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Introductory Statement and Rationale
Introductory Statement This document is a statement of the aims and objectives, principles and strategies for implementing the mathematics programme at Saint Hugh’s N.S. It was formulated by the school staff at a staff meeting in March 2005 and reviewed in October 2013. It is informed by the Curriculum Statements and Curriculum Guidelines, needs of the children and the expertise and experience of the staff.
Vision and Aims
Vision: Maths is a very important subject relating to the overall development of all our pupils. We hope that our pupils will enjoy their maths work and enjoy the practical and aesthetic elements in the 1999 Curriculum. We will try to focus on the presentation of Maths in a very real life environment where the children will benefit from the acquisition of life-skills. We also will try to allow each pupil to experience success in their work with a real emphasis on problem solving and understanding.
Aims:
We endorse the aims and objectives of the Curriculum for mathematics.
- To develop a positive attitude towards mathematics and an appreciation for 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 level of development and ability.
- To enable the child to acquire proficiency in fundamental mathematical skills and in recalling basic number facts
- To increase the standard of Maths in our school
- To give all pupils an opportunity to succeed regardless of ability.
- To ensure sharing of resources and most effective teaching approaches by staff members.
- To emphasise the practical aspects of maths using problem solving and social maths.
- To ensure that revision and assessment form an essential part of our maths teaching.
- To promote the idea that Maths is FUN, and can be enjoyed by all members of the school
Content of Plan
Curriculum:
1. .Strands and Strand Units:
For content overview see Curriculum: Infants p.17; First & Second classes p. 37; Third & Fourth classes p.61; Fifth & Sixth classes p. 85) Class teachers are familiar with strand/content objectives for their class levels, and plan accordingly.
2.Approaches and Methodologies:
We aim to teach the Maths Curriculum using the following and methodologies:
1 Talk and Discussion: We see a need for use of and development of language throughout all classes.
2 Active Learning/guided discovery: Children are encouraged to use concrete materials at all class levels to facilitate their learning. Use of games will also be deployed to further thinking and concept development.
3 Collaborative/co-operative learning. Pupils will work together on problem solving and many mathematical exercises allowing them to learn from each other.
4 Problem Solving: We will use lateral thinking, practical activities, open-ended questions, puzzles, games and contradictory surplus data to aid levels of problem solving.
5 Using the environment: Using Maths Trails and measuring activities, catalogues, league tables in sport, Cinema listings, bus timetables to enhance maths learning.
6 Skills through Content: That the children will develop their skills through the maths work in school.
The school will adopt a common approach to all areas to ensure continuity and consistency especially when transferring from the Junior groups to the senior groups. The school as a whole will encourage the accurate and effective use of mathematical language.
Books
The ‘Action Maths’ (Folens) scheme is by 3rd, 4th, 5th and 6th Class.
The ‘Planet Maths’ scheme is used by Junior Infants, Senior Infants, First, Second and Third Class.
‘Work it Out’ 1st – 6th Class
Tabletoppers 1st Class
Tables Champions 2nd – 6th
Brainsnack
Problem-solving in mathematics (Prim-Ed, Book D, E, F and G)
Enigmathics: Book A, B and C
Understanding Shapes and Measures
Maths Grid Games (Prim-Ed)
Maths Grid Games Number (Prim-Ed)
Schematic Teaching of Addition Tables
Addition Tables
- + 0 When I add 0 I make no change
- + 1 When I add 1 I meet my best friend up the ladder.
- + 2 Using a number strip (e.g. magnetic counters/peg boards).
3 + 2 = 5
- Doubles one to one correspondence e.g. using counters.
4 + 4 = 8
5.Near doubles 4 + 5 =4 + 4 + 1or5 + 5 - 1
5 + 6 =5 + 5 + 1or6 + 6 - 1
6. Commutative Law Buy one get one free.
4 + 3 is the same as 3 + 4.
7. Ten Facts 1 + 9, 2 + 8, 3 + 7, 4 + 6. Use the ten frame.
8. Through ten 10 + 2 = 12 ; 10 + 4 = 14 etc. Use the ten frame.
Multiplication/Division Tables
- Multiplication/Division tables will be introduced as repeated addition and repeated subtraction.
- Begin with 10 times tables followed by 5 times tables because they are the easiest ones to remember. These two will be the benchmarks for all others.
- Then teach 2X, 4X and 8X, followed by 3X, 6X, 9X
- Drill the multiples up/down the multiples ladder.
- Children will be taught strategies to assist understanding and easy recall of the basic facts.
- Commutative law
- Doubles
- One set more/one set less.
- Use of fingers for calculating 9 times
- Twice a known fact
- Use of games e.g. Snakes and ladders, Playing cards
- Use of dice
- Loop games
- Computer software: ‘Interactive Maths Games’ and ‘100 Maths Interactives’
3+0=3Three and/plus zero equals three
5-5=0 Five take away/minus/from five equals zero
0x2=0 Zero by/multiplied by two equals zero
5/5=1 Five divided by five equals 1
Language and the number operations
Addition
1.We introduce the addition of 3 add ends horizontally but this must lead to addition vertically.
In senior infants and 1st class 4+3+2= is the same as:4
3
+ 2
Always start adding from the bottom.
Addition using larger numbers
T U 1st/2nd
28
+ 2 15
53
Subtraction
1. Subtraction is performed using the ‘Borrow/Payback’ system
1
73
- 1 1 9
54
STANDARDISATION OF SOME MATHEMATICAL PROCEDURES IN THE SCHOOL
It has been decided to standardise the following mathematical procedures throughout the school in order to help children with learning difficulties.
1) Subtraction:
Subtraction is performed using the ‘Borrow/Payback’ system
2) Long Multiplication: 54
X 23
162
1080
1242
Golden zero strategy
3) Long Division:
0214
28 5992
-56
39
-28
112
-112
0
4) Time Calculations:
1 hr 35 mins.
+ 2 hrs 45 mins.
3 hrs 80 mins. (1hr. 20 mins.)
= 4 hrs 20 mins.
5) Finding a Fraction of a Number:
(a) Use Unitary Method. e.g. Find 3/8’s of 72
8/8 = 72
1/8 = 9 8 72
3/8 = 27 9
x3
27
(b) of = multiply
Find 3/8 of 72 3 x 72
8 1
6) Given a fraction find the whole number:
e.g. 7/9 of a number is 42 find the whole number.
7/9 = 42
1/9 = 6
9/9 = 54
9/9 = 6 x 9 = 54
7) Fractions: Addition of Mixed Numbers.
2 5/6 + 3 ¾ LCD = 12
= 2 10/12 + 3 9/12
= 5 19/12
= 5 + 1 7/12 - 6 7/12
8) Subtraction of mixed numbers:
Change to ‘Improper Fractions’, subtract the Numerators and revert to a ‘Mixed Number.’
Decimals:
3rd Class learn to link decimals to the fractions they have learnt: ½, ¼, ¾, 1/10s,
From Fourth Class on when dealing with decimals we will use money so that children will understand the place-value of the digits within a decimal number and learn from the physicality of the operation:
e.g.
€38 . 38=> T U . 1/10 1/100 Money
3 8 . 3 8 Place value
The decimal point is used to separate the pieces from the wholes.Decimals:The decimal point never moves in addition and subtraction:
e.g.2.4 + 3.76 + 1.957 2.4
3.76Snowman effect
+ 1.957
Fractions:Fractions will be introduced by using first using Fraction Circles.
e.g.
1 unit = 2 halves = 4 quarters
Paper folding will also be used to explain the equivalence of fractions:
2/8 = ¼4/8 = ½6/8 = ¾
Problem Solving: The focus is on real life problem solving
Types of problems
- Word problems
- Practical tasks
- Open-ended investigations
- Puzzles
- Games
- Projects
- Front – end estimation, e.g.347
- Rounding skills which are more precise than front-end estimation. By the time children leave 6th Class they should be able to round to the nearest 10/100/1000.
- Using paired numbers, e.g.
- Clusters e.g.
- 227 + 346 + 493 + 529 + 652 = roughly 500 x 5
Estimation Procedure for number
- Estimate first
- Write down your estimate
- Solve the problem
- Compare your estimate with the actual result
- lengths
- heights
- widths
- distances
- weights
- volume
- capacity
- Estimate
- Discuss or consider
- Measure or do
- Record or report
1. The calculator will not replace the basic facts (i.e. tables)
2. The first reason for using a calculator is for checking answers.
3. If problem solving is the main objective of the exercise, use a calculator.
4.Use a calculator for teaching place – value:e.g. 7846 - change to 7046
(800 has to be subtracted, not 8) 7846 - change to 7806 etc.
5.Mental Strategies: e.g. 85 + 96. The 9 key is broken. How do you do this sum on the
calculator? Find ways of making 96 without the 9 key, e.g. 85+ (100 – 4).
Language:in Mathematics
Junior Infants:sortobjectcolour
same as, match/mark, joinsame length, weight, height
big, bigger etc, tall heavier etcfull, empty, ‘holds’small
long, all terms re. Time, moving etc.to, from, before, after
short – lighter, lightestearly, lateset
curved, round, inside, abovemore, less few/fewer, othersstraight, corner, outside, below
too many, enoughcircle, rectangle, squareroll, stacked
triangle
how many more?Who? How? Why?Pattern
first, second, third etc.zerocoins,
shapenumerals one, two etc.how much
Senior Infants as Junior Infants: plus the following:
compareleastmost, heaviest, etc
addsame ashow far/how far more?
greater than/less thanmoneybreak up groups
high, lowcount on / backwide narrow
today, yesterday, tomorrowthick/thinmonths, seasons
days of week etc.holds more than/less thano’clock
holds most/least/the sameover, under, on, in, open,amount
joined, between, next toclosedhow long, short, heavy
straightcharts,measure
out, front, back, high lowsubtract/take away, go backcopy
around, 3D shapes, names,words for numerals
number strip cube,/cuboid
1st Class:as infants plus the following:
less, more,addition,missing numeral
numbersubtractionmake the same as
smaller, greaterrest of themsingle digit
take awaymeasurecentimetre
how many morechangegroup, order
days of weektens/ones/unitcalendar
between monthssubtract, steps
clock,make tenshalf past
problemdienes blocksabacus
circle, square, rectanglegraphbar chart
triangle, side, cornercube, cuboid, pyramidpictogram
faces, edgessphere, cylinder, conecounting in 2’s etc.
left overmagic squaresymmetry
number line100 squarecapacity
fraction odd, even. kgs
2nd Class: as 1st plus the following:
missing numbers half quartersforward, backwards
shaded setrenameplace value
in ordergridadd, group
metre, centimetresigndifference between
hundreddecimetrecounting
shapedbase 10’s etc.distance
number sentenceminutes/hours, quarter past/todifferent
digitalcodemidnight
subtractmiddaymagic square
timetableseasons2D, 3D hexagon
tessellatea.m. p.m.pictogram
prism, cuboid, cylinderblack graph. kgs
3rd Class: as 2nd plus the following:
Symmetrycovering area
Language of division and multiplicationmathematic sentence versus written 2X3 = 6
Divide,/divided by/division etc.capacity/liquid/litres, kls
Product weight – grammes / kgs
Factorslength – metres, cms, mms.
Setpictogramme
Angle, right angle, horizontal, vertical, diagonalsdecimal
Rectangle, cuboid, triangle, perimeterfractions – halves, quarters
4th Class: as 3rd plus the following:
capacity
division and multiplication – estimate, remaindermore/less. Litre, millilitres
quantityinto, by, from, under, value, more, less
weight shapes
G. kg. Light, lighter, etc. heavy objects.Horizontal, vertical, sloping, parallel, congruent,
Pointed, straight, square, solid, angle, acute,half, quarter, eighth etc/divide, shade, frame,
Obtuse etc.figure.
5th & 6th Class: as 4th plus the following:
fractionsshapes,
percentageoctagon,
arearhombus, quadrilateral,
length, width, surface, diameteroval, polygon
circumference, radius, base, perpendicular height,3D – cylinder – sphere, cone, cube, cuboid, pyramid
axis, reflection, image, parallel,triangular prism, tetrahedron
protractor.rotation, symmetrical
The Language of the Major Operations including Equals
additionsubtraction
more thantotal minus decrease
subtract
andsum of less than
add increase
difference take away
division
multiplication group
square multiply
divide
share
power of times split
product of of
equals
same as
means
=
answer is will be
represents
is
Mental Maths: It is school policy that mental arithmetic is a feature of daily mathematical activity.
Resources used include:
- Bingo Boards
- Target Boards
- Number fans
- Tables
- Work it Out
- Pizza Fraction Fun
Assessment is an integral part of the teaching and learning process. All strands of the maths programme will be assessed using a variety of assessment tools.
Teacher Observation
Interview Method
- Error Analysis
- Home work/Parental feedback
- Work samples
- Teacher designed tasks and tests
- Standardised Tests
- Diagnostic Tests
4. Children with Different Needs:
Children in each class will show a wide range of ability, attainment and learning styles. Consequently the mathematics programme will be flexible to accommodate children of different levels of ability and will reflect their needs.
Adapting to the needs of the less abled mathematical child:
- Use easily computed figures when introducing new concepts
- While the children will be exposed to all aspects of the curriculum certain areas must be prioritised
- Adapting the programme to suit their ability
- More individual attention
- More concrete approach
- Emphasising maths language
- Maths games
- Maths software
- Problem solving books/Brain Teaser Books
- Maths Facts Book
- Maths games
- Maths software
6. Timetable: The time spent on Maths was increased in January 2012 to 3 hours 35 minutes per week for infants classes and to 4 hours and 10 minutes for students with a full day to comply with the ‘The National Strategy to Improve Literacy and Numeracy among children and Young People 2011-2020.’
7. Homework:
Homework is given at the discretion of the teacher. Homework should not require teaching at home. It should be reasonable and achievable. Concepts for homework should be already well established in classroom practice. To prevent parents giving a child the wrong methodology no homework will be given on a particular concept until it has been well established in classroom practice.
Types of homework:
- Written consolidation of work done in class
- Tables
- Problem solving
- Practical assignments
- Research
- Collecting data
Like the calculator, the computer is a tool to enhance the implementation of the Revised Curriculum.
Some of the uses of ICT in Mathematics are:
- drill and practice
- data bases
- spreadsheets
Planning across the strands is detailed in short term and yearly plans by individual teachers.
10. Staff Development:
Maths as a subject is discussed at staff meetings & particular areas discussed & updated. Reference material is kept in the staff room & the principal has a lot of material relating to the Maths Primary Curriculum, which staff is encouraged to borrow.
10. Parental Involvement - Home School Links:
Communicating with parents about the correct terminology/language and methods being used involves:
- Advisory notes as the need arises
- Writing language of tables in the table book
- Parent -teacher meetings
Success Criteria
The use of assessment, as discussed earlier, is central to the monitoring of pupils’ progress in Maths. Success in Maths is determined by individual pupil achievement relative to their age & ability. Constant review & monitoring of skill development in all areas of Maths are important. Emphasis will be placed on interpreting the results of standardised tests at individual, class and whole-school level, to target areas of concern that may arise.
Implementation
(a)Roles and Responsibilities:
Implementation of the Maths curriculum falls to individual teachers in their classrooms. The class teacher has responsibility for all their pupils and constant liaising with support teachers is necessary. The principal has a role in ensuring that the overall teaching of the subject is in line with the school plan and to offer assistance & guidance where necessary.
(b)Timeframe:
The implementation of the curriculum is on-going but the current school plan should be evidenced in all classes by the end of 2013.
Review
(a)Roles and Responsibilities:
(b)Timeframe: A general review of this plan will take place in the second term of the 2007 – 2008 school year. This plan will subsequently be reviewed every three years.
Ratification and Communication
All teachers will be given a copy of this plan.
______Principal ______Chairperson BOM
______Date
Measures / DataSeptember
October
November
December
January
February
March
April
May
June
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