0845 Primary Mathematics Teacher Guide 2016

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Teacher GuideMathematicsi

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ContentsSECTION 1: INTRODUCTION.11.1 How to Use this Teacher Guide .21.2 Cambridge Primary.21.3 The Curriculum Framework.4SECTION 2: PLANNING .62.1 Getting Started .62.2 A Consistent Approach .62.3 Descriptions of the Planning Stages .82.4 Phase 1 – Creating a Long-TermPlan . 112.5 Phase 2 – Creating a Medium-TermPlan .202.6 Phase 3 – Creating a Short-TermPlan .28SECTION 3: TEACHING APPROACHES .33SECTION 6: THE LEARNINGENVIRONMENT.586.1 Classroom Organisation.586.2 Creating a Positive Atmosphere.60SECTION 7: SUPPORT ANDRESOURCES .617.1 Resources from Cambridge.617.2 Training Available from Cambridge .617.3 Support with Administration for PrimaryCheckpoint .627.4 Enquiries .627.5 Resources Recommended byCambridge .637.6 A Further Note on MathematicsResources .633.1 Working in Groups, Pairs and asIndividuals .33APPENDIX A: TEACHER TRAININGACTIVITIES.713.2 Sharing the Learning Intention.35A1 Agreeing Terminology .723.3 Active Learning .37A2 Producing a Lesson Plan Format . 743.4 Differentiation .38A3 Preparing and Delivering a Lesson .78SECTION 4: ASSESSMENT .40A4 Sharing Learning Intentions.794.1 What is Assessment? .40A5 Creating Success Criteria withLearners .824.2 Using Formative Assessment to RaiseAchievement .414.3 Developing Assessment in theClassroom .444.4 Assessment Techniques.444.5 Assessment Available fromCambridge .52SECTION 5: INFORMATIONCOMMUNICATION TECHNOLOGY ANDMATHEMATICS .55A6 Taking Stock of Formative AssessmentSkills.83A7 Using Questions Effectively .88APPENDIX B: SAMPLE SCHEMES OFWORK .89APPENDIX C: SAMPLE LESSON PLANS. 101APPENDIX D: OPPORTUNITIES FORICT . 112APPENDIX E: PLANNING TEMPLATES. 134iii

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Section 1: IntroductionSECTION 1: INTRODUCTIONWelcome to the Cambridge Primary Teacher Guide for Mathematics.This guide is designed to provide a suggested approach to the implementationand management of Cambridge Primary in your school.It offers: An introduction to the Cambridge Primary Mathematics curriculumframework Step-by-step guidance on the planning process, with exemplification at eachpoint and helpful teacher training activities with resources Advice on differentiation and how to integrate this into your teaching Suggested techniques for implementing formative assessment andintegrating this into your lesson planning Sample lesson plans and some ideas on activities and resources to help getyou started Advice on monitoring Advice on classroom practice Advice on resources Information on Progression Tests and Cambridge Primary Checkpoint tests Guidance on support and training available from Cambridge Guidance on administrationA comprehensive scheme of workIn addition to extracts provided in this guide a full scheme of work coveringthe entire programme has been provided as a starting point. Full coverage isprovided in this way to accommodate new schools starting at any stage in theprogramme. As we will explain, a scheme of work is a process rather than arigid structure and these plans should be constantly amended in response toyour own observations as a classroom teacher and other local considerationsincluding the resources you may already have available at your school. Theseschemes of work are therefore in no way compulsory but simply offer asuggested starting point for covering the content of the curriculum withina suggested year of three terms each of 10 weeks duration. These can beexpanded to suit the number of weeks available in your own terms and theholiday arrangements at your school.1

Cambridge Primary Mathematics Teacher Guide1.1 How to Use this Teacher GuideThis guide provides guidance and advice on the essential processes of implementingCambridge Primary and it is designed to cater for: Schools that are teaching a Cambridge programme for the first time and need to move from acompletely different system of planning Schools that already deliver one or more Cambridge programmes but are new to CambridgePrimarySchools new to Cambridge will find all sections of the Teacher Guide will be relevant to them.It provides a step-by-step guide through the process of implementing Cambridge Primary,offering a suggested breakdown of the curriculum across the available teaching time, samplelesson plans and sample lessons to get you started.Existing Cambridge schools may be more familiar with certain aspects covered in this guide,especially if they already deliver the lower secondary phase of the Cambridge programme(now called Cambridge Secondary 1). This guide is written so that schools new to Primary canmake use of the sections most relevant to them (e.g. Section 2: Planning or Section 3: TeachingApproaches).1.2 Cambridge PrimaryCambridge Primary is an education programme for young learners. It combines a world-classcurriculum, high-quality support for teachers and integrated assessment. The programmehas been developed by University of Cambridge International Examinations and is used inprimary schools around the world. Cambridge Primary helps schools develop learners who areconfident, responsible, innovative and engaged.Cambridge Primary covers English English as a Second Language Mathematics Sciencefor learners aged 5–11. It provides curriculum frameworks with integrated assessment for eachsubject.2

Section 1: IntroductionCambridge Primary provides a solid foundation for later stages of education.It starts learners on an educational journey, focusing on what they should be able to do at eachstage of primary education. It develops skills, knowledge and understanding that will preparethem for a smooth transition to Cambridge Secondary 1 and beyond.Cambridge Primary offers optional, integrated assessment.The assessment structure tracks learner progression through primary education. Learnerstaking Cambridge Primary Checkpoint receive a Statement of Achievement and detailedfeedback on strengths and weaknesses.Cambridge Primary supports teachers in providing the best teaching and learning.Schools adopting Cambridge Primary gain access to first-class support for teachers throughpublications, online resources, training and professional development.Cambridge Primary is practical and flexible.No part of the Cambridge Primary curriculum is compulsory, giving schools the flexibility tochoose the elements that are right for their learners. This means that they can use CambridgePrimary while following their school or national curriculum, or offer the entire programme.Cambridge Primary has been developed by University of Cambridge International Examinations,the world’s largest provider of international education programmes and qualifications for 5–19year olds. Our programmes and qualifications are taken in over 160 countries in 9,000 schoolsand recognised by universities, education providers and employers across the world.Cambridge international education programmes and qualificationsCambridge Primary (5–11 years*)Cambridge Secondary 1 (11–14 years*)Cambridge Secondary 2 (14–16 years*)Cambridge Advanced (16–19 years*)Cambridge PrimaryCambridge Primary CheckpointCambridge Secondary 1Cambridge CheckpointCambridge IGCSECambridge International AS and A LevelCambridge Pre-U*Age ranges are for guidance only.3

Cambridge Primary Mathematics Teacher Guide1.3 The Curriculum FrameworkThe Cambridge Primary Mathematics framework provides a comprehensive set of learningobjectives for Mathematics. The objectives deal with what the learner should know and whatthey should be able to do in each year of primary education. The learning objectives providea structure for teaching and learning and a reference against which learners’ ability andunderstanding can be checked.There are six stages. Each stage reflects the teaching targets for a year group. Broadlyspeaking, stage 1 covers the first year of Primary teaching, when learners are approximatelyfive years old. Stage six covers the final year of Primary teaching when learners areapproximately eleven years old. It may be appropriate to introduce this framework at slightlydifferent ages to suit your own particular circumstances.The Mathematics framework is presented in five content areas. The first four content areasare all underpinned by Problem Solving. Mental strategies are also a key part of the Numbercontent.Strands in the Curriculum FrameworkMATHEMATICSCURRICULUM OLVINGContinuity, progression and balanceThe framework allows for continuity and progression both within and between the stages.You can pick any objective and trace its pathway through the stages of the framework.This continuity allows the curriculum to be consistent and ‘uninterrupted’ between stageswhilst progression ensures that learners move forward steadily. The table below shows howknowledge and skills can be traced through the framework.4

Section 1: IntroductionAn example of progression through the frameworkStage 1Stage 6NumberBegin partitioning two-digit numbers into tens andones and reverse.NumberKnow what each digit represents in wholenumbers up to a million.GeometryName and sort common 3D shapes usingfeatures such as number of faces, flat or curvedfaces.GeometryVisualise and describe properties of 3D shapes,e.g. faces, edges and vertices.MeasureBegin to understand and use some units of time,e.g. minutes, hours, days, months and years.Handling DataAnswer a question by sorting and organising dataor objects in a variety of ways.Problem SolvingChoose appropriate strategies to carry outcalculations, explaining working out.MeasureRecognise and understand the units for measuringtime (seconds, minutes, hours, days, weeks,months, years, decades and centuries); convertone unit of time into another.Handling DataSolve a problem by representing, extracting andinterpreting data in tables, graphs, charts anddiagrams.Problem SolvingExplain why they chose a particular method toperform a calculation and show working.The strands of the curriculum framework have been selected in order to provide balancedcoverage of the fundamental skills and knowledge of the subject at this level and they havealso been designed to provide a sound foundation for stages seven to nine. Learners should beprepared at the end of stage six to move on smoothly to stage seven.The selection of content in the framework at each level has been chosen to ensure a coherentprogression for the learner. The curriculum framework has been designed to allow sufficienttime for each learner to develop a true understanding of the skills and knowledge required.Teachers themselves are best placed to know the capabilities of their learners and can, ofcourse, choose to supplement the framework as appropriate. What is within the curriculumframework is the content that will be assessed and analysed using the Cambridge ProgressionTests on the Cambridge Primary support site. It is also tested in the Cambridge PrimaryCheckpoint tests for which feedback reports are provided.Whilst it is important to be able to identify the progression of objectives through the curriculum,it is also essential for teachers to bring the different strands together into a logical whole sothat their teaching makes learning meaningful, purposeful and enjoyable. This can be achievedthrough detailed planning and with the teacher’s ability to constantly re-tune their teaching tothe needs of the learners.5

Cambridge Primary Mathematics Teacher GuideSECTION 2: PLANNING2.1 Getting StartedThis section will look at the process of planning, ensuring that you cover all ofthe content of the curriculum for stages 1 to 6, given the teaching time youhave available within each year.We will start with identifying exactly what you need to plan: Complete coverage of the Mathematics content for all of the stages, or thosethat you teach Progression and continuity of the relevant underpinning skills and content ofMathematics The best order in which to teach the required units Detailed lessons, led by clear learning objectives that the learners willunderstandAnd why you need to plan: To ensure appropriate timings are given to the different aspects of thecurriculum To be clear about what can be assessed as a result of a lesson/unit of work To ensure a mix of teaching and learning styles in delivery – according to yourlearners’ needs To ensure that all resources are available to deliver a successful lessonThe following section lays out a step-by-step guide to the planning processincluding how you can build in flexibility to allow you to adapt coverage, deliverystyle and timing to suit your needs.2.2 A Consistent ApproachDownload the curriculum framework for Mathematics from the CambridgePrimary support site www.cambridgeprimary.cie.org.uk and familiariseyourself with the coverage and structure of the programme. Next we are goingto consider how to begin breaking this work down. We can do this in threeclear stages but first it is worth getting all the primary teachers together tocoordinate a consistent approach.6

Section 2: PlanningLook at the diagram below. Start by thinking about the decisions in the white box: approach,terminology and formats.A pathway to implementationPRODUCELONG-TERM M REATE ACHECKLIST OFRESOURCESTEACHApproach:The general approach will largely be decided by colleagues in management.This, for example, may concern the whole curriculum and not justMathematics. Some schools merge subjects across the curriculum. For thepurpose of this guide we assume that Mathematics is going to be taught as aseparate subject.Terminology:Everyone involved needs to understand the terminology used so that, forexample, ‘long-term’ plan means the same to all. This is true whatever theoverall approach within a school.Training Activity: Agreeing Terminology (Appendix A1)In the appendices of this guide you will find an exercise that may becarried out by groups of teachers to reach an understanding of theplanning terms:Long-term [overview],Medium-term [scheme of work] andShort-term [lesson plan].It also includes other relevant terms. When the terminology has beenagreed, planning can begin.7

Cambridge Primary Mathematics Teacher GuideFormats:It is not vital to all use the same documentation for planning but it is veryhelpful for communication and common understanding. They may vary fromsubject to subject if considered necessary, but it is particularly helpful if theformats used for planning are the same for each stage. Templates for all stagesare provided at the back of the guide. Here it is suggested that formats for eachstage of planning are used by all teachers who deliver Mathematics. These willbe discussed in more detail later.Evaluation:Perhaps the most important box is the ‘Evaluation’ box. It is always a goodidea to check how well something works. The diagram shows that this canbe for any stage. If there is a problem delivering a lesson, it is often assumedthat there is something wrong with the lesson plan. This can be true, butsometimes it may be because the medium or long term plan that is beingused needs changing in some way. The white box issues may also need to berevisited.2.3 Descriptions of the Planning StagesLong-term planning involves considering the whole Mathematics curriculum for the wholeschool. This includes taking account of the school calendar for the academic year and allocatinga specific percentage of time for Mathematics to be taught throughout the school. This isgenerally carried out by senior management.It requires pre-planning in terms of required resources, whether these are shared, limited orneed buying in. The most important consideration is timing, thinking about when you will bedelivering a new unit and how often skills need to be re-visited throughout the year. You willneed to think about the order in which knowledge and skills need to be learned.You will need to manage a balance between Number, Geometry, Measures and Handling Data.Problem Solving skills need to be ongoing and sequential.Medium-term planning involves planning coverage of the curriculum in units across an entirestage. This includes taking account of seasons, school events and possible visits to enhancethe learning process.Again, you will need to manage a balance between Number, Geometry, Measure and HandlingData. Problem Solving skills need to be ongoing and sequential across all units taught.Medium-term planning is usually broken down into individual terms. The Scheme of Workprovided by Cambridge for each stage has assumed covering three units per term in anacademic year structured as three terms of 10 weeks each. Term length varies around the worldso we have chosen a relatively compact approach so that you should be able to add further timeas necessary.The units of work can be arranged in various ways to provide a varied and interesting approachto delivering and ensuring coverage of the Mathematics curriculum at each stage.8

Section 2: PlanningAt this point in the process, planning generally considers specific units and the best orderin which they can be taught, building on previous learning and developing knowledge andunderstanding throughout the year. Depending on what you decide, this permits units to betaught in isolation, or in a cross-curricular way, particular to each school’s policies. Over time,you will be able to adapt these plans according to resources and available teaching time, and inthe light of your own particular teaching expertise and confidence.New Teacher’s Tip: If you are new to teaching and unsure about the length of time it takesto deliver a particular topic, then we have provided a comprehensive plan for all stagesfrom which you can make a start. This is not intended to be followed to the letter; it onlyprovides an initial starting point. Do not expect your plan to be perfect first time. Start withan estimate of how long you think a subject will take and adjust your long, medium andshort term plans as you go along so that as you are delivering it you are also fine-tuning it.You are the best judge of the capabilities of your learners and how long it will take them tounderstand each topic, given their existing knowledge.Short-term planning is a lesson plan for a particular lesson. Most commonly, this evolves intoa weekly plan. This is a detailed, working document and is led by the learning objectives for thatsession.It provides: Essential information for all adults involved in the learning and considers the learning needs ofall learners, including those with special educational needs (SEN) and/or gifted and talented Continuity in the absence of regular teaching staff, for example, in times of absence An outline of resources, timings, working groups and assessmentThe real value of a short-term plan is that it influences the next steps in the light of the learner’sresponse to the learning opportunities presented. Detailed examples and templates areprovided in the appendices.The following sections provide a step-by-step guide to the planning process, including someadvice about meeting the training needs of colleagues.The steps of the planning process (1–8) outlined in the diagram overleaf are divided into threelogical phases that form the sub-sections of this section of the guide:2.4 Phase 1 – Creating a Long-term Plan (steps 1–4)2.5 Phase 2 – Creating a Medium-term Plan (steps 5–6)2.6 Phase 3 – Creating a Short-term Plan (steps 7–8)The 8 steps of the process are dealt with in each related sub-section as shown above.9

Cambridge Primary Mathematics Teacher GuideThe Planning Process2.4 Phase 1Creating a Long-term PlanStep 1. Teaching timeFind out:– how many hours there are to teach the subject?– how is the teaching time divided?– how many units you will be able to comfortablyfit into a term.Step 2. ApproachThink about:– how you want to structure the teaching of thesubject?Step 3. Allocate the strandsAllocate the strands for each stage across thenumber of units available per term. Think about thedifferent proportion of work required for each strand.Step 4. Learning objectives by term– Look at the curriculum framework.– Decide which learning objectives will be coveredin each part of the year, e.g. each term within astage.– Decide which learning objectives will be coveredon an ongoing basis throughout the year.– Decide where you are going to fit in the ProblemSolving objectives.You can mark up the curriculum framework (e.g. usea colour code) to show the results.2.5 Phase 2Creating a Medium-term Plan2.6 Phase 3Creating a Short-term PlanLook at Long-Term Planning 2You can use this to record your decisionson when each learning objective should beintroduced in the year.Look at Long-Term Planning 3You can use this to show the results ofyour decisions in Long-Term Planning 2term by term.Step 5. Creating Units– Group ongoing and other learning objectives intotopics and themes creating a logical, progressivesequence of learning including Problem Solving.– Rearrange for challenge, balance, timing, paceand appeal.– Organise the number of units to match theestimated time available from step 1.Print and cut out the individual learningobjectives so you can try differentarrangements on a separate sheet beforefinalising if it is helpful.Step 6. Creating Medium-Term PlansIdentify suitable activities and resources to deliverthe learning objectives in each unit.Indicate how the lesson is to be taught.Look at Medium-Term Planning 1You can record your decisions withcomments and timings on this templatealongside the other information.Medium-Term Planning 2does not have these additional columns.Step 7. Creating Lesson PlansIdentify what you are going to teach and how youare going to teach it.Look at Short-Term PlanningInstructions are printed on the template onPage 31 of the Planning section.Step 8. Evaluate the lesson and the planningAmend your scheme of work and lesson plans tobest suit the needs of your learners.10Look at Long-Term Planning 1You can show the allocation of strandshere across the terms.Later you can use this grid to show howthe units are allocated either for one stageor all six, by entering their titles instead.

Section 2: Planning2.4 Phase 1 – Creating a Long-Term PlanStep 1. Teaching TimeFirst you will need to establish the number of terms available, the length of the terms and thenumber of teaching units you will roughly be able to fit into each term. In this guide we willfollow a structure of three terms of ten weeks, per stage.Step 2. ApproachNext, you will need to decide the over all approach you want to take to the teaching structure ofthe subject. Here are a few helpful prompts to get you thinking along the right lines. Do I have a preferred way of working? How are Mathematics resources available in school? (If they are shared, this could dictatewhen you need to teach specific strands.) How can I ensure that I cover the whole curriculum for the stage during the year? How will I provide opportunities for Problem Solving continuously throughout the year? What is the best order of learning for Problem Solving skills, given the order and content ofthe rest of the learning? How can I sensibly group learning objectives from the curriculum framework to incorporatethem into meaningful units of study?Different planning models may be useful in deciding the most effective way of meetinglearners’ needs. Models can be either linear (each topic delivered consecutively) or spiral (seebelow) or even a combination of both. In this guide and in the published Cambridge Scheme ofWork (which is available on the Cambridge Primary support site to all registered centres) wehave chosen a model in which a combination of all strands are covered within each term.Problem Solving objectives are worked in to every teaching unit as these skills underpin allother strands and help learners understand mathematical relationships and functions moreholistically. This model is sometimes referred to as ‘the spiral curriculum’.NumberGeometryMeasuregolvinProblem STimeHandling DataThe Spiral Planning ModelThe spiral model, shown here, provides astructure where the different strands,represented by the vertical arrows, arevisited and then revisited in a continuousteaching and learning process that allowseach strand to support progress andunderstanding in the other strands.The practical nature of the skills andknowledge of the Problem Solving strandmeans they form part of the substanceand structure of that process.11

Cambridge Primary Mathematics Teacher GuideStep 3. Allocating the StrandsStage 6Stage 5Stage 4Stage 3Stage 2Stage 1Think about how you might distribute the strands over the teaching time available for eachstage. Following the spiral model for example, you might include Problem Solving alongsideyour delivery of every other strand. An overview of the whole six stages might look somethinglike the table below.12Term 1Term 2Term 3NumberProblem SolvingNumberProblem SolvingNumberProblem SolvingGeometryProblem SolvingHandling DataProblem SolvingHandling DataProblem SolvingMeasureProblem SolvingMeasureProblem SolvingMeasureProblem SolvingTerm 1Term 2Term 3NumberProblem SolvingNumberProblem SolvingNumberProblem SolvingGeometryProblem SolvingHandling DataProblem SolvingGeometryMeasureProblem SolvingMeasureProblem SolvingMeasureProblem SolvingTerm 1Term 2Term 3NumberProblem SolvingNumberProblem SolvingNumberProblem SolvingGeometryProblem SolvingMeasureProblem SolvingGeometryProblem SolvingMeasureProblem SolvingHandling DataProblem SolvingMeasureHandling DataTerm 1Term 2Term 3NumberProblem SolvingNumberProblem SolvingNumberProblem SolvingMeasureProblem SolvingGeometryProblem SolvingMeasureProblem SolvingHandling DataProblem SolvingMeasureProblem SolvingHandling DataProblem SolvingTerm 1Term 2Term 3NumberProblem SolvingNumberProblem SolvingNumberProblem SolvingGeometryProblem SolvingHandling DataProblem SolvingGeometryProblem SolvingMeasureProblem SolvingMeasureProblem SolvingMeasureProblem SolvingTerm 1Term 2Term 3NumberProblem SolvingNumberProblem SolvingNumberProblem SolvingMeasureProblem SolvingMeasureProblem SolvingMeasureProblem SolvingGeometryProblem SolvingHandling DataProblem SolvingGeometryProblem Solving

Section 2: PlanningYou will need to decide your approach collectively at the outset of the planning process.Step 4. Ordering the Learning ObjectivesNext you need to work through all the learning objectives in the order in which they appear inthe curriculum framework writing alongside each one which Term or Terms (Term 1 (T1), Term2 (T2) or Term 3 (T3)) you think each one should be delivered in within each stage. An objectivemay need to be revisited in subsequent terms so could appear in T1 and T3 for example. Youwill need to think about the order of learning difficulty in allocating the objectives. The templateLong-Term Planning – 2 has been produced to help you record term allocations, it has acolumn on the right hand side in which you can write the appropriate timing for delivery.You will find that some learning objectives relate to skills that apply to many strands as well asacross the three terms. We have called these ‘Ongoing’ objectives in this guide. You will needto identify these in the curriculum framework and put an ‘O’ beside them in your list. See thecompleted example of Long-Term Planning – 2 included on page 15.Next you will need to consider the Problem Solving objectives. As explained earlier, these aredesigned to be addressed alongside the other strands and this means that they can easily befitted into the content of your final teaching units.Problem Solving in MathematicsThe strand Problem Solving in the Mathematics framework provides a structure for developinga set of skills for investigating and exploring the relationships between functions, skills andknowledge, drawing together the other strands into an articulate whole. This continuousexposure to methods of Problem Solving creates a network of associations in learners’ mindsthat link multiple aspects of the curriculum together. It improves learners’ willingness to try andsolve problems and their perseverance in doing so because over time they will see the successof this method and be able to believe that the systematic nature of it gets results. One crucialaspect of applying Problem Solving techniques is that learners come to understand that thereis more than one way to solve a problem. This leads them on to the understanding that there isa selection of strategies they could employ to solve a particular problem and that they have thepower to select the most effective.Once you have allocated

Cambridge Primary offers optional, integrated assessment. The assessment structure tracks learner progression through primary education. Learners taking Cambridge Primary Checkpoint receive a Statement of Achievement and detailed feedback on strengths and weaknesses. Cambridge Primary suppo

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