit number) recall basic division facts; divide whole number by long division with or without remainder; Writing numbers as products of factors. Recalling basic division facts mentally. Carrying out long division without a remainder. Money, number lines rulers divide measures by whole numbers. Carrying out long division with onedigit remainders. Addition of proper fractions (where denominators are the same and no more than 3 terms are involved.) add three proper fractions with the same denominator. Subtraction of proper fractions subtract proper fractions with the same denominators. Dividing measures by numbers. Adding proper fractions. Number lines, fraction charts, fraction diagrams Subtracting fractions with the same denominators, for example, 75 = Number lines, fraction charts, diagrams 13 GRADE 4
15 CONCEPT Multiplication of proper fractions and conversion of mixed numbers (with denominators from 2 to 10 inclusive and 100) multiply fractions by whole numbers; change mixed numbers to improper fractions and vice versa; express fractions with denominators 100 as percentages. Changing improper fractions to mixed numbers. Changing mixed numbers to improper fractions. Expressing fractions with denominator 100 as a percentage such as 30 = 30% 100 Number lines fraction chart percentage square grid Multiplying fractions by whole numbers. Finding fractions of numbers and measures such as ¾ of $12 Addition of decimals (up to two places) add decimals. Revising place values in decimals. Adding decimal numbers such as 324, ,38 Abacuses number lines work cards counters Subtraction of decimals (with up to the two decimal places.) subtract decimals. Subtracting decimals such as 725,68316,79 Abacuses Number lines work cards counters 14 GRADE 4
16 GRADE 4 / TOPIC : MEASURES CONCEPT Money (Money up to $100,00) express money in decimal form; write money in expanded form; convert cents to dollars and vice versa. Identifying all Zimbabwean coins and bank notes. Listing all Zimbabwean bank notes and coins. Real coins and bank notes Plastic or card representations of money 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 = $ ( GRADE 4
17 CONCEPT Time use units of time; convert time from one unit to another; tell time to the nearest 5 minutes ; use a.m. and p.m., noon and midnight to tell time. Giving times when events occurred. Giving the duration of an event. Converting units of time from one form to another for example. 60min = 1hr 14 days = 2 weeks = fortnight Calendars Watches sun dials conversion charts clockfaces 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. Mass convert kilograms to grams and vice versa; find the mass of different objects by weighing. Using a.m. p.m. noon and midnight to tell time. Expressing kilograms as grams and vice versa. Finding and comparing masses of objects. Scales, balances, beam balances, containers 16 GRADE 4
18 CONCEPT Length (up to 100m.) measure lengths to the nearest mm, cm or m; estimate lengths using spans and paces. Stating and using the conversions: 10mm = 1cm 100cm = 1m 1000mm = 1m Strings, Rulers, tape measures, click wheels, trundle wheels Estimating lengths Finding lengths of objects. Comparing lengths. Rate compare two quantities. Linking two measures correctly to express rate for example kilometres per hour (km/h) Distance tables, clock faces. Area find areas of rectangles using the formula Area of rectangle = L x W. Using nonstandard units to estimate lengths and widths. Square and rectangular shapes, rubber bands (assorted colours), Estimating area of squares and rectangles by using spans or paces. string 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. Using formula to find area of rectangles. 17 GRADE 4
19 CONCEPT Volume and capacity 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. Graduated containers, water 1  litre containers Converting millilitres to litres and viceversa using 1 litre = 1000 millilitres. ½  litre containers ¼  litre containers Directions, angles and lines indicate North, South, East and West; recognise 1, 2, 3 or 4 right angles. Indicating N, S, E, W. Drawing a compass and labelling cardinal points. Identifying and telling the number of right angles on the compass. Compass, maps card strips, diagrams, rectangular cards, rulers 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 GRADE 4
20 CONCEPT Shapes identify different solid and plane shapes; identifying various shapes in given patterns. Identifying, naming and drawing representations of cylinders, cubes, rectangular prisms, squares, rectangles, rightangled 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
21 GRADE 4 / TOPIC: RELATIONSHIPS CONCEPT 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; 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 collect and record data. Classifying data. Using information to draw bar graphs. Reading and interpreting information on bar and straight line graphs. /im 20 GRADE 4
22 GRADE 5 SYLLABUS 21 G
23 GRADE 5 / TOPIC : NUMBER CONCEPT Whole numbers Range (0 to ) Place value of any digit count forwards and backwards; say, read and write numbers in the range; 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. Saying, reading and writing in numerals and words numbers in the range. 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, Abacuses flash cards charts counters 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 = G
24 CONCEPT Proper fractions (where the denominators are 2 to 10, 20, 50 and 100) say, write and read fractions with denominators in the given range; compare fractions; write fractions in their equivalent forms as well as their lowest terms; differentiate between numerator and denominator. Breaking down wholes into equal parts and relating them to the whole. Comparing fractions using <, > and = signs. Writing fractions in their equivalent forms and reducing them to their lowest terms. Fraction charts work cards flash cards Arranging a set of fractions in ascending or descending order. Mixed numbers identify mixed numbers; solve problems involving mixed numbers; Using the terms numerator and denominator. Forming mixed numbers by putting together wholes and fractions of wholes for example. Fraction charts, Diagrams Regular objects convert mixed numbers to improper fractions and viceversa; 2 and 3 4 use <, > and = signs correctly when comparing mixed numbers Reading, interpreting and writing mixed numbers. Using diagrammatic representations of mixed numbers. Converting mixed numbers into improper fractions and viceversa. 23 G
25 CONCEPT Numeration systems (Arabic and roman numerals) say, read and write Roman numerals; convert Roman numerals to Arabic numerals and vice versa. Comparing two mixed numbers using signs <, > and = signs. Familiarising pupils with Roman numerals from 1 to 50 and 100. Writing numbers 1 to 20 in Roman numerals. Number cards Conversion charts Decimals (up to 3 places) say, read and write in numerals, decimals with 1, 2 or 3 decimal places; determine place value of a digit in a given decimal; interpret diagrammatic representations of decimals; round off to the nearest unit, tenth and hundredth; compare decimals using the <, >, and = signs. Showing how the Roman numeration system is built from basic numerals for 1,5, 10 and 50. Saying, reading and writing in numerals up to 3 decimal places. Giving values of digits in numbers up to 3 decimals places with no more than 5 digits. Interpreting diagrammatic representation of decimals. Comparing decimals using the <, > and = signs. Rounding off decimals to the nearest unit, tenth and hundredth. Abacuses Diagrams of fractions, decimal fraction charts 24 G
26 CONCEPT Percentages express fractions as percentages and vice versa; express one quantity /amount as a percentage of another; compare percentages using the <, > and = signs. Expressing percentages as fractions and vice versa. Expressing one quantity /amount as percentages of another. Comparing percentages using the <, > and = signs. Finding percentages equivalent to ,, and square grid, charts 25 G
27 GRADE 5 / TOPIC: OPERATIONS CONCEPT Addition of whole numbers (involving carrying in 4 places within the range 0 to ) Pupils should be able to: recall basics addition facts; add with carrying involved; add measures; Recalling basic addition facts, such as, 8+7=15 9+6=15. Adding with carrying. Abacuses flash cards work cards counters use the associative law. Adding measures where whole numbers are involved. Deducing and generalising the associative and commutative laws. Subtraction of whole numbers (0 to ) recall basic subtraction facts; subtract by decompositional equal additions; subtract measures. Recalling basic subtraction facts. Subtracting measures where whole numbers are involved. Subtracting by decomposition and equal additions up to 4 places. Abacuses flash cards. work cards counters 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 ) recall basic multiplication facts; multiply by one digit number; multiply by two digit numbers; multiply by multiples of 10 and 100; Recalling basic multiplication facts up to 10x10 including product values of 0. Multiplying by one digit numbers for example x 9 = Multiplying by 2 digit number for example 756 x 24 = Multiplication chart dial for multiplication counters deduce and generalise multiplication processes; Multiplying by multiples of 10 for example 948 x 80 multiply measures. Multiplying by multiples of 100 for example 72 x 300 = 26 G
28 CONCEPT Pupils should be able to: Multiplying measures where whole numbers are involved. Division of whole numbers recall basic division facts; Deducing and generalising on multiplication of numbers for example 2x3=3x2, (2x3)x4=2x(3x4) Recalling basic division facts. Charts and (to include long division by two digit numbers and multiples of 10 and 100 up to 1000 within the range 0 to ) carry out long division by one/two digit number divisors, with or without remainders; divide numbers involving measures where whole numbers are involved. Dividing by one digit numbers using long division. Dividing by two digit numbers using long division. tables counters Dividing by multiples of 10 and 100. Addition and subtraction of decimals (up to 2 decimal places.) add and subtract decimals; convert fractions to percentages and vice versa. Identifying decimals and place values. Adding and subtracting decimals. Abacuses flash cards work cards Adding and subtracting decimal measures. Multiplication and division decimals identify place value; multiply and divide decimals. Recalling multiplication and division facts. Multiplying and dividing by multiples of ten, single digit whole numbers and two digit whole numbers. Abacuses flash cards work cards Converting fractions to decimals and vice versa. 27 G
29 CONCEPT 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; Identifying numerators and denominators. Adding and subtracting fractions with the same denominators. Equivalent fraction Charts. rods and blocks add and subtract proper fractions with different denominators. Finding common denominators. Finding equivalent fractions. Adding and subtracting proper fractions with different denominators. Multiplication of fractions (by whole numbers not exceeding 10 and the use of percentages.) multiply proper fractions by whole numbers; change fractions to percentages and vice versa; Recalling basic multiplication facts. Multiplying whole numbers by proper fractions and vice versa. Number lines, diagrams on ratio represent ratio in three ways; Changing fractions to percentages and vice versa. use "of" to mean multiply. Using the word "of " such as of 12, 25% of Writing ratio in 3 ways. Finding part of a whole by multiplying by a fraction. 28 G
30 CONCEPT Combined operations Addition and subtraction Pupils should be able to: work out exercises which combine addition and subtraction. Adding and subtracting whole numbers by first adding before subtracting such as = = 119 = 2 Adding and subtracting fractions by first adding before subtracting such as = = = G
31 CONCEPT Pupils should be able to: Multiplication and division work out exercises which combine multiplication and division of whole numbers; Dividing whole numbers by multiplying with the inverse of the divisor such as = x = 3 and x2 = x x = work out problems which combine multiplication and division of fractions. Dividing fractions by multiplying with the inverse of the divisor such as: = 4 1 x 1 2 = 2 1 and x = x x = G
32 GRADE 5 / TOPIC: MEASURES CONCEPT Money give relationships between coins and bank notes Calculate change. Identifying all the denominations of the Zimbabwean Currency. Applying knowledge of money for example in shopping, selling and paying bills. Shop articles Zimbabwean coins and bank notes. Bills and statements. Time read and use time. 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 Watches Clockfaces Sundials Sand bottle/egg Timer Calendars Digital watches Telling time to the nearest minute, using a.m and p.m. Estimating time from shadows and from the position of the sun. 31 G
33 CONCEPT 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. Mass (quantities up to 5kg) find masses of quantities/objects; estimate masses up to 5kg. Establishing that 1000grammes = 1 kilograme. Measuring the masses of quantities up to 5 kilograms to the nearest 50grams. 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 32 G
34 CONCEPT Length estimate and measure length using standard and nonstandard units; find the perimeter of a figure using formulae. Rate relate two quantities as rate. Measuring distances up to 1km using nonstandard 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 Linking two measures correctly to express rate, for example kilometres per hour (km/h), cents per litre. 30cm rulers Metre rules tape measures rope or string conversion table rectangular shapes square shapes Work cards, charts 33 G
35 GRADE 5 / TOPIC : RELATIONSHIPS CONCEPT Data handling collect data and use it to draw graphs; discuss methods of collecting and organising data; read and interpret information; make observations and report.; Collecting data in groups and presenting it on a graph and table. Interpreting data for example marks for different classes. Reading and extracting information from given diagrams/time tables. Charts Graphs Time tables construct their own time tables. Drawing line graphs and interpreting them. Drawing conclusions on observations. 34 G
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