Learning and Teaching the Curriculum

CountingConcepts of Addition and Subtraction

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

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

Activity

• Close your eyes• Bring to the forefront of your

consciousness an image of the number three

Discussion

Key vocabulary

Aspects of number• Nominal• Cardinal• Ordinal

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

Sukoku

http://www.jigsawdoku.com/

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

The cardinal aspect

Cardinal numbers serve ‘as indications of how many there are in a set of things.’

Haylock and Cockburn, 2008, p.34

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

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

Play Alphabetland

• Number names are A, B, C, D…

• Do not‘translate’ these number names into the number names one, two, three,…

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

My world in numbers

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?)

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

Beautiful numbers

International perspectives

How many?

How many?

Resources to support counting

• Cuisenaire• Numicon• Bead strings• Dienes

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)

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)

What does learning to count entail? Rochel Gelman’s Counting Principles

• Stable orderYou need to know the counting words and be able to recite them in thecorrect order each time – it is impossible to count up to seven if you knowonly the first six counting words.• One to oneOne, and only one, number word has to be matched to each and everyobject; lack of co-ordination is a source of potential error.• CardinalityWhen correctly following the first two principles, the number name allocated to the last object tells you how many objects you have counted.• AbstractionYou can count anything – visible objects, objects of different shapes andsizes, things that are too far away to touch, objects that cannot be moved,moving objects, hidden objects, imaginary objects, sounds, etc.• Order irrelevanceObjects may be counted in any order provided no other counting principle isviolated.

http://www.teachers.net.qa/Math_CfBT_Workshops/workshop2/Ma2_Session8a.pdf

Early Years Foundation Stage

Early Years Foundation Stage

Mathematics involves providing children with opportunities to •Develop and improve their skills in counting•Understand and use numbers •Calculate simple addition and subtraction problems•Describe shapes, spaces, and measures

EYFS and Counting

Children are able to•Count reliably with numbers from 1 to 20•Place numbers in order •Say which number is one more or one less than a given number

The Structure and Content of the National Curriculum for Mathematics

The 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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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 data

Level 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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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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PNS- Primary Framework for Literacy and Mathematics

Mathematics There 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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ELPS Developing Rich Learning Experiences

Experience – give children concrete experienceLanguage – set up opportunities for children to talkPictures – use visual imagery to develop maths conceptsSymbols – use symbolic representation

(Pamela Liebeck)

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 possibleAddition 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 know

Additions to 100 and related subtractions should be done mentally/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

Activity

• Write a number sentence to match these objects

Suggest a number sentence

1 2 3 10987654

Start the number track with 1, not 0

Using a number line

0 421 3 5 76 108 9

What number sentences can we make?

Using a blank number line

12

+ 7

179

What number sentences can we make?

Why are these visual models important?

One reason is that many young children get stuck with questions like:

Using visual models

12 + = 19

•In pairs role play the teacher and child•The teacher must help the child use an appropriate visual model in order to find the answer•Set the child a more challenging problem to solve

DiscussionWhat is your view about using ICT to support the learning and teaching of Mathematics in the Early

Years?

What is your view about using ICT to support the learning and teaching of Mathematics in the Early

Years?Refer to

examples from placement to support your

view.

Refer to examples from placement to support your

view.?

BREO task 1

Prepare a list of resources for your Early Years Mathematics box

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

Task for Monday 15th October

• 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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