Numeracy Mathematics Experiences Outcomes Tcm4-539878

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    Numeracy and mathematics: experiences and outcomes 1

    Numeracy and mathematicsExperiences and outcomes

    My learning in mathematics enables me to:

    develop a secure understanding of the concepts, principles and processes of mathematics and apply these in different contexts, including the world of work

    engage with more abstract mathematical concepts and develop important new kinds of thinking

    understand the application of mathematics, its impact on our society past and present, and its potential for the future

    develop essential numeracy skills which will allow me to participate fully in society

    establish firm foundations for further specialist learning

    understand that successful independent living requires financial awareness, effective money management, using schedules and other related skills

    interpret numerical information appropriately and use it to draw conclusions, assess risk, and make reasoned evaluations and informed decisions

    apply skills and understanding creatively and logically to solve problems, within a variety of contexts

    appreciate how the imaginative and effective use of technologies can enhance the development of skills and concepts.

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    Numeracy and mathematics: experiences and outcomes 2

    Number, money and measure

    Early First Second Third Fourth

    Estimation androunding

    I am developing asense of size andamount by observing,exploring, using andcommunicating withothers about things inthe world around me

    1

    I can share ideas withothers to develop waysof estimating theanswer to a calculationor problem, work outthe actual answer,then check my solutionby comparing it withthe estimate.

    MNU 1-01a

    .MNU 0-01a

    I can use my knowledge ofrounding to routinelyestimate the answer to aproblem then, aftercalculating, decide if myanswer is reasonable,sharing my solution withothers.

    MNU 2-01a

    I can round a number usingan appropriate degree ofaccuracy, having taken intoaccount the context of theproblem.

    MNU 3-01a

    Having investigated thepractical impact ofinaccuracy and error, I canuse my knowledge oftolerance when choosing therequired degree of accuracyto make real-life calculations.

    MNU 4-01a

    Number andnumberprocessesincluding addition,subtraction,multiplication, divisionand negative numbers

    I have explorednumbers,understanding thatthey representquantities, and I canuse them to count,create sequences anddescribe order.

    MNU 0-02a

    I use practicalmaterials and cancount on and back tohelp me to understandaddition and

    subtraction, recordingmy ideas and solutionsin different ways.

    MNU 0-03a

    I have investigatedhow whole numbersare constructed, canunderstand theimportance of zerowithin the system andcan use my knowledgeto explain the linkbetween a digit, itsplace and its value.

    MNU 1-02a

    I can use addition,subtraction,multiplication and

    division when solvingproblems, making bestuse of the mentalstrategies and writtenskills I havedeveloped.

    MNU 1-03a

    I have extended the range ofwhole numbers I can workwith and having exploredhow decimal fractions areconstructed, can explain thelink between a digit, its placeand its value.

    MNU 2-02a

    Having determined whichcalculations are needed, Ican solve problems involvingwhole numbers using arange of methods, sharingmy approaches and solutions

    with others. MNU 2-03a

    I can use a variety ofmethods to solve numberproblems in familiar contexts,clearly communicating myprocesses and solutions.

    MNU 3-03a

    Having recognisedsimilarities between newproblems and problems Ihave solved before, I cancarry out the necessarycalculations to solve

    problems set in unfamiliarcontexts.

    MNU 4-03a

    1The numeracy experiences and outcomes, which are the responsibility of all teachers, are shown in italics.

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    Numeracy and mathematics: experiences and outcomes 3

    Number, money and measure (continued)

    Early First Second Third Fourth

    Number andnumber processesincluding addition,subtraction,multiplication, divisionand negative numbers(continued)

    I have explored the contextsin which problems involvingdecimal fractions occur andcan solve related problemsusing a variety of methods.

    MNU 2-03b

    Having explored the need forrules for the order of

    operations in numbercalculations, I can applythem correctly when solvingsimple problems.

    MTH 2-03c

    I can continue to recallnumber facts quickly and usethem accurately whenmaking calculations.

    MNU 3-03b

    I have investigated howintroducing brackets to anexpression can change theemphasis and candemonstrate myunderstanding by using thecorrect order of operationswhen carrying outcalculations.

    MTH 4-03b

    I can show my understandingof how the number lineextends to include numbersless than zero and haveinvestigated how thesenumbers occur and are used.

    MNU 2-04a

    I can use my understandingof numbers less than zero tosolve simple problems incontext.

    MNU 3-04a

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    Numeracy and mathematics: experiences and outcomes 4

    Number, money and measure (continued)

    Early First Second Third Fourth

    Multiples, factorsand primes

    Having explored the patternsand relationships inmultiplication and division, Ican investigate and identifythe multiples and factors ofnumbers.

    MTH 2-05a

    I have investigated strategiesfor identifying commonmultiples and commonfactors, explaining my ideasto others, and can apply myunderstanding to solverelated problems.

    MTH 3-05a

    I can apply my understandingof factors to investigate andidentify when a number isprime.

    MTH 3-05b

    Powers and roots Having explored the notationand vocabulary associatedwith whole number powersand the advantages of writingnumbers in this form, I canevaluate powers of wholenumbers mentally or usingtechnology.

    MTH 3-06a

    I have developed myunderstanding of therelationship between powersand roots and can carry outcalculations mentally or usingtechnology to evaluate wholenumber powers and roots, ofany appropriate number.

    MTH 4-06a

    Within real-life contexts, I can

    use scientific notation toexpress large or smallnumbers in a more efficientway and can understand andwork with numbers written inthis form.

    MTH 4-06b

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    Numeracy and mathematics: experiences and outcomes 5

    Number, money and measure (continued)

    Early First Second Third Fourth

    Fractions, decimalfractions andpercentagesincluding ratio andproportion

    I can share out agroup of items bymaking smaller groupsand can split a wholeobject into smallerparts.

    MNU 0-07a

    Having exploredfractions by taking partin practical activities, Ican show myunderstanding of:

    how a single itemcan be sharedequally

    the notation andvocabularyassociated withfractions

    where simplefractions lie on thenumber line.

    MNU 1-07a

    Through exploring howgroups of items can beshared equally, I canfind a fraction of anamount by applyingmy knowledge ofdivision.

    MNU 1-07b

    Through taking part in

    practical activitiesincluding use ofpictorialrepresentations, I candemonstrate myunderstanding ofsimple fractions whichare equivalent.

    MTH 1-07c

    I have investigated theeveryday contexts in whichsimple fractions, percentagesor decimal fractions are usedand can carry out thenecessary calculations tosolve related problems.

    MNU 2-07a

    I can show the equivalentforms of simple fractions,decimal fractions andpercentages and can choosemy preferred form whensolving a problem, explainingmy choice of method.

    MNU 2-07b

    I have investigated how a setof equivalent fractions can becreated, understanding themeaning of simplest form,and can apply my knowledgeto compare and order themost commonly usedfractions.

    MTH 2-07c

    I can solve problems bycarrying out calculations witha wide range of fractions,decimal fractions andpercentages, using myanswers to makecomparisons and informedchoices for real-lifesituations.

    MNU3-07a

    By applying my knowledge ofequivalent fractions andcommon multiples, I can addand subtract commonly usedfractions.

    MTH 3-07b

    Having used practical,pictorial and written methodsto develop myunderstanding, I can convertbetween whole or mixednumbers and fractions.

    MTH 3-07c

    I can choose the mostappropriate form of fractions,decimal fractions andpercentages to use whenmaking calculations mentally,in written form or usingtechnology, then use mysolutions to makecomparisons, decisions and

    choices.MNU 4-07a

    I can solve problemsinvolving fractions and mixednumbers in context, usingaddition, subtraction ormultiplication.

    MTH 4-07b

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    Numeracy and mathematics: experiences and outcomes 6

    Number, money and measure (continued)

    Early First Second Third Fourth

    Fractions, decimalfractions andpercentagesincluding ratio andproportion (continued)

    I can show how quantitiesthat are related can beincreased or decreasedproportionally and apply thisto solve problems ineveryday contexts.

    MNU 3-08a

    Using proportion, I cancalculate the change in onequantity caused by a changein a related quantity andsolve real-life problems.

    MNU 4-08a

    Money I am developing myawareness of howmoney is used andcan recognise and usea range of coins.

    MNU 0-09a

    I can use money topay for items and canwork out how muchchange I shouldreceive.

    MNU 1-09a

    I have investigatedhow differentcombinations of coinsand notes can be usedto pay for goods or begiven in change.

    MNU 1-09b

    I can manage money,compare costs from differentretailers, and determine whatI can afford to buy.

    MNU 2-09a

    I understand the costs,benefits and risks of usingbank cards to purchasegoods or obtain cash andrealise that budgeting isimportant.

    MNU 2-09b

    I can use the terms profit andloss in buying and sellingactivities and can makesimple calculations for this.

    MNU 2-09c

    When considering how tospend my money, I cansource, compare andcontrast different contractsand services, discuss theiradvantages anddisadvantages, and explainwhich offer best value to me.

    MNU 3-09a

    I can budget effectively,making use of technologyand other methods, tomanage money and plan forfuture expenses.

    MNU 3-09b

    I can discuss and illustratethe facts I need to considerwhen determining what I canafford, in order to managecredit and debt and lead aresponsible lifestyle.

    MNU 4-09a

    I can source information onearnings and deductions anduse it when makingcalculations to determine netincome.

    MNU 4-09b

    I can research, compare andcontrast a range of personalfinance products and, after

    making calculations, explainmy preferred choices.MNU 4-09c

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    Numeracy and mathematics: experiences and outcomes 7

    Number, money and measure (continued)

    Early First Second Third Fourth

    Time I am aware of howroutines and events inmy world link withtimes and seasons,and have exploredways to record anddisplay these usingclocks, calendars andother methods.

    MNU 0-10a

    I can tell the time using12 hour clocks,realising there is a linkwith 24 hour notation,explain how it impactson my daily routineand ensure that I amorganised and readyfor events throughout

    my day.MNU 1-10a

    I can use a calendar toplan and be organisedfor key events formyself and my classthroughout the year.

    MNU 1-10b

    I have begun todevelop a sense ofhow long tasks take bymeasuring the timetaken to complete arange of activitiesusing a variety oftimers.

    MNU 1-10c

    I can use and interpretelectronic and paper-basedtimetables and schedules toplan events and activities,and make time calculationsas part of my planning.

    MNU 2-10a

    I can carry out practical tasks

    and investigations involvingtimed events and can explainwhich unit of time would bemost appropriate to use.

    MNU 2-10b

    Using simple time periods, Ican give a good estimate ofhow long a journey shouldtake, based on myknowledge of the linkbetween time, speed anddistance.

    MNU 2-10c

    Using simple time periods, Ican work out how long ajourney will take, the speedtravelled at or distancecovered, using myknowledge of the linkbetween time, speed anddistance.

    MNU 3-10a

    I can research, compare andcontrast aspects of time andtime management as theyimpact on me.

    MNU 4-10a

    I can use the link betweentime, speed and distance tocarry out related calculations.

    MNU 4-10b

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    Numeracy and mathematics: experiences and outcomes 8

    Number, money and measure (continued)

    Early First Second Third Fourth

    Measurement I have experimentedwith everyday items asunits of measure toinvestigate andcompare sizes andamounts in myenvironment, sharingmy findings withothers.

    MNU 0-11a

    I can estimate howlong or heavy anobject is, or whatamount it holds, usingeveryday things as aguide, then measureor weigh it usingappropriateinstruments and units.

    MNU 1-11a

    I can estimate the areaof a shape by countingsquares or othermethods.

    MNU 1-11b

    I can use my knowledge ofthe sizes of familiar objectsor places to assist me whenmaking an estimate ofmeasure.

    MNU 2-11a

    I can use the common unitsof measure, convert between

    related units of the metricsystem and carry outcalculations when solvingproblems.

    MNU 2-11b

    I can explain how differentmethods can be used to findthe perimeter and area of asimple 2D shape orvolumeof a simple 3D object.

    MNU 2-11c

    I can solve practicalproblems by applying myknowledge of measure,choosing the appropriateunits and degree of accuracyfor the task and using aformula to calculate area orvolume when required.

    MNU 3-11a

    Having investigated differentroutes to a solution, I can findthe area of compound 2Dshapes and the volume ofcompound 3D objects,applying my knowledge tosolve practical problems.

    MTH 3-11b

    I can apply my knowledgeand understanding ofmeasure to everydayproblems and tasks andappreciate the practicalimportance of accuracy whenmaking calculations.

    MNU 4-11a

    Through investigating real-life problems involving thesurface area of simple 3Dshapes, I can explore waysto make the most efficientuse of materials and carryout the necessarycalculations to solve relatedproblems.

    MTH 4-11b

    I have explored with othersthe practicalities of the use of3D objects in everyday lifeand can solve problemsinvolving the volume of aprism, using a formula tomake related calculations

    when required. MTH 4-11c

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    Numeracy and mathematics: experiences and outcomes 9

    Number, money and measure (continued)

    Early First Second Third Fourth

    Mathematics its impact on theworld, past,present and future

    I have discussed theimportant part thatnumbers play in theworld and explored avariety of systems thathave been used bycivilisations throughouthistory to recordnumbers.

    MTH 1-12a

    I have worked with others toexplore, and present ourfindings on, howmathematics impacts on theworld and the important partit has played in advancesand inventions.

    MTH 2-12a

    I have worked with others toresearch a famousmathematician and the workthey are known for, orinvestigated a mathematicaltopic, and have prepared anddelivered a shortpresentation.

    MTH 3-12a

    I have discussed theimportance of mathematics inthe real world, investigatedthe mathematical skillsrequired for different careerpaths and delivered, withothers, a presentation onhow mathematics can beapplied in the workplace.

    MTH 4-12a

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    Numeracy and mathematics: experiences and outcomes 10

    Number, money and measure (continued)

    Early First Second Third Fourth

    Patterns andrelationships

    I have spotted andexplored patterns inmy own and the widerenvironment and cancopy and continuethese and create myown patterns.

    MTH 0-13a

    I can continueanddevise more involvedrepeating patterns ordesigns, using avariety of media.

    MTH 1-13a

    Through exploringnumber patterns, I canrecognise andcontinue simplenumber sequencesand can explain therule I have applied.

    MTH 1-13b

    Having explored morecomplex number sequences,including well-known namednumber patterns, I canexplain the rule used togenerate the sequence, andapply it to extend the pattern.

    MTH 2-13a

    Having explored numbersequences, I can establishthe set of numbers generatedby a given rule anddetermine a rule for a givensequence, expressing itusing appropriate notation.

    MTH 3-13a

    Having explored how real-lifesituations can be modelledby number patterns, I canestablish a number sequenceto represent a physical orpictorial pattern, determine ageneral formula to describethe sequence, then use it to

    make evaluations and solverelated problems.MTH 4-13a

    I have discussed ways todescribe the slope of a line,can interpret the definition ofgradient and can use it tomake relevant calculations,interpreting my answer forthe context of the problem.

    MTH 4-13b

    Having investigated thepattern of the coordinatepoints lying on a horizontal orvertical line, I can describethe pattern using a simpleequation.

    MTH 4-13c

    I can use a given formula togenerate points lying on astraight line, plot them tocreate a graphicalrepresentation then use thisto answer related questions.

    MTH 4-13d

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    Numeracy and mathematics: experiences and outcomes 11

    Number, money and measure (continued)

    Early First Second Third Fourth

    Expressions andequations

    I can collect like algebraicterms, simplify expressionsand evaluate usingsubstitution.

    MTH 3-14a

    Having explored thedistributive law in practicalcontexts, I can simplify,multiply and evaluate simplealgebraic terms involving abracket.

    MTH 4-14a

    I can find the factors ofalgebraic terms, use myunderstanding to identifycommon factors and applythis to factorise expressions.

    MTH 4-14b

    I can compare,describe and shownumber relationships,using appropriatevocabulary and thesymbols for equals,not equal to, less thanand greater than.

    MTH 1-15a

    When a picture or

    symbol is used toreplace a number in anumber statement, Ican find its value usingmy knowledge ofnumber facts andexplain my thinking toothers.

    MTH 1-15b

    I can apply my knowledge ofnumber facts to solveproblems where an unknownvalue is represented by asymbol or letter.

    MTH 2-15a

    Having discussed ways toexpress problems orstatements usingmathematical language, I canconstruct, anduseappropriate methods tosolve, a range of simpleequations.

    MTH 3-15a

    I can create and evaluate a

    simple formula representinginformation contained in adiagram, problem orstatement.

    MTH 3-15b

    Having discussed thebenefits of usingmathematics to model real-life situations, I can constructand solve inequalities and anextended range of equations.

    MTH 4-15a

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    Numeracy and mathematics: experiences and outcomes 12

    Shape, position and movement

    Early First Second Third Fourth

    Properties of 2Dshapes and 3Dobjects

    I enjoy investigatingobjects and shapesand can sort, describeand be creative withthem.

    MTH 0-16a

    I have explored simple3D objects and 2Dshapes and canidentify, name anddescribe their featuresusing appropriatevocabulary.

    MTH 1-16a

    I can explore anddiscuss how and whydifferent shapes fittogether and create atiling pattern withthem.

    MTH 1-16b

    Having explored a range of3D objects and 2D shapes, Ican use mathematicallanguage to describe theirproperties, and throughinvestigation can discusswhere and why particularshapes are used in theenvironment.

    MTH 2-16a

    Through practical activities, Ican show my understandingof the relationship between3D objects and their nets.

    MTH 2-16b

    I can draw 2D shapes andmake representations of 3Dobjects using an appropriaterange of methods andefficient use of resources.

    MTH 2-16c

    Having investigated a rangeof methods, I can accuratelydraw 2D shapes usingappropriate mathematicalinstruments and methods.

    MTH 3-16a

    I have explored therelationships that existbetween the sides, or sidesand angles, in right-angledtriangles and can select anduse an appropriate strategyto solve related problems,interpreting my answer forthe context.

    MTH 4-16a

    Having investigated therelationships between theradius, diameter,circumference and area of acircle, I can apply myknowledge to solve relatedproblems.

    MTH 4-16b

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    Numeracy and mathematics: experiences and outcomes 13

    Shape, position and movement (continued)

    Early First Second Third Fourth

    Angle, symmetryandtransformation

    In movement, games,and using technology Ican use simpledirections anddescribe positions.

    MTH 0-17a

    I can describe, followand record routes andjourneys using signs,words andanglesassociated withdirection and turning.

    MTH 1-17a

    I have investigated angles inthe environment, and candiscuss, describe andclassify angles usingappropriate mathematicalvocabulary.

    MTH 2-17a

    I can accurately measure

    and draw angles usingappropriate equipment,applying my skills toproblems in context.

    MTH 2-17b

    Through practical activitieswhich include the use oftechnology, I have developedmy understanding of the linkbetween compass points andangles and can describe,follow and record directions,routes and journeys usingappropriate vocabulary.

    MTH 2-17c

    Having investigated where,

    why and how scale is usedand expressed, I can applymy understanding to interpretsimple models, maps andplans.

    MTH 2-17d

    I can name angles and findtheir sizes using myknowledge of the propertiesof a range of 2D shapes andthe angle propertiesassociated with intersectingand parallel lines.

    MTH 3-17a

    Having investigatednavigation in the world, I canapply my understanding ofbearings and scale tointerpret maps and plans andcreate accurate plans, andscale drawings of routes andjourneys.

    MTH 3-17b

    I can apply my understandingof scale when enlarging orreducing pictures andshapes, using differentmethods, includingtechnology.

    MTH 3-17c

    Having investigated therelationship between aradius and a tangent andexplored the size of theangle in a semi-circle, I canuse the facts I haveestablished to solve relatedproblems.

    MTH 4-17a

    I can apply my understandingof the properties of similarfigures to solve problemsinvolving length and area.

    MTH 4-17b

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    Numeracy and mathematics: experiences and outcomes 14

    Shape, position and movement (continued)

    Early First Second Third Fourth

    Angle, symmetryandtransformation(continued)

    I have developed anawareness of wheregrid reference systemsare used in everydaycontexts and can usethem to locate anddescribe position.

    MTH 1-18a

    I can use my knowledge of the coordinate system to plot anddescribe the location of a point on a grid.

    MTH 2-18a / MTH 3-18a

    I can plot and describe theposition of a point on a4-quadrant coordinate grid.

    MTH 4-18a

    I can apply my understandingof the 4-quadrant coordinatesystem to move, anddescribe the transformation

    of, a point or shape on a grid.MTH 4-18b

    I have had fun creatinga range of symmetricalpictures and patternsusing a range ofmedia.

    MTH 0-19a

    I have exploredsymmetry in my ownand the widerenvironment and cancreate and recognisesymmetrical pictures,patterns and shapes.

    MTH 1-19a

    I can illustrate the lines of symmetry for a range of 2D shapesand apply my understanding to create and completesymmetrical pictures and patterns.

    MTH 2-19a / MTH 3-19a

    Having investigated patternsin the environment, I can useappropriate mathematicalvocabulary to discuss therotational properties ofshapes, pictures andpatterns and can apply myunderstanding whencompleting or creatingdesigns.

    MTH 4-19a

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    Numeracy and mathematics: experiences and outcomes 15

    Information handling

    Early First Second Third Fourth

    Data andanalysis

    I can collect objectsand ask questions togather information,organising anddisplaying my findingsin different ways.

    MNU 0-20a

    I can match objects,

    and sort using my ownand others criteria,sharing my ideas withothers.

    MNU 0-20b

    I can use the signsand charts around mefor information, helpingme plan and makechoices and decisionsin my daily life.

    MNU 0-20c

    I have explored avariety of ways inwhich data ispresented and can askand answer questionsabout the information itcontains.

    MNU 1-20a

    I have used a range ofways to collectinformation and cansort it in a logical,organised andimaginative way usingmy own and otherscriteria.

    MNU 1-20b

    Having discussed the varietyof ways and range of mediaused to present data, I caninterpret and drawconclusions from theinformation displayed,recognising that thepresentation may bemisleading.

    MNU 2-20a

    I have carried outinvestigations and surveys,devising and using a varietyof methods to gatherinformation and have workedwith others to collate,organise and communicatethe results in an appropriateway.

    MNU 2-20b

    I can work collaboratively,making appropriate use oftechnology, to sourceinformation presented in arange of ways, interpret whatit conveys and discusswhether I believe theinformation to be robust,vague or misleading.

    MNU 3-20a

    When analysing informationor collecting data of my own,I can use my understandingof how bias may arise andhow sample size can affectprecision, to ensure that thedata allows for fairconclusions to be drawn.

    MTH 3-20b

    I can evaluate and interpretraw and graphical data usinga variety of methods,comment on relationships Iobserve within the data andcommunicate my findings toothers.

    MNU 4-20a

    In order to comparenumerical information in real-life contexts, I can find themean, median, mode andrange of sets of numbers,decide which type of averageis most appropriate to useand discuss how using analternative type of averagecould be misleading.

    MTH 4-20b

    Using technology andother methods, I candisplay data simply,clearly and accurately

    by creating tables,charts and diagrams,using simple labellingand scale.

    MTH 1-21a

    I can display data in a clear way using a suitable scale, bychoosing appropriately from an extended range of tables,charts, diagrams and graphs, making effective use oftechnology.

    MTH 2-21a / MTH 3-21a

    I can select appropriatelyfrom a wide range of tables,charts, diagrams and graphswhen displaying discrete,

    continuous or grouped data,clearly communicating thesignificant features of thedata.

    MTH 4-21a

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    Numeracy and mathematics: experiences and outcomes 16

    Information handling (continued)

    Early First Second Third Fourth

    Ideas of chanceand uncertainty

    I can use appropriatevocabulary to describethe likelihood of eventsoccurring, using theknowledge andexperiences of myselfand others to guideme.

    MNU 1-22a

    I can conduct simpleexperiments involvingchance and communicate mypredictions and findingsusing the vocabulary ofprobability.

    MNU 2-22a

    I can find the probability of asimple event happening andexplain why theconsequences of the event,as well as its probability,should be considered whenmaking choices.

    MNU 3-22a

    Byapplying myunderstanding of probability,I can determinehow manytimes I expect an event tooccur, and use thisinformation to makepredictions, risk assessment,informed choices and

    decisions. MNU 4-22a

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    Numeracy and mathematics: experiences and outcomes 17

    Appendix Explanations

    MNU 1-10aDeveloping a childs understanding of 12 hour time in depth takes place through first level. Young learners willbecome familiar with 24 hour notation in their surroundings through TV listings, computers, cookers, DVD playersand videos. They will naturally make links with 24 hour notation and the routines in their day. The next stage ofdevelopment, the formal manipulation of 24 hour time, is included in MNU 2-10a understanding and usingtimetables.

    MNU 4-03aThe ability to apply and transfer familiar concepts to solve problems is fundamental for mathematicaldevelopments. As one example, young people will be familiar with the fact that 2.5 is a quarter of 10 and will knowhow to find 10% of a quantity. When asked to consider a less familiar calculation e.g. 2.5% of 840 the combinationof these previously-acquired skills could lead them to suggest 1/4 of 84 to be a possible solution.

    MNU 3-07a and MNU 4-07aMNU 3-07a develops skills that allow learners to carry out calculations involving fractions, decimal fractions andpercentages and then make decisions and choices. For example: which is the better buy, 3 for the price of 2 or a30% discount?

    MNU 4-07a develops the skills that allow learners to use their knowledge of interrelationships between fractions,decimal fractions and percentages to choose an elegant route to the solution. As an example, when asked toevaluate a discount of 12.5% on an item costing 800, an elegant solution would involve the understanding that12.5% is 1/8, and that calculating 1/8 of 800 will provide the answer to the size of the discount.

    MTH 3-11bAs this is a third level outcome, it is envisaged that the majority of shapes and objects will be formed from

    rectangles and triangles. However, for young people with well-developed understanding, problems involvingcircular properties could be introduced and investigated.

    MNU 4-10aUsing time efficiently is necessary in the work place, in lifelong learning, leisure time and all other aspects of dailylife. The ability to estimate how long different tasks take and then build a programme of sequential tasks is a criticalnumeracy skill which is fundamental to effective time management.

    MNU 4-01a, MNU 4-11a

    MNU 4-01a and MNU 4-11a are closely related. MNU 4-01a develops the concept of tolerance within estimatingand rounding whereas MNU 4-11a is the practical application within measurement. The ability to work to theappropriate degree of accuracy is an essential numeracy skill. The degree of accuracy demanded varies of courseaccording to the task. For example, the degrees of accuracy needed for measuring the dimensions of a roombefore buying a new carpet, measuring the opening when fitting a new door or machining a moving part within acombustion engine will be quite different. Or again, when a 4 metre length of wood is cut into 7 equal pieces,should each length be 0.57142 metres or will 0.57 metres be acceptable? The ability to handle spurious precisionand report using an appropriate degree of accuracy should always be encouraged.

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    MTH 3-15a, MTH 3-15b and MTH 4-15a MTH 3-15a promotes the ability to form and solve simple equations from written statements and pictorial

    representation (as an example, think of a number, double it and add seven, the answer is 23. What is theoriginal number?)

    MTH 3-15b promotes the ability to construct mathematical formulae from pictorial representations. Afundamental teaching point is that a formula has an output solution which will vary depending on the inputnumber. A possible case could be a progression of diagrams where red tiles are surrounded by white tiles.When the patterns are analysed, the formula W = 2R + 6 is found to represent the pattern in each of the

    diagrams MTH 4-15a promotes the ability to form inequalities from written and pictorial information, then demonstrate an

    understanding that inequalities are solved through a set of appropriate numbers. It also promotes the ability toform and solve equations, using the ability to simplify through balancing.

    MNU 4-20aThis experience and outcome relates to a learner's developing skills in interpreting a data set or the informationcontained in, for example, box plots, stem and leaf diagrams, line graphs, bar graphs, histograms and pie charts.Having considered this information it is important for learners to understand key features of these different ways ofpresenting information in order to be able to select appropriate forms and communicate findings to others.

    MNU 4-22aMNU 4-22a is intended to develop the link between simple probability and expected frequency. Having gained anunderstanding of these two concepts, the ability to assess the impact of a particular course of action based on risksand benefits is a very important skill for life.