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^CompObjVSPELLINGgramme is followed through all classes.
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 Cooperative Learning
Collaborative and cooperative 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 cooperative 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.
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Kilcoe National School
Mathematics School Plan
Ratified by the Board of management:
Date& & & & & & .. Signed: & & & & & & & & & & & &
(Chairperson of the Board of management)
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 problemsolving abilities and a facility for the appreciation 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.
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
An inventory of all Maths equipment in each class room is available.
All Maths equipment bought with school funds remains the property 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.
Where a teacher deems it necessary supplementary materials will be designed/supplied.
Planet Maths protdoors to help teach mathematical concepts to children and make them aware of mathematics in their environment. Children display their mathematical work in their classrooms.
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 (see Maths Language Policy) 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
SENIOR INFANTS:
Introduction of signs: +, =
Vocabulary to match this: plus, equals (and, makes initially used as in junior infants)
FIRST CLASS:
PLACE VALUE: THE WORD UNITS WILL BE USED RATHER THAN ONES
RENAMING/GROUPING WILL BE THE METHOD USED THROUGHOUT THE SCHOOL
SECOND CLASS:
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.
FIFTH/SIXTH CLASSES
Tables
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 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), 4x3=12 (four threes 12), 5x3=15 (five threes fifteen). All teachers teach tables this way in order to ensure consistency and avoid confusion as children move from one class to the next.
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.
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 problemsolving children will be taught to apply the following strategies:
RUDE approach
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.
Solving the problem
Look for a pattern
Guess and check
Write an equation
Break the problem down and solve each part
Additional Help
Draw pictures
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,
U nderline the key words,
D raw a diagram of the problem,
E stimate 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 senior classes include the following:
Brain Snack, Countdown, Teacher designed booklets, PrimEd books, 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  end of term tests
Using concrete materials, manipulatives
Number stories, Number rhymes (Junior classes)
Birthday chart/ graph of favourite fruit/ colour etc.
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 selfassessment, conferencing, portfolio, conceptmapping, questioning, teacher observation, teacher designed tasks and tests, pupil profile, and standardised testing.
The following are other assessment tools used by teachers:
Teacher observation
Worksheets and work in copies
Extension and enrichment activities based on the strand unit being taught. Samples can be seen in the Teacher s Manual
Ongoing teacherdesigned tests. Children will bring the tests and the results of such tests home for signing. Test results are kept in pupil profiles in the office.
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 throughout the year. The results of each child s tests will be kept in their school file to be stored in the office. Results of the standardised test are communicated to parents at the parentteacher meetings and to the Board of Management.
Selfassessment
Following assessment teachers may do the following:
Give extra help to individuals who need it
Redo aspects of work that more than one child found difficult
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 (learning Support and Resource Teachers) 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.
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. Timetable
Two hours and 15 minutes for Mathematics is allocated for Infant classes. Class teachers timetables 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. Numeracy will also be addressed during appropriate areas of other subjects eg geography.
7. Homework
See the school Homework Policy.
.
8. ICT
Calculators From fourth class upwards children are permitted to use calculators alongside traditional paperandpencil 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.
Maths Software
See audit of software in the school for reinforcing the Mathematics curriculum.
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 Mosil.
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 June. At these meeting parents will be informed of the Maths programme for the coming 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 twoway communication between teacher and parent on progress in Mathematics or to other issues.
Individual parent/teacher meetings are held annually. 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.
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:
Ongoing 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.
Progress made during the school year will be reviewed in June of each year at a staff meeting and will be based on results of assessments across all classes and on teachers views as to the effectiveness of the plan.
An action plan may be compiled by all teachers to address weak areas.
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 2nd )
Addition:
Language: and, makes, add, is the same as, altogether makes
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
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
Addition:
7+3+8= 18
7 plus 3 plus 8 equals 18 (7 plus 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.
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, of
Multiply 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: Divisible by/ not divisible by, share among
12 4
all signs used , / etc.
12 shared among 4
12 divided by groups of 4 Repeated subtraction.
Fractions
of 32
7/2
Share 32 among 4 and/or 32 divided by 4
7 divided by 2
is equivalent to 2/4 (4th class)
is the same as 2/4
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
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
+ =
__ + __ __
4 4 = 4

__ _ __ __
4 4 = 4
Mixed numbers
+ and
3  1 =
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 + 2 ]! =
1 4/8 + 2 ]! = 3 9/8 = 4 1/8
(b) 1
+ 2 ]!
1 4/8
+ 2 ]!
3 9/8 = 4 [!
Method two:
(a) 1 + 2 ]! = 6/4 and 21/8
12 + 21 = 33
8 8 = 4 [!
(b) 1 + 2 ]! = 1 4/8 + 2 ]!
= 12/8 + 21/8 = 33/8 = 4 [!
Subtraction of fractions
Method one:
(a) 3 S!  1 7/9 = 2 12/9 1 7/9 = 1 5/9
(b) 3 S!
 1 7/9
2 12/9
 1 7/9
1 5/9
Method two:
3 S!  1 7/9 = 10/3 16/9
30 16 = 14 = 1 5/9
9 9
Multiplication
S! 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
5 =
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
1 1 1
Visual aids used by teacher
Decimals
1/10, 1/100, 1/1000 tenths, hundredths, thousandths
Addition
Subtraction
Rounding decimals
Multiplication of decimals
Division by decimals
Converting 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 bottom)
or
if possible you change the number to tenths/ hundredths and then convert to decimal. Look out for , , 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
Addition
Subtraction
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.
Coordination
Introduce (x,y) axis
Explain x comes before y in the alphabet. This will help them remember which comes first.
Area
Rectangle/ square
Length x width (l x w). breadth = width
Ares (1 Are = 100m, 1 hectare = 10,000m )
Relationship of sq.m to sq.cm.
Area of room from scale plan
Surface 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 = 360
Identify regular tetrahedrons, nets, construct
mber
Multiplying a decimal by a decimal
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