Module 4: Problem Solving INTRODUCTION

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1 INTRODUCTION Mathematics is conceptualised as the art of understanding and using numbers to acquire and develop numeracy, computational skills, and problem solving ability. This Mathematics syllabus is designed for learners from Standards 1 to 4. It is observed that when learners begin school they already have acquired some mathematical knowledge and skills from their environment through daily living activities. Therefore, this syllabus is expected to enhance the knowledge and skills learners already have and build on these to introduce new concepts. The syllabus is organised into modules as follows: Module 1: Numbers and Operations The module aims at developing learners concepts on numbers and pre number work. It covers Sorting and Classification, Matching, Counting, Addition, Subtraction and Money. Module 2: Geometry The module deals with geometric flat shapes and solids. Learners will identify flat shapes such as squares, rectangles, triangles and circles. They will also identify solids such as cubes, cuboids, cylinders and spheres. Module 3: Measures The module intends to develop in learners the skill in measuring length, area, mass, capacity and time. The learners will compare, estimate and measure objects in the environment using non standard and standard instruments and units. Module 4: Problem Solving The module introduces learners to activities such as playing mathematical games, solving simple puzzles, carrying out simple investigations and solving real life, non - routine and challenging problems. The activities will serve as a basic form of introduction to real Problem Solving. The module will also help learners realise that mathematics is not abstract but has a variety of functional applications in their own lives. Module 5: Statistics The module involves collecting, recording and representing data in pictographs and bar charts as well as interpreting data given in graphs. The modules are subdivided into topics whose focus is given by general objectives. The general objectives give rise to specific objectives, which describe the behaviour pupils should display after being taught specific content. To address the objectives of this syllabus, teachers are expected to develop activities relevant and accessible to the learner s environment. The activities should be learner centred. Emerging issues are catered for in Statistics where learners would conduct simple survey on HIV / AIDS and the environment. Teachers are expected to use examples of the emerging issues where appropriate in the teaching of this syllabus. This mathematics syllabus is designed and developed on the basis that mathematics would be allocated at least four hours per week in the Primary School timetable. RATIONALE Mathematics plays a key role in everyday life as a communication tool that makes extensive use of symbolic notation. It stirs the intellectual challenge, the outcome of which is cognitive development that assists in sustaining the thinking span. It helps to develop mental processes that enhance logical and critical thinking, accuracy and problem solving; all of which are very important in decision making. i

2 Mathematics provides a foundation for logical and lateral thinking essential in acquiring and organising knowledge, developing concepts and skills, and understanding principles for further learning. It empowers learners to make associations and generalisations, which are important in the study of natural, physical and social sciences as well as in the operation of industry and business. It is also seen in nature and thus helps in the interpretation of the environment. Its study will develop in learners the appreciation of its cultural and traditional development. The subject demands the active participation of learners to explore the world around them through investigation as well as application of learned principles. 1 AIMS OF THE PRIMARY SCHOOL MATHEMATICS PROGRAMME To develop in all learners 1. competence and confidence in the application of computational skills in order to solve day to day problems 2. inquiry skills, creativity, critical thinking and problem solving ability 3. an awareness of mathematics as a language to analyse and communicate information and ideas 4. an awareness of the interrelationship of topics within mathematics and with other subjects 5. positive attitudes and values toward mathematics and its integration with other subjects 6. numeracy and literacy skills compatible with technological and scientific developments 7. the ability to demonstrate the use of acquired mathematical concepts and skills in making informed decisions and drawing conclusions 8. appropriate and adequate concepts for further study of mathematics and other related subjects 9. an awareness and appreciation of the role of mathematics in cultural and traditional activities within the environment 10. an awareness of emerging issues in relation to mathematics. ATTAINMENT TARGERTS At the end of four years of primary education every learner should be able to: - Read and write numbers count the number of objects in a set of less than 1000; read and write in numerals any given whole number less than 1000; read and write whole numbers in words less than 1000; read and write multiples of 2, 3, 4, 5 and 10 through 100; classify whole numbers up to 100 into odd, even and multiples; identify, read and write, in numerals, money values through 100 Pula; find the value of digits in numbers less than 1000; put in order up to five whole numbers less than 1000; using a reference point, identify the ordinal position of any object in a set of no more than 1000; using the correct symbol, (=,<,>), to indicate the correct relationship between two numbers less than 1000 Compute fractions read and write basic fractions; divide a given whole into equal parts: - halves, fourths, fifths, eighths and tenths; identify one-half, one-third and one-fourth of a given region; add two proper fractions having like denominators; subtract one proper fraction from another having like denominators; order fractions with same denominators in terms of size. Carryout basic operations add two 3-digit numbers with carrying given in vertical and horizontal notation giving sum less than 1000; subtract up to 3-digit numbers vertically and horizontally; multiply a 1-digit by a 2-digit or 3-digit number giving an answer below 1000; divide up to a 3-digit number by a 1-digit number with and without a remainder; divide by ten with and without remainder; recognise the relationship among the four basic operations. ii

3 Carryout and compute measurements use a given unit of measurement (non-standard and standard) to determine the length of an object in whole units; estimate length using centimetres and metres; find perimeter of given shapes and objects; determine length, width, and height by measuring shapes/objects in centimetres and metres; find areas by counting squares; state the days of the week in consecutive order; name the months of the year in consecutive order; state the date by day, month, and year from a calendar; state the dates of special events of the year; tell and write time on the hour, half-hour, quarter-hour and in minutes of multiples of 5; estimate capacity of objects; determine capacity of objects by measuring quantities in teaspoons, tablespoons, cups, ml and litres; estimate mass of objects; determine mass of objects in grams and kilograms. Identify geometric figures and shapes identify a circle, a square, a rectangle and a triangle; draw a square, a rectangle, a triangle and a circle; identify solids: cube, cuboid and cylinder; identify a right, acute, obtuse and straight angle. Solve problems use addition, subtraction, multiplication and division to solve problems; play mathematical games; solve simple mathematical games; Carry out simple investigations to solve problems involving numbers, geometry and measures. Interpret graphs read, interpret and draw pictographs and bar graphs iii

4 STANDARD ONE MODULE 1: NUMBERS AND OPERATIONS TOPICS General Objectives Specific Objectives 1.1 Sorting, Classification and Matching acquire knowledge on sorting, classifying and matching objects identify objects according to colour, size, texture and shape group objects by colour, size, texture and shape match objects using one-to-one correspondence 1.2 Counting develop counting skills use number rhymes to count from 1 to use concrete objects to count from 1 to count numbers forward and backwards from 1 to 20 in ones and twos read numbers from 1 to 20 in numerals write numerals from 0 to match objects with numerals and number names arrange numbers in descending and ascending order up to Addition and subtraction 1.4 Classification of numbers add and subtract whole numbers find the total by counting on with sum up to relate addition to putting together use the symbols (+) and (=) in addition of numbers sum up to 20 using concrete and semi concrete objects add horizontally numbers with sum up to relate subtraction to taking away use the symbols ( - ) and (=) in subtraction of numbers 1 to 20, using concrete and semi concrete objects subtract horizontally numbers from 1 up to acquire knowledge on classification of numbers 1.5 Money Carry out addition and subtraction involving money classify numbers from 1 to 20 as odd and even differentiate between counting numbers and position numbers up to identify and name Botswana coins add in multiples of 5 up to 20 thebe subtract in multiples of 5 within 20 thebe 1

5 MODULE 2: GEOMETRY TOPICS General Objectives Specific Objectives 2.1 Lines develop skills in drawing lines identify vertical, horizontal and slanting lines draw vertical, horizontal and slanting lines draw patterns using horizontal, vertical and slanting lines 2.2 Shapes acquire knowledge on geometric shapes/figures MODULE 3: MEASURES identify, sort and name solids as box, tin and ball identify, sort and name flat shapes and figures triangle, rectangle, square, circle TOPICS General Objectives Specific Objectives 3.1 Measuring develop manipulative skills on measurement compare length, area, weight and mass of objects use non-standard units and instruments to estimate the length, area, weight and mass of objects use non-standard units and instruments to check the length, area, weight and mass of objects describe and compare the capacity of containers 3.2 Time acquire knowledge on time identify different times of the day by name and events state the days of the week, months and seasons of the year relate events to the time of their occurrence in the past, present and future state the names of national calendar events 2

6 MODULE 4: PROBLEM SOLVING TOPICS General Objectives Specific Objectives 4.1 Games and Puzzles develop knowledge and skills in problem solving play counting games play simple number games involving addition and subtraction play matching games solve simple puzzles 3

7 STANDARD TWO MODULE 1: NUMBERS AND OPERATIONS 1.1 Counting develop further knowledge on counting skills 1.2 Addition and Subtraction 1.3 Multiplication and Division 1.4 Classifications of numbers count up to 50 in 1s, 2s, 5s and 10s compare sets of objects by their number properties read and write numbers in numerals up to read and write number names up to add and subtract whole numbers identify and use place value of up to Tens add whole numbers with sum up to subtract whole numbers from 50 without decomposition relate addition to subtraction (subtraction reverses addition) multiply and divide whole numbers relate multiplication to repeated addition use symbols (x) and (=) in multiplication of one digit numbers with product up to multiply one digit numbers with product up to relate division to repeated subtraction, grouping or equal sharing use symbols ( ) and (=) in division of numbers up to 50 by divide even numbers up to 50 by relate multiplication to division (division reverses multiplication) develop further knowledge on classification of numbers classify numbers as odd and even (numbers from 1 to 50) 1.5 Fractions identify and represent fractions identify equal parts, halves, thirds and quarters read and write fractions 1, 1 2, 1 3, 1 4, 1.6 Money carry out addition and subtraction involving money add halves; add thirds and quarters of shapes and objects to show one whole identify half of an even number for numbers up to carry out additions up to 50 thebe carry out subtraction up to 50 thebe obtain change from up to 50 thebe 4

8 MODULE 2: GEOMETRY 2.1 Lines develop further knowledge in drawing lines 2.2 Shapes acquire further knowledge on geometric shapes/figures and solids MODULE 3: MEASURES draw intersecting lines identify T junctions and crossroads from the local environment identify and describe flat shapes and figures by number of sides: square, rectangle, triangle make pictures by tracing around shapes name solids as cube, cuboid, sphere, cylinder 3.1 Length and area carry out activities involving length and area 3.2 Capacity, weight and mass carry out activities involving capacity, weight and mass compare and order up to 3 objects by length, height and area use non standard instruments and units (including parts of the body) to measure and record length, height and area measure and record lengths of objects in metres estimate and measure objects in metres compare and order up to 3 objects by capacity, weight and mass use non-standard instruments to measure capacity, weight and mass measure and record capacity of objects in litres 3.3 Time acquire knowledge on time identify and name non standard and standard instruments of time use non standard and standard instrument to measure time show time as o clock by setting clock hands read, tell and write time as o clock show in sequence daily activities according to their time of occurrence as o clock sequence days of the week and months of the year state, read and write the date (day, month, year) 5

9 MODULE 4: PROBLEM SOLVING 4.1 Games and puzzles develop further Knowledge and skills on problem solving MODULE 5: STATISTICS solve simple problems involving numbers, geometry and measures play games solve puzzles decode information using letters and numbers 5.1 Pictographs acquire knowledge on pictographs collect and record information in tabular form represent the information on pictographs read and interpret information given on pictographs 6

10 STANDARD THREE MODULE 1: NUMBERS AND OPERATIONS 1.1 Numbers acquire further knowledge on numbers count on and backwards within read and write numbers up to 100 in numerals read and identify number names for tens up to a hundred read and write number names up to count in multiples of 2, 3, 4, 5 and 10 up to generate simple number patterns and sequences use the appropriate symbols (=, >, <) to compare two whole numbers up to Addition and Subtraction 1.3 Multiplication and Division acquire further knowledge on addition and subtraction develop further knowledge on multiplication and division use place value of up to Hundreds add hundreds, tens and units by changing the place value (horizontal and vertical) subtract hundreds, tens and units by changing the place - value (horizontal and vertical) find the missing number by counting on fill in the box to represent the missing number in an equation solve word problems involving addition and subtraction build multiplication tables:1, 2, 3, 4, 5 and10, product up to divide numbers up to 100 by 2, 3, 4, 5 and 10 without remainder solve word problems involving multiplication and division 7

11 1.4 Fractions acquire further knowledge on fractions divide a shape into 2, 3 and 4 equal parts describe given diagrams as mixed numbers involving halves, thirds and quarters represent fractions including mixed numbers, using shapes write mixed numbers involving halves, thirds and quarters 1.5 Money gain further knowledge on money identify all local coins and notes compare and order all local coins by value add up to P 100 in Pula only obtain change in Pula up to P make simple bills - sum up to P use the four basic operations to solve real life problems involving money MODULE 2: GEOMETRY TOPICS General Objectives Specific Objectives 2.1 Lines develop further knowledge on lines draw figures and shapes using horizontal, vertical and slanting lines identify diagonals of a square and rectangle draw diagonals of a square and rectangle 2.2 Solids acquire further knowledge on solids identify, describe and name three dimensional figure by number of faces, edges and vertices model three dimensional objects using available materials 8

12 MODULE 3: MEASURES TOPICS General Objectives Specific Objectives 3.1 Length and area develop the skills of measuring and estimation in length and area 3.2 Capacity develop the skill of measuring and estimating in capacity 3.3 Mass develop the skill of measuring and estimating in mass measure and record length in mm, cm and m estimate and record length in mm, cm and m find the area of different shapes by counting whole squares estimate the area of different surfaces in unit squares and check by counting squares measure and record capacity in litres and ml estimate and record capacity in litres and ml measure and record mass in kg and g estimate and record mass in kg and g 3.4 Time acquire further knowledge on time read the calendar read, tell and write time in whole hours, half hours and quarter hours. MODULE 4: PROBLEM SOLVING 4.1 Games and Puzzles develop further skills on Problem solving 4.2 Investigations develop an skills on simple investigations MODULE 5: STATISTICS play games solve puzzles carry out simple investigations involving numbers, geometry and measures make mobiles from shapes 5.1 Graphs acquire knowledge on graphs collect and record information in tabular form using tally marks represent information on pictographs and bar charts read and interpret information given in pictographs an bar charts 9

13 STANDARD FOUR MODULE 1: NUMBERS AND OPERATIONS 1.1 Sorting and classification acquire further knowledge on sorting and classification identify a set of numbers according to multiples of 2, 3, 4, 5, 10 up to find factors of selected numbers up to Number acquire further knowledge on numbers count in 10s and 100s up to use place value of up to Thousands read and write in numerals and words numbers up to describe a number in terms of its nearness (position) to another number using number lines use symbols (=, >, <) to compare numbers up to generate patterns involving even, odd numbers and multiples of 2, 3, 4, 5, 10 up to Addition and Subtraction acquire further knowledge on addition and subtraction add two to three numbers (up to 3 digits) sum up to subtract up to 3 digit numbers within solve word problems involving addition and subtraction 10

14 1.4 Multiplication and Division develop further knowledge on multiplication and division build multiplication tables from 1 to multiply up to a three digit number by a one digit number with product up to multiply up to two digit number by divide up to a three digit number by a one digit number without remainder divide up to a three digit number by a one digit number with remainder divide up to a three digit number by 10 with and without remainder carry out multiplication and division in box notation solve word problems involving multiplication and division 1.5 Fractions acquire further knowledge on fractions identify fifths, eighths and tenths illustrate with the aid of diagrams, fifths, eighths and tenths order sets of fractions with same denominators in terms of value add two proper fractions with same denominators subtract proper fractions with same denominators solve word problems involving addition and subtraction of fractions with same denominators up to Money develop further knowledge on money write money in Pula and thebe convert up to P 10 to thebe and vice-versa determine equivalent amounts of up to P100 using coins and notes perform the four basic operations involving money up to P obtain change from up to P make simple bills sum up P solve word problems involving money up to P100 11

15 MODULE 2: GEOMETRY 2.1 Angles acquire knowledge on angles draw two straight lines that meet / cross each other to show angles identify and draw / sketch, right, acute and obtuse angles identify right, acute and obtuse angles within triangles, squares and rectangles in the environment MODULE 3: MEASURES 3.1 Length acquire further knowledge and skills on length 3.2 Area develop further knowledge and skills on area 3.3 Capacity develop further knowledge and skills on capacity 3.4 Mass acquire further knowledge and skills on mass 3.5 Time develop further knowledge and skills on time estimate and record lengths of objects in terms of m and cm, then check actual measurement measure and record lengths of objects using standard instruments and units identify the properties of a square and rectangle measure and state perimeter of shapes in mm, cm and m discover the formula for finding the perimeter of a square and rectangle convert units of length from mm to cm and vice versa convert units of length from cm to m and vice versa discover formula for finding areas of square and rectangle find areas of squares and rectangles in cm 2 using the formula use standard instruments and units to measure capacity measure, compare and record capacity of given container in l and ml use standard instruments to measure mass of objects in g and kg convert units of mass from g to kg and vice - versa use the four basic operations in solving mass problems read, tell and write time from digital displays / watches (restrict to 12 hour notation) read, tell and write the time in hours and minutes from digital displays and clock faces state as a.m. or p.m. in terms of 12 hour clock time of the day read and use simple time - tables involving same day and single journey 12

16 MODULE 4: PROBLEM SOLVING 4.1 Games and Puzzles develop further knowledge and skills on problem solving 4.2 Investigations develop further understanding on simple investigations MODULE 5: STATISTICS play games solve puzzles carry out simple investigations involving numbers, geometry, and measures conduct a simple research project 5.1 Graphs acquire further knowledge and skills on graphs conduct a simple survey on emerging issues and the environment represent data in a tabular form draw pictographs and bar graphs using information from the survey interpret information given in a graph find mode from a given data 13