More efficient than counting in ones Less open to error
Check which students have experience of working with Numicon and ensure they are together with a different resource to explore A quote from the NCETM website re use of Cuisenaire When I was at infant school I was very lucky to be taught mathematics by an excellent teacher using Cuisenaire rods. I have a vivid mental image of myself lining up three green-three rods and a white- one rod against an orange – ten. I can also remember crawling all over the floor to find the missing white-ones before we could go out to play! Whenever I find that old box, I appreciate that teacher and the images that she gave me at an early age.
12 10-10 counting
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Learning and Teaching the Curriculum CountingConcepts of Addition and Subtraction
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Quizz• What is the biggest number?• How many numbers are there between 1 and 20?• Give an example in which the operation of subtraction leads to a larger number
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Aims of the session• To consider how we use numbers in our everyday lives• To understand the processes involved in counting• To consider some basic models of addition and subtraction• To become familiar with curriculum documents
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Activity• Close your eyes• Bring to the forefront of your consciousness an image of the number three
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Key vocabularyAspects of number• Nominal• Cardinal• Ordinal
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The nominal aspect‘The 3 on a number 3 bus is indeed just a label, a number being used in what is called the nominal aspect.’ Haylock and Cockburn, 2008, p.33
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The ordinal aspect‘...the image of a number line is one that embodies most strongly the ordinal aspect of number.’ Haylock and Cockburn, 2008, p.34
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The cardinal aspectCardinal numbers serve ‘as indications of how many there are in a set of things.’ Haylock and Cockburn, 2008, p.34
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Connecting cardinal and ordinal aspects• The last number you get to when you are counting a set is the number in the set – e.g. Seven is one more than six, because it is the next number after six.• Teachers to make explicit that the previous number is alwasy one less
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Pre-counting experiences• Sorting objects into sets and categorisation – Play sorting games• Using language such as ‘one more’ and ‘another one’• Distinguish between sets of different sizes understand that sets of different sizes have different labels
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Play Alphabetland • Number names are A, B, C, D… • Do not‘translate’ these number names into the number names one, two, three,…
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Play Alphabetland in pairs• Can you count backwards from J?• Answer the following questions: – C+D – B+E – K–B – G–D – E+E – E+F• Articulate the strategies you use
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Activity• Count the number of people in the room• Make notes about the process• Consider whether there was – Recitation – Coordination (head nodding, pointing, 1-1) – Keeping track (Where did I start? Who have I counted/not counted?)
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Counting exercises• Count forwards• Count backwards• Count from x to y• What number comes before x?• What number comes after x?• Put number mats in order
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Resources to support counting• Cuisenaire• Numicon• Bead strings• Dienes
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Addition Strategies• Counting all• Counting on from the first number• Counting on from the larger number• Using a known fact – (E + E = J)• Deriving a new fact from a known fact – (e.g. E + F, using the answer to E + E)
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Subtraction Strategies• Counting out – (e.g. G – D: put up G fingers, fold down D fingers and count out what’s left).• Counting back the second number – (e.g. K – B, saying J, I).• Counting from one number to the other – (e.g. counting on from D to G keeping track of how many have been counted on)
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What does learning to count entail? Rochel Gelman’s Counting Principles • Stable order You need to know the counting words and be able to recite them in the correct order each time – it is impossible to count up to seven if you know only the first six counting words. • One to one One, and only one, number word has to be matched to each and every object; lack of co-ordination is a source of potential error. • Cardinality When correctly following the first two principles, the number name allocated to the last object tells you how many objects you have counted. • Abstraction You can count anything – visible objects, objects of different shapes and sizes, things that are too far away to touch, objects that cannot be moved, moving objects, hidden objects, imaginary objects, sounds, etc. • Order irrelevance Objects may be counted in any order provided no other counting principle is violated. http://www.teachers.net.qa/Math_CfBT_Workshops/workshop2/Ma2_Session8a.pdf
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Early Years Foundation StageMathematics involves providing children withopportunities to•Develop and improve their skills in counting•Understand and use numbers•Calculate simple addition and subtractionproblems•Describe shapes, spaces, and measures
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EYFS and CountingChildren are able to•Count reliably with numbers from 1 to 20•Place numbers in order•Say which number is one more or one less thana given number
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09/10/12 The Structure and Content of the National Curriculum for MathematicsThe Structure• Programmes of study set out what pupils should be taught at KS1 and KS2.• Attainment targets- the programmes of study are sub-divided into attainment targets• Knowledge, skills and understanding in the programme of study identify the main aspects of mathematics to be taught at each key stage;
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09/10/12 The NC Attainment TargetsThe knowledge, skills and understanding that pupils of different abilities and maturities are expected to have by the end of each key stage.There are four attainment targets in mathematics1. Ma 1: Using and applying mathematics2. Ma 2: Number and algebra3. Ma 3: Shape space and measures4. Ma 4: Handling dataLevel descriptions – the attainment targets consist of eight level descriptions of increasing difficulties, ranging from level 1 to level 5 for KS1 / KS2. The level descriptions provide the basis for making judgements about pupils’ performance at the end of a key stage.
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09/10/12 The KS1 Programme of Study By the end of Key Stage 1, pupils should have developed knowledge skills and understanding of the following aspects of mathematics:Ma 1: Using and applying mathematicsMa 2: NumberMa 3: Shape, space and measures
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09/10/12 PNS- Primary Framework for Literacy and MathematicsMathematicsThere are seven strands: Using and applying mathematics Counting and understanding number Knowing and using number facts Calculating Understanding shape Measuring Handling dataObjectives are aligned to the seven strands and these are subdivided into core learning by year group and core learning by strand
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ELPSDeveloping Rich Learning Experiences Experience – give children concrete experience Language – set up opportunities for children to talk Pictures – use visual imagery to develop maths concepts Symbols – use symbolic representation (Pamela Liebeck)
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Key ideas about addition and subtraction Developing secure mental arithmetic skills is critical Subtraction is the inverse of addition – they should be worked on at the same time as often as possible Addition is commutative and associative – subtraction isn’tThere are different ways to calculate. Talk about these,encourage them. Different strategies suit different sums Use what you know to work out what you don’t knowAdditions to 100 and related subtractions should be donementally/informally, not using a formal written method It’s OK to ‘write down’ mental arithmetic! Writing down sums horizontally invites you to try them mentally
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Activity • Write a number sentence to match these objects
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Suggest a number sentence1 2 3 4 5 6 7 8 9 10 Start the number track with 1, not 0
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Using a number line0 1 2 3 4 5 6 7 8 9 10 What number sentences can we make?
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Using a blank number line +7 12 9 17What number sentences can we make?
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Why are these visual models important?One reason is that many young children getstuck with questions like:
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Using visual models12 + = 19•In pairs role play the teacher and child•The teacher must help the child use anappropriate visual model in order to find theanswer•Set the child a more challenging problem tosolve
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DiscussionWhat is your view about What is your view aboutusing ICT to support the using ICT to support thelearning and teaching of learning and teaching ofMathematics in the EarlyMathematics in the Early Years? Years? Refer to Refer to examples from examples from placement to placement to support your support your view. view. ?
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BREO task 1Prepare a list of resources for your Early YearsMathematics box
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Success Criteria• I can explain to my friend – What ELPS stands for and why how it can be used to support young children to develop their counting skills – What is involved in counting• I can suggest some models and images that might help a child who is stuck with a question like 32 - = 19
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09/10/12 Task for Monday 15 October th• Identify an online resource to share with the class, e.g. a game, a puzzle, a show, that supports children’s understanding of simple addition• Be prepared to show it to the class• Be prepared to justify your choice and suggest some disadvantages
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