Multiplication/Division Tables - Ballinaglera, Dowra, Co ...



Saint Hugh’s N.S. Maths Plan.Introductory Statement and RationaleIntroductory Statement This document is a statement of the aims and objectives, principles and strategies for implementing the mathematics programme at Saint Hugh’s N.S. It was formulated by the school staff at a staff meeting in March 2005 and reviewed in October 2013. It is informed by the Curriculum Statements and Curriculum Guidelines, needs of the children and the expertise and experience of the staff. Vision and AimsVision: Maths is a very important subject relating to the overall development of all our pupils. We hope that our pupils will enjoy their maths work and enjoy the practical and aesthetic elements in the 1999 Curriculum. We will try to focus on the presentation of Maths in a very real life environment where the children will benefit from the acquisition of life-skills. We also will try to allow each pupil to experience success in their work with a real emphasis on problem solving and understanding.Aims: We endorse the aims and objectives of the Curriculum for mathematics.To develop a positive attitude towards mathematics and an appreciation for its practical and its aesthetic aspects. To develop problem-solving abilities and a facility for the application of mathematics to everyday life.To enable the child to use mathematical language effectively and accurately.To enable the child to acquire an understanding of mathematical concepts and processes to his/her level of development and ability.To enable the child to acquire proficiency in fundamental mathematical skills and in recalling basic number factsIn addition, we in St. Hugh’s aim:To increase the standard of Maths in our schoolTo give all pupils an opportunity to succeed regardless of ability.To ensure sharing of resources and most effective teaching approaches by staff members.To emphasise the practical aspects of maths using problem solving and social maths.To ensure that revision and assessment form an essential part of our maths teaching.To promote the idea that Maths is FUN, and can be enjoyed by all members of the school community.Content of Plan Curriculum:1. .Strands and Strand Units: For content overview see Curriculum: Infants p.17; First & Second classes p. 37; Third & Fourth classes p.61; Fifth & Sixth classes p. 85) Class teachers are familiar with strand/content objectives for their class levels, and plan accordingly.2.Approaches and Methodologies: We aim to teach the Maths Curriculum using the following and methodologies: 1 Talk and Discussion: We see a need for use of and development of language throughout all classes.2 Active Learning/guided discovery: Children are encouraged to use concrete materials at all class levels to facilitate their learning. Use of games will also be deployed to further thinking and concept development.3 Collaborative/co-operative learning. Pupils will work together on problem solving and many mathematical exercises allowing them to learn from each other.4 Problem Solving: We will use lateral thinking, practical activities, open-ended questions, puzzles, games and contradictory surplus data to aid levels of problem solving.5 Using the environment: Using Maths Trails and measuring activities, catalogues, league tables in sport, Cinema listings, bus timetables to enhance maths learning.6 Skills through Content: That the children will develop their skills through the maths work in school.The school will adopt a common approach to all areas to ensure continuity and consistency especially when transferring from the Junior groups to the senior groups. The school as a whole will encourage the accurate and effective use of mathematical language.BooksThe ‘Action Maths’ (Folens) scheme is by 3rd, 4th, 5th and 6th Class. The ‘Planet Maths’ scheme is used by Junior Infants, Senior Infants, First, Second and Third Class. ‘Work it Out’ 1st – 6th ClassTabletoppers 1st Class Tables Champions 2nd – 6th BrainsnackProblem-solving in mathematics (Prim-Ed, Book D, E, F and G)Enigmathics: Book A, B and CUnderstanding Shapes and MeasuresMaths Grid Games (Prim-Ed)Maths Grid Games Number (Prim-Ed)Schematic Teaching of Addition TablesAddition Tables+ 0 When I add 0 I make no change+ 1 When I add 1 I meet my best friend up the ladder.+ 2 Using a number strip (e.g. magnetic counters/peg boards).+ 2 = 5Doubles one to one correspondence e.g. using counters.4 + 4 = 8 5.Near doubles 4 + 5 =4 + 4 + 1or5 + 5 - 1 5 + 6 =5 + 5 + 1or6 + 6 - 1 6. Commutative Law Buy one get one free. 4 + 3 is the same as 3 + 4. 7. Ten Facts 1 + 9, 2 + 8, 3 + 7, 4 + 6. Use the ten frame. 8. Through ten 10 + 2 = 12 ; 10 + 4 = 14 etc. Use the ten frame. Multiplication/Division TablesMultiplication/Division tables will be introduced as repeated addition and repeated subtraction.Begin with 10 times tables followed by 5 times tables because they are the easiest ones to remember. These two will be the benchmarks for all others.Then teach 2X, 4X and 8X, followed by 3X, 6X, 9XDrill the multiples up/down the multiples ladder.Children will be taught strategies to assist understanding and easy recall of the basic mutative lawDoublesOne set more/one set less.Use of fingers for calculating 9 timesTwice a known factActivities for tablesUse of games e.g. Snakes and ladders, Playing cardsUse of diceLoop gamesComputer software: ‘Interactive Maths Games’ and ‘100 Maths Interactives’ Language of tables3+0=3Three and/plus zero equals three5-5=0 Five take away/minus/from five equals zero0x2=0 Zero by/multiplied by two equals zero5/5=1 Five divided by five equals 1Language and the number operationsAddition 1.We introduce the addition of 3 add ends horizontally but this must lead to addition vertically. In senior infants and 1st class 4+3+2= is the same as:43 + 2 Always start adding from the bottom.Addition using larger numbers8 plus 5 is 13.Put down the ‘3’ and carry the ‘1’. T U 1st/2nd 28 + 2 15 53Subtraction 1. Subtraction is performed using the ‘Borrow/Payback’ system 1 73Borrow ‘1’ - 1 1 9 54Payback ‘1’STANDARDISATION OF SOME MATHEMATICAL PROCEDURES IN THE SCHOOLIt has been decided to standardise the following mathematical procedures throughout the school in order to help children with learning difficulties.Subtraction: Subtraction is performed using the ‘Borrow/Payback’ systemLong Multiplication: 54 X 23 162 1080 1242Golden zero strategyLong Division: 0214 28 5992-56 39 -28 112 -112 0 4) Time Calculations: 1 hr 35 mins.+ 2 hrs 45 mins. 3 hrs 80 mins. (1hr. 20 mins.)= 4 hrs 20 mins. Finding a Fraction of a Number:(a) Use Unitary Method. e.g. Find 3/8’s of 728/8 = 721/8 = 9 8 723/8 = 27 9 x3 27 (b) of = multiply Find 3/8 of 72 3 x 72 8 1Given a fraction find the whole number:e.g. 7/9 of a number is 42 find the whole number.7/9 = 421/9 = 6 9/9 = 549/9 = 6 x 9 = 54Fractions: Addition of Mixed Numbers.2 5/6 + 3 ? LCD = 12= 2 10/12 + 3 9/12 = 5 19/12= 5 + 1 7/12 - 6 7/12Subtraction of mixed numbers:Change to ‘Improper Fractions’, subtract the Numerators and revert to a ‘Mixed Number.’Decimals:3rd Class learn to link decimals to the fractions they have learnt: ?, ?, ?, 1/10s, From Fourth Class on when dealing with decimals we will use money so that children will understand the place-value of the digits within a decimal number and learn from the physicality of the operation:e.g.€38 . 38=> T U . 1/10 1/100 Money 3 8 . 3 8 Place value The decimal point is used to separate the pieces from the wholes.Decimals:The decimal point never moves in addition and subtraction:e.g.2.4 + 3.76 + 1.957 2.43.76Snowman effect +1.957Fractions:Fractions will be introduced by using first using Fraction Circles.e.g. 1 unit = 2 halves = 4 quartersPaper folding will also be used to explain the equivalence of fractions: 2/8 = ?4/8 = ?6/8 = ?Problem Solving: The focus is on real life problem solvingTypes of problemsWord problemsPractical tasksOpen-ended investigationsPuzzlesGamesProjectsEstimation:It is school policy that estimation skills be used and honed right throughout all strands of the curriculum from Junior Infants to Sixth Class. The main forms of estimation to be encouraged are:Front – end estimation, e.g.347 + 296Answer = roughly 500Rounding skills which are more precise than front-end estimation. By the time children leave 6th Class they should be able to round to the nearest 10/100/1000.Using paired numbers, e.g.€ 3.72 + € 2.46 + € 1.49 + € 7.38 + €3.59 = roughly €18.00Clusters e.g.346 + 227 + 493 + 629 + 652- 227 + 346 + 493 + 529 + 652 = roughly 500 x 5Estimation Procedure for numberEstimate firstWrite down your estimateSolve the problemCompare your estimate with the actual result Measures; At all levels we take every opportunity to have the children practise estimation of:lengthsheightswidthsdistancesweightsvolumecapacityKey strategies for Measures:EstimateDiscuss or considerMeasure or doRecord or reportCalculators 1. The calculator will not replace the basic facts (i.e. tables) 2. The first reason for using a calculator is for checking answers. 3. If problem solving is the main objective of the exercise, use a calculator. 4.Use a calculator for teaching place – value:e.g. 7846 - change to 7046(800 has to be subtracted, not 8) 7846 - change to 7806 etc. 5.Mental Strategies: e.g. 85 + 96. The 9 key is broken. How do you do this sum on the calculator? Find ways of making 96 without the 9 key, e.g. 85+ (100 – 4).Language:in MathematicsJunior Infants:sortobjectcoloursame as, match/mark, joinsame length, weight, heightbig, bigger etc, tall heavier etcfull, empty, ‘holds’smalllong, all terms re. Time, moving etc.to, from, before, aftershort – lighter, lightestearly, latesetcurved, round, inside, abovemore, less few/fewer, othersstraight, corner, outside, belowtoo many, enoughcircle, rectangle, squareroll, stackedtrianglehow many more?Who? How? Why?Patternfirst, second, third etc.zerocoins,shapenumerals one, two etc.how muchSenior Infants as Junior Infants: plus the following:compareleastmost, heaviest, etcaddsame ashow far/how far more?greater than/less thanmoneybreak up groupshigh, lowcount on / backwide narrowtoday, yesterday, tomorrowthick/thinmonths, seasonsdays of week etc.holds more than/less thano’clockholds most/least/the sameover, under, on, in, open,amountjoined, between, next toclosedhow long, short, heavystraightcharts,measureout, front, back, high lowsubtract/take away, go backcopyaround, 3D shapes, names,words for numeralsnumber strip cube,/cuboid1st Class:as infants plus the following:less, more,addition,missing numeralnumbersubtractionmake the same assmaller, greaterrest of themsingle digittake awaymeasurecentimetrehow many morechangegroup, orderdays of weektens/ones/unitcalendarbetween monthssubtract, stepsclock,make tenshalf pastproblemdienes blocksabacuscircle, square, rectanglegraphbar charttriangle, side, cornercube, cuboid, pyramidpictogramfaces, edgessphere, cylinder, conecounting in 2’s etc.left overmagic squaresymmetrynumber line100 squarecapacityfraction odd, even. kgs2nd Class: as 1st plus the following:missing numbers half quartersforward, backwardsshaded setrenameplace valuein ordergridadd, groupmetre, centimetresigndifference betweenhundreddecimetrecountingshapedbase 10’s etc.distancenumber sentenceminutes/hours, quarter past/todifferentdigitalcodemidnightsubtractmiddaymagic squaretimetableseasons2D, 3D hexagontessellatea.m. p.m.pictogramprism, cuboid, cylinderblack graph. kgs3rd Class: as 2nd plus the following:Symmetrycovering areaLanguage of division and multiplicationmathematic sentence versus written 2X3 = 6Divide,/divided by/division etc.capacity/liquid/litres, klsProduct weight – grammes / kgsFactorslength – metres, cms, mms.SetpictogrammeAngle, right angle, horizontal, vertical, diagonalsdecimalRectangle, cuboid, triangle, perimeterfractions – halves, quarters4th Class: as 3rd plus the following:capacitydivision and multiplication – estimate, remaindermore/less. Litre, millilitresquantityinto, by, from, under, value, more, lessweight shapesG. kg. Light, lighter, etc. heavy objects.Horizontal, vertical, sloping, parallel, congruent,Pointed, straight, square, solid, angle, acute,half, quarter, eighth etc/divide, shade, frame,Obtuse etc.figure.5th & 6th Class: as 4th plus the following:fractionsshapes,percentageoctagon,arearhombus, quadrilateral, length, width, surface, diameteroval, polygoncircumference, radius, base, perpendicular height,3D – cylinder – sphere, cone, cube, cuboid, pyramidaxis, reflection, image, parallel,triangular prism, tetrahedronprotractor.rotation, symmetricalThe Language of the Major Operations including Equals addition subtractionmore thantotal minus decrease subtractandsum of less than add increase difference take away division multiplication groupsquare multiplydividesharepower of times split product of of equals same as means =answer is will be represents isMental Maths: It is school policy that mental arithmetic is a feature of daily mathematical activity.Resources used include:Bingo BoardsTarget BoardsNumber fansTablesWork it OutPizza Fraction Fun3. Assessment and Record Keeping:Assessment is an integral part of the teaching and learning process. All strands of the maths programme will be assessed using a variety of assessment tools.Teacher Observation Interview MethodError AnalysisHome work/Parental feedbackWork samplesTeacher designed tasks and testsStandardised TestsDiagnostic TestsDrumcondra Maths tests will be administered in Saint Hugh’s each year. Records will be kept safely in the filing cabinet. They will be available to parents on request. They can also be used to determine children who need learning support/resource hours. 4. Children with Different Needs:Children in each class will show a wide range of ability, attainment and learning styles. Consequently the mathematics programme will be flexible to accommodate children of different levels of ability and will reflect their needs.Adapting to the needs of the less abled mathematical child:Use easily computed figures when introducing new concepts While the children will be exposed to all aspects of the curriculum certain areas must be prioritisedAdapting the programme to suit their abilityMore individual attentionMore concrete approachEmphasising maths languageMaths gamesMaths softwareSuggesting strategies for challenging the better abled mathematical child:Problem solving books/Brain Teaser BooksMaths Facts BookMaths gamesMaths softwareORGANISATION6. Timetable: The time spent on Maths was increased in January 2012 to 3 hours 35 minutes per week for infants classes and to 4 hours and 10 minutes for students with a full day to comply with the ‘The National Strategy to Improve Literacy and Numeracy among children and Young People 2011-2020.’ 7. Homework:Homework is given at the discretion of the teacher. Homework should not require teaching at home. It should be reasonable and achievable. Concepts for homework should be already well established in classroom practice. To prevent parents giving a child the wrong methodology no homework will be given on a particular concept until it has been well established in classroom practice. Types of homework:Written consolidation of work done in classTablesProblem solvingPractical assignmentsResearchCollecting data8. Resources and ICT: Like the calculator, the computer is a tool to enhance the implementation of the Revised Curriculum. Some of the uses of ICT in Mathematics are:drill and practicedata basesspreadsheets9. Individual Teachers’ Planning and Reporting: Planning across the strands is detailed in short term and yearly plans by individual teachers.10. Staff Development: Maths as a subject is discussed at staff meetings & particular areas discussed & updated. Reference material is kept in the staff room & the principal has a lot of material relating to the Maths Primary Curriculum, which staff is encouraged to borrow.10. Parental Involvement - Home School Links:Communicating with parents about the correct terminology/language and methods being used involves:Advisory notes as the need arisesWriting language of tables in the table bookParent -teacher meetingsSuccess CriteriaThe use of assessment, as discussed earlier, is central to the monitoring of pupils’ progress in Maths. Success in Maths is determined by individual pupil achievement relative to their age & ability. Constant review & monitoring of skill development in all areas of Maths are important. Emphasis will be placed on interpreting the results of standardised tests at individual, class and whole-school level, to target areas of concern that may arise.Implementation(a)Roles and Responsibilities:Implementation of the Maths curriculum falls to individual teachers in their classrooms. The class teacher has responsibility for all their pupils and constant liaising with support teachers is necessary. The principal has a role in ensuring that the overall teaching of the subject is in line with the school plan and to offer assistance & guidance where necessary.(b)Timeframe:The implementation of the curriculum is on-going but the current school plan should be evidenced in all classes by the end of 2013.Review(a)Roles and Responsibilities:(b)Timeframe: A general review of this plan will take place in the second term of the 2007 – 2008 school year. This plan will subsequently be reviewed every three years.Ratification and CommunicationAll teachers will be given a copy of this plan.__________________________Principal _____________________Chairperson BOM__________________________ Date\sMeasuresDataSeptemberOctoberNovemberDecemberJanuaryFebruaryMarchAprilMayJune ................
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