Mathematics Teacher’s Guide - Pdf.usaid.gov

content, action, standard for performance. The conditions, content and action should also belinked to the way the assessment is done. Class settingHere we give advice to the teacher on how to organize the class room. In most cases we advisethe teacher to arrange desks so as to allow pair/group work. We also specify if a lesson is to takeplace outside or indoor. MaterialsHere we mention all the teaching aids needed for delivering a period content. For every periodthe teacher needs to look at the list of materials provided at the beginning of every period andprepare them in advance. These materials are very useful for the understanding of the period(lesson). Therefore the teacher should try and find them and whenever they need to be broughtby pupils, they need to be told in advance. ReferencesHere we have included the resources (books and articles from websistes) that we have usedto produce each period. When the teacher is preparing her/his lessons she/she is advisedto mention all the references (resources) he/she used, following the models provided in thisteacher guide. Steps/TimingIn this column we provide the main parts of a lesson and time allocated to each part. These partsare: Introduction (5 minutes), Development (25 minutes) and Conclusion (10 minutes). Teacher’s activitiesIn this column we provide all the steps/activities that the teacher has to follow/do in order tofacilitate the period (lesson). Pupils’ activitiesThis part includes activities that the pupils have to do in response to teacher’s guidance. Generic competences and cross cutting issues to be addressedIn this column we provide cross cutting issues and competences developed in each part of theperiod (lesson) with a brief explanation on how they have been integrated in the different partsof the period/ lesson.b) Other periodsEach sample period is followed by other periods which are in different formats: Periods introducing new conceptsThey are not in a table like the sample period. They are not as detailed as the sample periods.But they follow the same main parts of a lesson as the sample period. They provide the teacherwith examples of problems (activities) and some suggestions on how to go about teaching theperiod, but the teacher should develop it further according to the needs of the pupils in theclass and write it up in the sample period format as all the lessons in class have to be taughtfollowing the format provided by Rwanda Education Board (REB). In the development part ofthese periods we have provided Math facts whose meaning is the same as the summary usedfor the sample period. Periods on exercises and word problemsThe title of these periods are planned in the unit at glance table but are not developed in thisguide.ix

II. Methodological note (advice to teachers)1) Steps of a lessonIn this teacher guide every period (lesson) introducing new a concept follows the following steps:a. IntroductionThe warm-ups and games introduce a period. However, a period can also be introduced by anothertype of activity or correction of the homework. It is good to vary ways of introducing a lesson.b. Developmenti. Presentation /DiscoveryThis is the first part of the development of a lesson. In learner centered approach, it includes activitiesthat lead to pupils’ discovery of concepts as presented below: Devolution of the taskA period introducing a new concept always starts with a scenario/situation instead of an exercisethat is a straight calculation. Pupils are engaged in learning activities in groups or individually. At thisstep, the teacher helps learners to form groups, provides clear instructions and required materialsso that they are facilitated to discover the new learning either through observations and discussions,manipulations, problem solving, etc. Didactic situation (Sharing/communication)One pupil (pair/group representative) shares the findings/answers with the whole class.Note:- At the end of every activity used in presentation, we have provided answers to help the teachersee how it should be done.- When a period (lesson) requires the use of teaching aids the teacher needs to avail them beforethe lesson starts.ii. Summary/Math factsInstitutionalization: this step is closely linked to the previous ones. After pupils have done activitiesand shared their findings (after discovering the new learning) the teacher needs to facilitate themto draw conclusions/ to make a summary of what has been learnt. He/she can for example proceedby asking them questions which lead them to making conclusions. Then finally he/she leads them tomake a synthesis from what they have said.iii. ApplicationThis is the third part of the development of a lesson. In this part we provide different activities toreinforce the learning. For every activity provided in this part it is good to indicate if the activities areto be done individually, in pairs or in groups – vary to avoid monotony!Whenever you give an activity, give clear guidance on how to do it.Where activities provided in this guide are few, you are advised to increase them using availableresources in your school as well as your creativity.c) Conclusioni. AssessmentThis is the first part of the conclusion. In this part we provide activities meant to check if theinstructional objectives have been achieved.ii. HomeworkThis is the second part of conclusion. Here the teacher provides homework activities and pupils copyx

them in order to do them at home.2) Developing competencesCompetences are acquired over time through cumulative effect of a competence approach tolearning. We should bear in mind what competences are. They are rarely developed in isolation. Theyare interconnected and developed simultaneously.To develop competences in math lessons, the teacher needs to use different methods and techniquesto develop pupils’ competences both generic and subject competences. Developing all competencesrequires math teachers to adopt approaches that encourage and enable pupils to think critically,to carry out research, to solve problems, to be creative and innovative, to communicate and to cooperate.You need for example to help pupils develop their communication skills by making sure they discussin English in pair/group work. Besides, when pupils are answering questions you need to encouragethem to answer by using complete sentences. This will enhance their language skills.You also need to help them develop their interpersonal and management skills by encouragingthem to choose a chair person, a secretary/ group representative while working in groups. After eachgroup work, a representative/secretary has to share findings /answers with the whole class. This alsohelps them develop their communication.The activities included in this guide aim to develop pupils’ critical thinking skills. The teacher isadvised to follow this model and avoid activities which are all similar.So whenever you provide activities try and find activities which are challenging, which require pupilsto think deeply in order to develop their critical thinking.Also try and give them activities which require research and problem solving. When preparing wordproblems try to give ones related to real life. This helps pupils see the importance of learning Mathand hence like it. You can also follow models provided in this teacher guide and improve them wherenecessary.Here are some of the techniques to be used:a) Unit warm-ups and gamesThe teacher is advised to ease into a lesson/period by facilitating chanting, playing mentalmath games or doing review activities for 5 minutes. (Note : each warm-up/game is explainedat the beginning of a unit). Chanting can be used for enhancing counting by following a certainrhythm. The rhythm may be done through clapping, thumping, beating on the desk, etc.When facilitating playing the games/warm-ups, the teacher should engage the pupils inlearning the games and make it fun. And when the activity seems too easy, it can be mademore difficult. When pupils are familiar with a particular game/warm-up, it is better to let onepupil leads the game. This motivates pupils as they participate more in their learning.b) Group/pair work and discussionTeachers are advised to increase group work and presentations by a team member to helppupils support each other and develop interpersonal and management skills, cooperation,communication as well as peace and values education.3) Inclusion of cross cutting issuesWhen preparing /delivering a period (lesson) the teacher needs to consider the cross cuttingissues suggested and make sure they are fully developed in the period(lesson). For example, forgender balance the teacher needs to make sure groups are well mixed with boys and girls. Andwhen choosing a pupil to answer a question or to present on the board the teacher needs tobalance between girls and boys.xi

When pupils are working in groups, you need to encourage each group to discuss peacefully andreach consensus. By doing this you develop peace and values education.For the other cross cutting issues such as: financial education, environment and sustainability,standardization culture (the mostly used in this teacher guide) pupils need to be given enough timeto discuss them so that they can understand them fully and be ready to apply them in their daily life.When preparing lessons, try to integrate as many cross cutting issues as possible so that pupils canlink Math with other aspects of life and be able to use them to solve their daily life problems.For inclusive education: It is really important to find ways to accommodate and include pupils withphysical or mental challenges. If for example, a pupil cannot see well, make sure you are giving clearverbal instruction and having another pupil help him or her out. If a pupil cannot walk easily, makesure you do not exclude him or her from activities that require movement. Find a way to involvethem – as a recorder of results, a timer, etc.4) Assessing competencesCompetences are developed over time and assessed through end unit assessment. To ensure theirprogressive development, each period is assessed. It is advised to encourage peer assessment. Afterpupils have done the assessment, they exchange notebooks then the teacher facilitates correctionon the board, or a volunteer shows the answer on the board. Finally pupils correct each other andgive feedback to the teacher. The homework is normally corrected in the next period.Note: For assessment and homework the teacher can sometimes vary the method and allow pupilsto correct themselves, after correction on the board.xii

1Lesson 6:Subtraction of fivedigit numbersLesson 5: Additionof five digit numbersLesson 4: OrderingnumbersLesson 3: Comparingfive digit numbersLesson 2: Placevalue in a five digitnumberLesson 1: Readingand writing numbersup to 100 000Period 2Exercises and problems on subtraction of two 5digit numbers without borrowingSubtraction of two 5 digit numbers withoutborrowing and its application to daily lifeExercises and problems on addition of two5 digit numbers without carrying, the sumdoesn’t exceed 99 999.Addition of two 5 digit numbers withoutcarrying (the sum doesn’t exceed 99 999) andits application to daily lifePeriod1Period 2Subtraction of two 5 digit numbers withborrowing and its application to daily lifePeriod3Addition of two 5 digit numbers withcarrying (the sum doesn’t exceed 99 999)and its application to daily lifePeriod 3Exercises and problems onsubtraction of two 5 digitnumbers with borrowingPeriod4Exercises and problemson addition of two 5 digitnumbers with carrying, thesum doesn’t exceed 99 999.Period 4Ordering numbers: descending order (and its application to daily life)Ordering numbers in ascending order (and its application to daily life)Period 1Period 2Period1Exercises on comparing two 5 digit numbers using place value and itsapplication to daily lifeExercises on readingand writing a five digitnumber (and 100 000)in figures and wordsusing place value (and itsapplication to daily life)Period 7Comparing two 5 digit numbers using place value and its application to daily lifeReading andwriting a five digitnumber(and 100000) in figuresand words usingplace value and itsapplication to dailylifePeriod 6Period2Reading andwriting afive digitnumber(and100 000)in figuresusing placevalue and itsapplication todaily lifePeriod 5Period 1Exercises on place value in a five digit numberExercises on readingand writing a fourdigit number infigures and in wordsusing place valueand its applicationto daily lifePlace value in a five digit numberReading and writinga four digit numberin figures and inwords using placeand its applicationto daily lifePeriod 4Period2Reading and writinga four digit numberin figures usingplace value and itsapplication to dailylifeReading and writinga two and threedigit number infigures and wordsusing place valueand its applicationto daily lifePeriod 3Period 1Period 2Period 1Topic area: Numbers and OperationsKey competence: To be able to read, write, compare and calculate whole numbers up to 100 000.Unit at GlanceUnit 1: Mathematical Operations on whole numbers up to 100 000

2Exercises and problems on addition and subtraction of five digit numbersPeriod 1Exercises and problems on multiplying a four digit number by atwo digit number, the product doesn’t exceed 99 999)Multiplying a four digit number by a two digitnumber (the product doesn’t exceed 99 999)and its application to daily lifeExercises and problems on multiplying a whole number by 10, 100, 1 000, 10 000, the productdoesn't exceed 99 999.Exercises and problems on division of a whole number by 10, 100, 1000, 10 000.Period 2Feedback and RemediationPeriod 1AssessmentLesson 16: Revision of the unitLesson 15: Assessment of unit 1 (part 2)Lesson 17:assessment of theunitExercises and problemson division of a five digitnumber by a 1 digit numberwith remainder.Dividing a whole number by 10, 100, 1000, 10 000and its application todaily lifeDivision of a five digit number by a 1digit number with remainder and itsapplication to dailyPeriod2Exercises and problems on division of a fivedigit number by a one digit number withoutremainderDivision of a five digit number by a one digitnumber without remainder and its applicationto daily lifePeriod 4Problems involving addition and multiplication andproblems involving subtraction and multiplication(using a four digit nu

Teacher’s Guide Primary 4 Primary 4. Mathematics Teacher’s Guide Primary 4. Authors Mary Sugrue . Unit 9: Area and land measurements . Here we mention all the teaching aids needed for delivering a period