# Mathematics Policy

## Introductory Statement and Rationale

(a) Introductory Statement

The existing approach to Mathematics was reviewed and changes necessary to implement the Mathematics curriculum were identified. In collaboration with the teaching staff the following plan was drawn up.

(b) Rationale

This plan is a record of whole school decisions in relation to Mathematics in line with the Primary Curriculum, 1999. It is intended to guide teachers in their individual planning for Mathematics.

## Vision and Aims

(a) Vision: In our school we recognise the potential of each child in our care and endeavour to develop those qualities that make each child unique.

(b) Aims: We endorse the aims and objectives of the curriculum for maths and, in addition, we aim:

To develop a positive attitude towards mathematics and an appreciation of both 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 appropriate level of development and ability

To enable the child to acquire proficiency in fundamental mathematical skills and in recalling basic number facts

Content of Plan

Curriculum Planning

1. Strand and Strand Units

Teachers should familiarise themselves with the strands and ensure that each strand and both strand units are given equal prominence during the maths programme for the year. The content objectives are divided between the two classes at each level. .

The contents of the Strand and Strand Units can be found in the following pages:

Curriculum: Infants p.17-35;

First & Second classes p. 37-59;

Third & Fourth classes p.61-83;

Fifth & Sixth classes p. 85-111

The strands are:

• Early Mathematical Activities (Infants)

• Number

• Algebra

• Shape and Space

• Measures

• Data

2. Approaches and Methodologies

The following approaches and methodologies are used

Talk and discussion

Active learning and guided discovery

Collaborative and co-operative learning

Problem solving

Use of the Environment

The following approaches and methodologies will be used throughout the year

2.1 Talk and discussion

· Talk and discussion is seen as an integral part of the learning process. Opportunities will be provided during the maths class for children to explain how they got the answer to a problem and discuss alternative approaches to solving it with the teacher, with other individual children and in groups.

Where applicable the following strategies

Guided discussions and discussion skills

Scaffolding

Integration

Linkage

Mathematical Language in context. See separate Language List.

Number Facts

2.2 Active Learning & Guided Discovery

1. Concrete Materials/ Manipulatives

A hands-on approach is essential if children are to understand mathematical concepts. They will need a wide variety of materials when exploring tasks. This is important right through to sixth class and will require access to a considerable amount of equipment. Available

equipment is listed at the end of this policy. The use of concrete equipment will be necessary in all strands. Working with equipment can be done individually, in pairs or in groups, depending on the task. Mathematical games are used formally and informally to support and

consolidate learning i.e. matching, multiplication facts.

2. Textbooks and workbooks

The Planet Maths programme by Folens is in use up to sixth class. These texts cover

all strand units in each class. Teachers do not rely totally on the textbook and use

active learning wherever possible. The teacher’s manual, work cards and other texts

are available at the teacher’s discretion for use with children who need more

challenging exercises and also for the children who need reinforcement of concepts

(e.g. Planet Maths Satellite book). Texts listed are under ongoing review and may be

changed with the general consensus of the staff.

3. Estimation

Estimation must be seen as a strategy to be used throughout all the strands and not

merely restricted to number alone. These skills must be developed and refined so that

guesses can become more realistic and more accurate. Children should be

encouraged to use the following strategies selecting which is most appropriate for the

task in hand:

• Front end

• Clustering

• Rounding

• Special numbers

These are explained in the Teacher Guidelines pages 32-34.

In strands such as measure and shape and space, the hands-on

approach is vital if children are to develop an understanding of quantities

such as litres, metres, etc. It is important to teach the children to develop their own personal

benchmarks to be used when estimating, particularly in the measures

strand e.g. the width of their finger is close to a centimetre.

4. Calculators

Calculators are in use from fifth to sixth classes. Calculators must be stand alone i.e. not

incorporated into a ruler and the keys must be of a reasonable size. Children must be

taught to make decisions about when it is appropriate to use them such as checking

answers or for particularly large numbers. Calculators must not replace competent

computational skills. The children will learn that estimation and calculators work hand in

hand. Pupils with specific learning difficulties may be given access to calculators when

judged to be beneficial after consultation between the special needs teacher and the

classroom teacher.

2.3 Collaborative and Co-operative learning.

The maths curriculum allows opportunities for the children to work in

pairs/small groups. It provides opportunities to learn the skills needed for

turn taking, listening to others and taking on responsibility for particular

tasks within a group e.g. measurement.

2.4 Using the Environment

· Each teacher will be responsible for creating a maths rich

environment in his/her classroom. The maths equipment will be

easily accessible within the classroom and the children’s maths

work will be displayed where appropriate. Some Maths activities which involve use of

our environment include:

· Numbers on doors, car registration numbers

· How many rooms/ windows,

· Observe shapes, angles.

· Maths trails. Trails will always be mindful of health & safety.

· Measuring – drawing 1 metre on playground with chalk,

· Maths work is displayed in classrooms.

In our Green Schools Project we endeavour to integrate maths with many of our activities e.g. surveys, data representation.

· Class teachers can have “Puzzle of the week” at their discretion

where and when appropriate.

2.5 Skills through content

Applying and problem solving, e.g. selecting appropriate materials and processes in science

Communicating and expressing, e.g. discussing and explaining the processes used to map an area in geography

Integrating and connecting, e.g. recognising mathematics in the environment

Reasoning, e.g. exploring and investigating patterns and relationships in music

Implementing, e.g. using mathematics as an everyday life skill

Understanding and recalling, e.g. understanding and recalling terminology, facts, definitions, and formulae

All classes use mental maths.

2.6 Language of Maths

Mathematics has its own vocabulary and grammar. It must be spoken before being read and read before being written down. It is important that there is an agreed strategy for teaching concepts. Consistency in the language used from class to class is important. See Language of Maths at the end of this policy.

We have agreed the following:

JUNIOR INFANTS

No signs used

Addition:

Language: and, makes, add, is the same as, altogether, makes, plus

Informal introduction of signs:+,-, =

SENIOR INFANTS

2

+ 1

3

Formal Introduction of signs: +, =

Vocabulary to match this: plus, equals (and, makes initially used as in junior infants)

Addition:

1 and 2 makes 3

1 plus 2 equals 3

2+1 =3

reads 2 and 1makes 3

2 plus1 equals 3

FIRST CLASS

34

+17

Addtition :Add the units first

Put down the units and carry the ten. Now add the tens.

Subtraction:

– is introduced as a symbol in First class

Language: take away, less than, left, rename

16

– 4

Vertical: start from the top using the words ‘take away’

16 take away 4 equals

Informally: 6units take away 4 units is 2, 1 ten take away 0 is 1

5 – 1=

Horizontal: Read from left to right using the words ‘take away’ minus, subtract , less

5 take away 1 equals

Place Value: The word ‘Units” will be used rather than “ones”.

Renaming will be the method used throughout the school.

SECOND CLASS

Addition:

7+3+8= 18

7 plus 3 plus 8 equals 18 (7plus 3 equals 10 plus 8 equals 18)

6

3

+6

6 plus 3 plus 6

Encourage the child to choose the easiest method to add the three digits e.g. 6+6+3

Subtraction

Language: subtraction, decrease, subtract, take away, from, less than, minus, difference

27

-18

7 take away 8, I cannot do so I rename a ten, 7+10= 17. 17 take 8 equals 9. 1 take away 1 leaves O.

THIRD CLASS/ FOURTH CLASS

Multiplication/ Division

Short multiplication

(4th class) Long multiplication

Multiply by 10

Multiply by 100

÷ and x are introduced as symbols in Third Class. The following vocabulary will be used:

÷ division, divide, divided by, split, share, shared between, group, how many in …

X. multiplication, multiply, times, of

Start with 4 groups of 3 move onto…

4 times 3, 4 multiplied by 3, 4 threes

Start at the bottom

When doing long multiplication children will estimate answers.

Start with the bottom number. Multiply by the units first. Then multiply by the tens. Any renamed units go on the line to be added on. Children will have lots of practice in the commutative and distributive properties of multiplication.

Add a zero

Add two zeros

Division

Language: goes into, Divided by, divisible by, share among

12 ÷ 4

12 shared among 4

12 divided by 4

4 into 12 goes

Fractions

¼ of 32

Share 32 among/between 4 and/or 32 divided by 4

½ is equivalent to 2/4 (4th class)

½ is the same as 2/4

½ is equal to 2/4

Decimals

1/10 is equal to 0.1 1/100 is equal to 0.01

Include zero before decimal point

FIFTH/SIXTH CLASSES

Number:

Multiplication/Division

Division

Language: square, prime, composite, rectangular numbers, square root, units, tens, hundreds, thousands, ten thousands, hundred thousands, rename, relationship, combine, split, compare

Finding common multiples by listing numbers

Finding common factors by listing factors.HCF, LCM

The words ‘product’ and ‘quotient’ are introduced. Problems involving sum, difference, products, quotients. Times, groups of, remainder

Children will have practice in division by 10, repeated subtraction, importance of estimation, front end estimation, find the remainder.

Fractions:

Numerator, denominator, improper, mixed numbers, equivalence, simplify, relationship

½ + ¼ =

__ + __ __ Use the same denominator

4 4 = 4

½ – ¼

__ _ __ __ Use the same denominator

4 4 = 4

Mixed numbers

+ and –

3 ½ – 1 ¾ =

Make sure the fractions have the same denominator. The process is based on equivalence of fractions. Do you need to rename a unit when subtracting? Make sure final answer is simplified .

Multiplication

3×1/3

1 X 1

3 2

Use of repeated addition

X means “of”, 1/3 of a 1/2, pupils will see a pattern emerge. Multiply numerator by numerator(multiply the top numbers)

denominator by denominator (multiply the bottom numbers)

Simplify/ break down

Division of whole number by fraction

5 ÷ ¼ = How many 1/4s are in 5? Pupils will see a pattern emerge.

Rename the whole number as a fraction and turn the divisor upside down and multiply.

How many quarters in 5 units 5 X 4 = 20

Visual aids used by teacher 1 1

Decimals

1/10, 1/100, 1/1000 – tenths, hundredths, thousandths, order, decimal point, decimal place

Addition

Subraction

Rounding decimals

Multiplication of decimals

Division of decimals

Converting a fraction to a decimal

to 3 decimal places (with/without calculator)

to 3 decimal places (with. without calculator) Pupils are directed to correctly align the numbers.

to the nearest whole number

to 1 decimal place

to 2 decimal places.

Multiplying a decimal by a whole number

Multiplying a decimal by a decimal

How many digits are after decimal point in the sum? Make sure there are the same no. in the answer

Importance of estimation and alignment of decimal points in the answer.

You divide the numerator by the denominator or

if possible you change the fraction to tenths/ hundredths and then convert to decimal. Look out for ½, ¼, 1/5, 1/10, 1/100

Percentages

expressing a fraction as a percentage

Percent, percentages

You multiply by a 100/1 or if possible you express the fraction as a hundredth.

2.7 Tables

Number facts up to 10 will be memorised. Addition facts up to 10 will be memorised by the end of Second Class and multiplication facts up to 12 by the end of Fourth Class. Both will be revised up to the end of Sixth Class. Multiplication is a natural progression from extended addition.

Pupils say tables like this: 1 time 4 is 4, 2 times 4 is 8, 3 times 4 is 12.

A variety of methods will be used including counting 2s, 3s, 4s …, reciting, using music tapes etc. Subtraction and division tables will be learned as the inverse of addition and multiplication.

Children from 2nd – 6th classes recite their tables regularly and tables are reinforced every day. Children are encouraged to memorise tables and tables are given every night for homework. Teachers keep a record of tables that have been learnt and identify children having difficulties with tables and will set them realistic targets ensuring steady progression.

2.8 Problem solving

· The ability to solve problems is at the heart of maths. It makes the learning of maths more interesting and enjoyable. It allows them to use the mathematical skills and knowledge they have already acquired. Problems can come in many different forms.

Types of problem solving used in school:

Real life problems.

Word problems.

Puzzles

Maths games.

Open problem solving – more than one way of doing it.

Maths trail.

Children need to be taught strategies to problem solve. The following are strategies that teachers might choose:

Strategies for solving:

Personalise story/problem.

Visualise – draw it out.

Act it out.

Estimation.

Solve simpler version.

The ROSE Approach

1. Read the problem. Paraphrase the problem Try substituting simpler

numbers for larger numbers or fractions or decimals. This makes

estimating easier.

2. Organise the mathematical operations you will use

3. Solve the problem

4. Evaluate your answer. Was it the best method? Does it match the

estimate?

RAVECCC

1. Read the problem carefully

2. Attend to the key words

3. Visualise the problem

4. Estimate the answer

5. Choose the numbers to use

6. Calculate the result

7. Compare the answer to the estimate

Problem solving RAVECCC bookmarks can be used. (Appendix 4)

The RUDE Approach

1. Read the problem.

2. Underline key words

3. Draw a picture or diagram

4. Estimate the answer.

2.9 Presentation of Work

Recording of maths work in infants is done in the maths text book.

From 1st class upwards, smaller copies are used unless particular difficulties arise.

In senior classes the presentation of written work in

Maths is as follows:

• Each page is to be divided into two categories/columns. The order of writing sums is to be written vertically down the page, as opposed to horizontally.

• A variety of options for presentation will be availed of where appropriate at teacher’s discretion for example drawing pictures to show result, concrete materials, diagram, verbally etc.

Integration

Maths is a living subject with endless possibilities for integration such as in art and science e.g. measuring temperature. We believe that the integration of mathematics with other subjects is an important factor in broadening the child’s education. Elements of number, time and measure – length can be applied to activities in physical education. Work in mathematics is needed when conducting surveys for the Green Flag School Project. Artwork is a very effective way of consolidating learning in shape – e.g. tessellations. A thematic approach to mathematics brings cross-curricular activities into play – e.g. in SESE, SPHE, Language, Physical Education, Arts education.

3.Assessment and Recording Keeping

Assessment is an essential element of the school plan for mathematics. It is used to monitor pupil progress and to inform future planning. The following assessment tools are in use.

Knowledge, skills development and participation levels are assessed by teachers.

Teachers select from the following range of assessment approaches:

o Teacher observation

o Teacher-designed tests and tasks

o Work samples, portfolios and projects

o Curriculum profiles

o Mastery records

o Diagnostic tests (mainly resource/learning-support)

o Standardised tests

o Self Assessment.

As part of our whole school assessment the Drumcondras are used from first class to sixth

class.

These standardised tests are carried out once a year by the class teachers. A copy is given to the Learning Support Teacher and is kept on file in the Principal’s office.

Other standardised tests that may be used are: Sigma T

• Teacher observation provides ongoing assessment of oral and written

class work and homework. The children’s work in their copies and folders

is a record of his/her progress.

See Assessment Policy..

4. Children with Different Needs

(a) Class Teachers use the following strategies to ensure the participation of children with special needs in relation to mathematics:

• Use of concrete materials

• Oral explanation and discussion to ensure pupils with literacy difficulties can participate in

the maths class.

• Direct teaching, demonstration and explanation by the class teacher.

• Teaching of the language of mathematics

• Discussion between the teacher and pupils.

• Group Activities

• Opportunities to practise and consolidate fundamental skills and routines using oral as well

as written examples.

(b) Children with special needs are provided with access to all strands of the mathematics curriculum.

(c) Teachers in mainstream classrooms provide a differentiated programme to cater for children with learning difficulties.

Supplementary teaching in mathematics is available for children with learning difficulties. Where children have a STEN score of 3 or less in the Drumcondra standardised test, then one to one assistance is offered. (This could be in-class or withdrawal).

See Learning Support Policy.

Withdrawal of pupils for supplementary teaching

It is important that there is collaboration between class teacher and resource/learning support teacher so as to ensure the child was not consistently absent for maths instruction.

Team teaching is also encouraged, where teachers can work with smaller groups

5. Equality of Participation and Access

The school plan for Mathematics is designed to allow all children full access to all aspects of the Mathematics Curriculum. Equal opportunity is given to boys and girls to access all parts of the curriculum. Pupils whose first language is not English are given extra help within the school. Children with special physical needs catered for to the fullest possible extent

Organisation

6. Timetable

In line with our numeracy & literacy strategy, maths time has been increased by 70 minutes per week:

· Junior/Senior Infants: 3 hours 25 mins.

· 1st-6th Class: 4 hours 10 minutes.

This extra time will be achieved by:

Numeracy will be increased by 70 minutes by supplementing regular maths time by doing mental maths for 10 minutes every day. This will be done using discretionary time.

7. Homework

• Homework is based on the concepts and content covered in class.

• Homework allocated should take account of the differing levels of ability in the class and

should be a positive experience for all. Maths homework will generally involve both a

written and oral element i.e. computation/problems and tables/mental maths

• Practical activities should be given from time to time (e.g. measuring) bearing in mind the

age and level of the class

• Time should be given for the correcting of the maths homework and an opportunity to discuss any problems that arose.

See Homework policy.

8. ICT

Software is stored in each classroom.

There is an Internet connection in each classroom and the pupils under

the supervision of an adult can use the Internet to enhance learning in

mathematics.

Websites:

· www.mathletics.ie

· www.mangahigh.com

· www.schoolhub.ie

Software:

· Numbershark

9. Individual Teacher’s Planning and Reporting

Teachers should base their yearly and short term plans on the approaches set

out in this whole school plan for maths. Work covered will be outlined in the

Cuntas Miosuil which will be submitted to the principal.

10. Staff Development

An atmosphere of open communication exists between all the staff members

and ideas and expertise is shared. Discussion and planning in class groupings is encouraged. Teachers are informed of maths related courses and encouraged to attend.

Information acquired on these courses is made available to other staff members.

Time is allocated at staff meetings for the discussion of maths related business when necessary.

11. Parental Involvement

The school recognises the importance of parents in a child’s education and welcomes their involvement in the implementation of the Mathematics programme. Such involvement could be as follows:

• A letter to infant parents with examples of number formations and recommendations on how to develop their child’s mathematical awareness through everyday activities is provided.

• Parents are encouraged to supervise and be involved in maths homework.

• Annual parent teacher meetings provide maths assessment information. Further meetings could be arranged at the request of the parents or teacher.

• Annual written reports are forwarded to all parents in June of every year. These provide details of the child’s progress in maths.

Success Criteria

The success of this plan will be measured using the following criteria:

· Continuity of content and methodology through the strands and class levels

· On going assessment will show pupils are developing a level of appreciation of Maths appropriate to their age and ability.

· Feedback from Inspectors, Parents, Second level schools

Implementation

(a) Roles and Responsibilities: Class teachers are responsible for the implementation of the Maths programme for their own classes.

(b) This policy shall be implemented with immediate effect.

Review

It is envisaged that this policy is reviewed over a 2-3 year period.

Ratification

This plan was ratified by the Board of Management on 7th November 2012