Mathematics

Aims:

We endorse the aims of the Primary School Curriculum for Mathematics which are:

  • To develop a positive attitude towards Mathematics and an appreciation of both its practical and aesthetics 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 proficiency in fundamental mathematical skills and in recalling basic number facts.
  • To enable the child to acquire an understanding of mathematical concepts and processes to his/her appropriate level of development and ability.

1. Strands and Strand Units

All teachers are familiar with the strands, strand units and content objectives in the Maths Curriculum and refer to them regularly when planning for their classes ensuring all strands and strand units are covered.

STRANDS STRAND UNITS
Early Mathematical Activities (Infants) Classifying, Matching, Comparing Ordering
Number Counting, Comparing and Ordering, Analysis of Number (introduced in Infants )
Numeration, Place Value, Operations: Addition, Subtraction, Fractions (introduced in 1st 2nd)
Multiplication, Division, Decimals (introduced in 3rd/4th )
Percentages, Number theory (introduced in 5th/6th)
Algebra Extending patterns (introduced in Infants)
Extending and using patterns (introduced in 1st/2nd)
Number patterns and sequences, Number sentences (introduced in 3rd/4th )
Directed numbers, Rules and properties, Variables, Equations (introduced in 5th/6th)
Shape and Space Spatial Awareness, 2D shapes 3D shapes (introduced in Infants)
Symmetry, Angles (introduced in 1st/2nd)
Lines and angles (introduced in 3rd/4th )
Measures Length, Weight, Capacity, Time, Money (introduced in infants)
Area (introduced in 1st/2nd)
Data Recognising and interpreting data (introduced in Infants)
Chance (introduced in 3rd /4th )

2. Resources

We acknowledge the importance of concrete materials in the development of mathematical concepts for children in all classes. Each class is supplied with Maths equipment suitable for that class level. The class teacher is responsible for checking these resources at the end of the year. A list of items that have to be repaired/replaced or additional items needed should be sent to Ms. Caroline Dolan.

  • An inventory of all Maths equipment in each class room is available from Ms. Caroline Gannon.
  • All Maths equipment bought with school funds remains the property of the school
  • Teachers may borrow equipment from other classes but must make sure that it is returned promptly
  • Mathematical books are stored in the staff room. Items must be signed for and returned within a week. A unit for Mathematical equipment for senior classes was built this September 2008. Equipment is stored in large plastic boxes. Infant teachers store Maths equipment in individual classrooms. A member from the curriculum support team is advised staff on the general restocking of Maths equipment in October 2008. The Parents Association donated €1,000 towards Maths equipment in 2009.

Resources are stored in a central area in a specifically assigned Maths press in the senior section of the school.

Textbooks are in line with the content objectives for each class level. Textbooks reinforce the concept taught and give adequate practice in each activity.

  • Teachers should not use the text chosen for the next class-level in the same scheme as this may lead to difficulties in terms of continuity and progression in the following year
  • Where a teacher deems it necessary supplementary materials will be designed/supplied

Jun. Sen. Infants: Figure it Out
1st/2nd classes: Planet Maths and New Wave Mental Maths
3rd – 6th classes: Planet Maths

3. Approaches and Methodologies

The following approaches and methodologies are used throughout the year:

  • The use of Manipulatives: Children will have access to and use a broad range of mathematical equipment during lessons. (see attached list of resources)
  • Talk and Discussion: Talk and discussion is seen as an integral part of the learning process and opportunities should be provided during the Maths class for children to discuss problems with the teacher, other individual children and in groups.
  • Active Learning/ Guided Discovery: As part of the Maths programme for each class children are provided with structured opportunities to engage in exploratory activities under the guidance of the teacher to construct meaning, to develop mathematical strategies for solving problems and to develop self motivation in mathematical activities.
  • Collaborative and Co-operative Learning

Collaborative and co-operative learning in junior – 6th classes is promoted using the following strategies:

  • Encouraging the children to listen
  • Encouraging the children to take turns
  • Seeing that others opinions are important
  • Children working in pairs while playing mathematical games.

Teachers use a variety of organisational styles to encourage co-operative and collaborative learning: pair work, group work and whole class work.

Using the environment/community as a learning resource: The school building is used as a resource to support the Maths programme. Teachers use the school environment to provide opportunities for mathematical problem solving e.g. numbers on doors, using hula hoops to sort children in PE, games on the playground, count trees in the playground, count windows, observe shapes of windows, doors etc.
Mathematical Trails are used outdoors to help teach mathematical concepts to children and make them aware of mathematics in their environment. Children display their mathematical work in their classrooms.
Metre measurements were painted in corridors in 2006 and height charts placed in the junior corridor.

Number:
The following number limits for each class will be adhered to:

Class Numerals
Junior Infants 0 – 5
Senior Infants 6 – 10
1st Class to 99
2nd class to 199
3rd class to 999
4th class to 9999

Data:
Children are encouraged to collect real data i.e. infant classes collect personal information and represent it on a pictogram for example; older children create and interpret bar charts and pie charts. Children are made aware of the importance of entering relevant data and asking clear question to extract the required information from the data.

Language – Concepts/ Skills
There is a strong link between language and concept acquisition. We feel it is important to have a common approach to the terms used and the correct use of symbol names. This language has been agreed at whole school level (2006 – 2007) in order to ensure consistency from one class to the next and also to help avoid confusion for children having difficulties with Mathematics. Our agreed strategies/language are on the following pages:

JUNIOR INFANTS:

No signs used

Addition: Language

SENIOR INFANTS:

Introduction of signs: +, =
Vocabulary to match this: plus, equals (and, makes initially used as in junior infants)

2
+  1
3
Top down: 
2 plus 1 equals 3
2 + 1 equals 3
2+1 =3 reads 2 plus 1 equals 3 or 2 and 1 makes 3

FIRST CLASS:

Subtraction: – is introduced as a symbol in First class
Language: take away, less than, left
 16
– 4
Vertical: start from the top using the words ‘take away’
16 take away four equals
5 – 1= Horizontal: Read from left to right using the words ‘take away’
5 take away 1 equals

PLACE VALUE: THE WORD ‘UNITS’ WILL BE USED RATHER THAN ‘ONES’
RENAMING/GROUPING 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  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 change a ‘ten’ to ten units,  7+10= 17. 17 take 8 equals 9. 1 take away 1 leaves O.

THIRD CLASS/ FOURTH CLASS

Rounding:
1, 2, 3 and 4 hey, ho, down we go
5, 6, 7 8 and 9 hey, ho up we go
Half way there which way we go?
Round me up hey, ho, ho.

Multiplication/ Division

 

 Short multiplication

Long multiplication

 Multiply by 10

÷ 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, ofMultiply top row by single digit in order, starting with units, then tens, then 100’s.
From bottom, units first. Language as above. Carry box used to distinguish the number carried over to be added, from the number being multiplied.When multiplying by 10, move digit one place to the left and replace the space with zero to show that the number was increased exponentially to the power of 10.Multiply by 100: Add two zeros
Division Language: Divisable by/ not divisable by, share among
  12 ÷ 4
all signs used ÷, / etc.
12 shared among 4
12 divided by groups of 4     Repeated subtraction.
Fractions
¼ of 32
7/2
Share 32 among 4 and/or 32 divided by 4
7 divided by 2½ 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
Tesselation Fit together with no spaces

FIFTH/SIXTH CLASSES:

Number: Multiplication / Division Language: square, prime, composite, rectangular numbers.
Finding common multiples by listing numbers
Finding common factors by listing factors
The words ‘product’ and ‘quotient’ are introduced. Problems involving sum, difference, products, quotients
Fractions: All children are taught to MEMORISE TABLE OF EQUIVALENT FRACTIONS, DECIMALS AND PERCENTAGES (see attached) 
Numerator, denominator
½ + ¼ = __ + __       __  
4       4    =   4
½ – ¼ __  _  __       __  
4         4    =   4
Mixed numbers
+ and –
3 ½ – 1 ¾ =
 Initially the children will be asked to deduce/hypothesise for themselves how to solve the addition and subtraction of mixed numbers. Those experiencing difficulties in this, through guided discovery by the teacher will be exposed to the following methods and from there will deduce the method they find logical to their thinking.

Addition of fractions

Method one:

(a) 1 ½  + 2 ⅝   =

1 4/8 + 2 ⅝ = 3 9/8 = 4 1/8

(b) 1 ½

 +   2 ⅝

1 4/8

+   2 ⅝

3 9/8 = 4 ⅛

Method two:

(a) 1 ½  + 2 ⅝  = 6/4 and  21/8

 12 + 21    = 33

8               8  =   4 ⅛

(b) 1 ½  + 2 ⅝  = 1 4/8 + 2 ⅝

= 12/8 + 21/8 = 33/8 = 4 ⅛

Subtraction of fractions

Method one:

(a) 3 ⅓ – 1 7/9 =

2 12/9 – 1 7/9 =

1 5/9

(b)  3 ⅓

_  1 7/9

 

2 12/9

_ 1  7/9

1 5/9

Method two:

3 ⅓ – 1 7/9 = 10/3 – 16/9

30 – 16 = 14  = 1 5/9

9           9

Multiplication

⅓ x 1/5

 

Multiply top number by top number
Bottom number by bottom number
Simplify/ break down

Division of whole number by fraction: Interactive board very valuable resource in teaching fractions (consult with Ms. Morris) 5 ÷ ¼ =
Change your whole number into a fraction and turn your second fraction upside down and multiply.
How many quarters in 5 units                           5  X   4  =  20
Visual aids used by teacher (see below)        1       1       1

 

Decimals 1/10, 1/100, 1/1000 – tenths, hundredths, thousandths
Addition
SubractionRounding decimalsMultiplication of decimalsDivision by decimalsConverting a fraction to a decimal 
to 3 decimal places (with/without calculator)
to 3 decimal places (with.without calculator)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
Count the numbers behind the decimal points in the question and make sure that there are the same amount of numbers behind the decimal point in the answer.
Multiply the divisor by 10/100 to change to whole number. If you multiply the divisor by 10/100 you must multiply the quotient by 10/100.You divide the numerator by the denominator ( divide the top by the the bottom)
or
if possible you change the number to tenths/ hundredths and then convert to decimal. Look out for ½, ¼, 1/5, 1/10, 1/100
Percentages 
Converting a fraction to a percentage
 

You multiply by a 100/1 or if possible you change the fraction to hundredths.

 

Time
AdditionSubtraction
 

Add minutes to minutes
Hours to hours and simplify (changing minutes to hours)

hrs.      mins.             hrs.      mins.

3            15               2          75

-2           33             – 2           33

If minutes number is bigger on the bottom line, convert… Take hour and change to 60 minutes. Add to other minutes and rewrite sum.

Co-ordination Introduce (x,y) axis
Explain x comes befor y in the alphabet. This will help them remember which comes first.
Area Rectangle/ square
Length x width (l x w). breadth = widthAres (1 Are = 100m, 1 hectare = 10,000m )
Relationship of sq.m to sq.cm.
Area of room from scale planSurface area
Find the area of one face. Count the faces and multiply by no. of faces.
Cube and Cuboid
Circle Radius, diameter, circumference, arc, sector,
Relate the diameter of a circle to its circumference by measurement. Measure the circumference of a circle using a piece of string.
Construct a circle of given radius/diameter
Examine area by counting squares.
Length

 

Irregular Shapes
Look for regular shapes. Divide the shape and draw diagrams.
Add areas a, b and c.
Lines and Angles Right angle, acute, obtuse, reflex, straight, degrees, protractor, ruler
2D shapes

 

3D shapes

Sum of the angles in a triangle = 180
Sum of the angles in a quadrilateral = 360
Sum of angles in a circle = 360Identify regular tetrahedrons, nets, construct

Tables
Addition facts up to 10 will be memorised by the end of Second Class (review 2012 – 2013) 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 e.g. 3 groups of 3, 4 groups of 3, 5 groups of 3 etc. Thus tables are recited throughout the school as follows: 3x 3 = 9 (three threes nine), 4×3=12 (four threes 12), 5×3=15 (five threes fifteen). All teachers are expected to teach tables this way in order to ensure consistency and avoid confusion as children mover from one class to the next. The bookMini book of tables is used by some teachers.

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

Children from 2nd – 4th 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. Class teachers identify children having difficulties with tables and with them set realistic targets ensuring steady progression. Children will have their tables discretely assessed (to avoid embarrassment) using teacher observation and weekly tests. Tables are continuously revised in 5th and 6th classes both incidentally through operations of various concepts/ core objectives but also formally through evaluations and games; “Fizz Buzz”, “Around the World! etc.

Skills
The following skills will be acquired by the children through the study of the various strands in the Curriculum:

  • Applying and Problem Solving
  • Communicating and Expressing
  • Integrating and Connecting
  • Reasoning
  • Implementing
  • Understanding and Recalling
  • Estimation

Every strand studied must provide opportunities for acquiring skills. Opportunities should also be provided for the transfer of these skills to other areas e.g. Science, Geography, Music.

Problem Solving
Children are encouraged to use their own ideas as a context for problem solving. With regard to problem-solving children will be taught to apply the following strategies:
Understanding the problem

• Read the problem
• Read it again
• Say, in your own words, what you are trying to find out
• Find the important information
• Look for key phrases
• Write what you know
• The Plan – Do – Review model (Hohmann et al 1979) is a useful strategy.

Pupil: I want to make a bed for Teddy
Teacher: Have you thought what you could use to make a bed?
The child is encouraged to think about the solution.
Start the project. Difficulties arise – bed too short etc.

Solving the problem

• Look for a pattern
• Guess and check
• Write an equation
• Break the problem down and solve each part

Additional Help

• Draw a picture
• Make an organised list or table
• Use objects to act out the problem
• Use easier numbers
• Work backwards

Answering the problem

• Use all the important information
• Check your work
• Decide if the answer makes sense
• Write the answer in a complete sentence

THE RUDE WAY OF SOLVING A MATHS PROBLEM: Children from 3rd – 6th classes, throughout the school are encouraged to use the following abbreviated model for solving a Maths problem – R ead, Underline the key words, Draw a diagram of the problem, Estimate your answer and then attempt to solve the problem. All children should be exposed to this model regularly and be very familiar with it by the time they reach 6th class.

Resources used for problem solving with 5th/6th classes include the following:

Brain Snack, Countdown, Teacher designed booklets, Prim-Ed books in staff library, internet and Planet Maths scheme.

Estimation
Estimation will form part of every Maths lesson. Children will be encouraged to use each of the following strategies selecting the most appropriate for the task in hand:

• Front end
• Clustering
• Rounding
• Special numbers

These strategies are explained on pages 32 – 34 of the Teacher Guidelines for Mathematics.

Presentation of work
There is an agreed approach to numeral formation in the junior classes. The rhymes or stories may vary but the formation is as follows:

• Straight down from the star
• Around from the star, then down, then straight
• Start at the star, then round and round
• Straight down from the star it goes, then across and put on its nose
• Go down from the star, around and put its hat on
• Start at the star then down we go, then all around halfway or so
• The star’s on his nose, go across, then straight down to his toe
• Around and around and up it goes until his tail can touch his nose
• Start at the star and around I go, then down a stick handle down below

In all classes Maths work is presented using a number of formats namely:

• Oral Presentation ◦ Teacher designed work sheets based on strand unit being taught.

◦ Work in class Maths Book which is an activity book
◦ Recording work.
◦ Using concrete materials to draw a picture, pictogram
◦ Number stories, Number rhymes (Junior classes)
◦ Birthday chart/ graph of favourite fruit/ colour etc.

A pencil only is used for writing numbers, and problems in Maths right up until the end of 6th class. Children are allowed to use erasers. A red biro is introduced in 3rd class for correction purposes only.

4. Assessment and Record Keeping:

Assessment is used by teachers to inform their planning, selection and management of learning activities so that they can make the best possible provision for meeting the varied mathematical needs of the children in our school. Teachers use a number of tools for assessing pupils’ work including self-assessment, conferencing, portfolio, concept-mapping, questioning, teacher observation, teacher designed tasks and tests, pupil profile, and standardised testing. Click here to see details on how these tools are used in 5th/6th classes.

In 2012 in an attempt to meet the needs of all pupils in mathematics, and to facilitate differentiation in the class, teachers used Mastery Record Sheets to identify specific targets for the ‘above average’, ‘average’ and ‘below average’ pupils. To download a copy of these sheets click on the class level you require.

Junior Infants       Senior Infants    1st Class      2nd Class

3rd Class             4th Class          5th Class      6th Class

The following are other assessment tools used by teachers:

• Teacher observation
• Worksheets and work in copies
• Assessment games
• Extension and enrichment activities based on the strand unit being taught. Samples can be seen in the Teacher’s Manual Mathemagic
• Ongoing teacher-designed tests. Children will bring the tests and the results of such tests home for signing. Test results are kept by the class teacher and passed on to the next teacher.
• Oral tests (tables, continuation of number patterns, …)
• Problem solving exercises that use a variety of mathematical skills
The Sigma T standardised test is administered every year during May from 1st – 6th classes while teacher designed tests are used througout the year. The results of each child’s tests will be kept in their school file to be stored by Ms. Kathryn Heneghan. Results of the standardised test are communicated to parents at the parent-teacher meetings. The full booklet is kept for one year after the test is administered. After this year, the front cover of the test with test scores is kept on file for ten years and the rest of the booklet is binned.
• Self-assessment including SALF (Self-assessment Learning Folders) and Maths Journals. For more information on Maths Journals click here.

Following assessment teachers may do the following:Give extra help to individual who need it

• Decide to increase time spent using concrete materials
• Discuss the situation with forwarding teacher at the end of the school year and beginning of new school year
• Discuss concerns with parents and encourage parents to help children informally e.g. Give me 3 spoons, Help me set the table, How many doors etc.
• Consult with the Special Needs team who will provide support when needed using available resources within the school.

5. Children with Different Needs

The Maths programme aims to meet the needs of all children in the school. This will be achieved by teachers varying pace, content and methodologies to ensure learning for all children.
Teachers are cautious not to label children as having difficulties in Mathematics especially in Junior and Senior infants. Records are stored in line with the school’s policy on Record Keeping.

Those children who receive scores at or below the 10th percentile on the standardised tests will have priority in attending the Learning Support teacher for supplementary teaching for Maths. The availability of supplementary teaching for Maths, however, depends on the case load of the Learning Support teacher. Arrangement will be in accordance with the recommended selection criteria as determined by the DES.

Class teachers of New Irish children and children from the travelling community will ensure appropriate Maths language is covered in class. Resource teachers will provide extra support for travellers falling behind, due to poor attendance.

Children in Junior and Senior Infants do not attend Learning Support. If a child is already attending the Learning support teacher for English, it may be possible, on occasion, for the child to receive some help with his/her Maths work as part of the supplementary teaching sessions.

Children with exceptional ability in Maths will be given extra work based on the concept being taught in class. ICT allows children to work at their own level and challenges children of all abilities. Parents will be consulted and opportunities for further development will be explored i.e contact Centre for Talented Youth Teachers should keep a record of the differentiated approach adopted for these children.

6. Time-table

Two hours and 15 minutes for Mathematics is allocated for Infant classes. Class teachers’ time-tables must record this time allocation form Mathematics. There is one hour discretionary time allocated for infant classes each week and this can occasionally be used for Maths.

7. Homework

See the school Homework Policy which is synopsised in the children’s school journal.

8. ICT

Calculators (In 2012 5th/6th class teachers decided that pupils would be encouraged to buy their own calculators as these can be carried onto Secondary school. )
From fourth class upwards children are permitted to use calculators alongside traditional paper-and-pencil methods. Calculators are particularly useful for handling larger numbers, to check answers, to explore the number system, to remove computational barriers for weaker children. They also allow the child to focus on the structure of the problem solving questions. It is important that the skill of estimation is developed along with the use of the calculator.
Calculators should meet the following requirements:

Calculators (90 in total) were purchased, following careful research, by Ms. Margaret Mannion during the 2006 – 2007 school year. It is intended that each child would have the use of a calculator at some stage during the school year. If parents wish to buy a calculator they must ensure the calculator uses Algebraic Logic as opposed to Arithmetic Logic. Algebraic logic uses priorities in sequences of operation which we call BOMDAS (brackets, of, multiplication, division, addition and subtraction)
• Keys should be of a reasonable size and have a positive click action
• They must have a display of at least 8 digits and be large enough for two or three children to see
• They should have a memory function

Maths Software
An audit of software in the school for reinforcing the Mathematics curriculum was done 2006 – 2007.

9. Individual Teachers’ Planning

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 Míosúil which will be submitted to the principal.

10. Staff Development

Teachers are made aware of any opportunities for further professional development through participation in courses available in Education Centres or other venues. Skills and expertise within the school are shared and developed through inputs at staff meetings.

11. Parental Involvement

Parents are encouraged to support the school’s programme for Maths. Meetings for parents take place in November. At these meeting parents will be informed of the Maths programme for the year. Particular attention will be drawn to:

• The importance of trial and error, estimation, the use of concrete materials and the role of calculators
• The school’s approach to e.g. subtraction, division, calculations using fractions..
• The fact that Maths homework may be used on practical activities
• The use of the Homework Journals as a vehicle for two-way communication between teacher and parent on progress in Mahtematics or toher issues.

Individual parent/teacher meetings are held annually in November. Teachers and parents are afforded this chance to discuss each individual child’s progress in Maths and other areas, and ways of assisting that progress. Parents and teachers are welcome to make individual arrangements to discuss matters of relevance at other times throughout the year.

Parents with particular expertise may be invited to address classes. Parents are invited to accompany field outings.

12. Community Links

Members of the local community may be invited to assist the school’s Maths programme. Proposed invitation must be discussed in advance with the principal.

13. Success Criteria

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

• On-going assessment, formal and informal, will show that pupils are acquiring an understanding of mathematical concepts and a proficiency in maths skills appropriate to their age and ability.
• Implementation of the school plan will be evident in teachers’ preparation and monthly reports.
• Teachers will know from their new classes in September that work/approaches as outlined in the plan have been covered by the previous teacher

14. Implementation, Review and Ratification

Class teachers are responsible for the implementation of the Maths programme for their own classes. The post holder with responsibility for Maths (Ms. Caroline Dolan) supports the implementation of the Maths programme and is responsible for the distribution and monitoring of resources.

Progress made during the school year will be reviewed in June of each year and will be based on results of assessments across all classes and on teachers’ views as to the effectiveness of the plan.

This 2006 plan was reviewed and updated 2011- 2012. It was ratified by the Board of Management in June 2012. The plan will be communicated to teachers and implemented in classes from September 2012.