Mathematics

Maths Whole School Plan
Holy Family N.S.,
Tubbercurry

Introductory Statement
This plan was formulated by the staff of our school, following review, on a school development planning day on 20June 2006 and updated in September 2009.

Rationale
Maths is an integral part of a child’s education and is a vital part of the curriculum. Planning for Maths is particularly demanding as it impinges on every part of a child’s life. We have decided to refocus on this subject, paying particular attention to Maths language and oral presentation of Maths problems.

Relationship to Characteristic Spirit of the School
Our school cherishes all pupils equally, and our school seeks to create a happy, tolerant and safe environment in which each child is encouraged to strive towards his or her potential. We strive to ensure that each child will be able to express him or her self, in a way which allows them to participate fully in society.

Aims
We endorse the aims of the revised curriculum, and place a particular emphasis on the following:
– To develop a positive attitude towards mathematics
To develop an appreciation of Mathematics.
To develop problem solving abilities.
To develop a facility for the application of maths to everyday life.
To use mathematical language effectively and accurately.
To acquire proficiency in fundamental mathematical skills and in recalling basic number facts.

Objectives

Skills development

That the children would be enabled to
apply mathematical concepts
communicate and express mathematical ideas
make mathematical connections within mathematics itself
recall and understand mathematical terminology, facts, definitions and formulae.

Number
That the children are enabled to:
understand, develop and apply place value
approximate, estimate and calculate mentally
understand the links between fractions, percentages and decimals

Algebra
That the children explore, perceive, use and appreciate patterns and relationships in number.

Shape and Space
That the children will be enabled to
develop a sense of spatial awareness
investigate, recognise, classify and describe the properties of lines, angles and two and three dimensional shapes
draw, construct and manipulate two and three dimensional shapes
identify symmetry in shapes and in the environment

Measure
That the children will be enabled to
estimate, measure and calculate length, area, weigth, capacity and speed, angles, time and money
recognise and appreciate measures in everyday use

Data
That the children are enabled to
collect, classify, organise and represent data using concrete materials and diagrammatic, graphical and pictorial representations.
Read, interpret and analyse tables, diagrams, bar charts, pictograms, line graphs and pie charts
Estimate and calculate

Children will be enabled to use acquired concepts, skills and processes in problem solving in all of the strands mentioned above.

Content of the Plan
Uniformity of approach

It has come to our attention that uniformity of approach and progress in and between classes is imperative. As a result, we are now highlighting consistent maths language and number operations in all classes.

Maths Language

Numbers:
One, two, etc. Zero, nothing or nought. All three words used. Zero more commonly used.

Addition:
Words used – and, plus, add, sum of, more, combine, count on. All words used and explained constantly. However, “and” is the most commonly used form. This is also used when learning tables by rote.
E.g. 2 + 4 = —– two and four

Equals:
Are, equals, makes, is, total(s), altogether, gives, means, will be, answer is, represent, sum of, product, estimate, equivalent.
“Are” and “makes” are the most commonly used form.

E.g. 2 + 4 = 6 ——- Two and four are six.

Subtraction:
Take away, take, subtract, minus, leave, difference between, how much less, compare, how many are left, split, regroup, count back, decrease, difference between.
Preferred Teaching Method: 8 – 7 = 1 ———- Eight take away seven is.

And

46 6 take 9, I cannot do.
-19
Go to my tens, take one, cross out the 4, I’m left with 3. 16 – 9 IS 7. 3 take 2 is 1. My answer is27.

Multiplication:
Times, multiply (by), total, altogether, power of, square, estimate.
Preferred Teaching Method: Five twos ten.

Division:
Divide, share, into, equal, left over, remainder, repeated subtraction, how many times does it go into, divide by, divide into, multiples, split, round, fits into, go into.
Preferred Teaching Method: 36 – 6 Thirty six divided by 6 (rote)

Or
How many times will 6 fit into 36?
Or
Six into 36 is 6

Fractions:
Whole, two parts, four parts, fold, sets, share between, half, halves, quarter, quarters,
Thirds, sixths, twelfths, fifths, equal parts, denominator, numerator, improper, mixed numbers, compare, simplify, order, equivalent, tenths, hundredths, thousandths, relationship.

Decimals:
Tenths, hundredths, whole numbers, order, estimate, percent, percentages, order, decimal, decimal point, decimal place.

Number theory:
Odd, even, square, rectangular, triangular, composite, prime factors, multiples, consecutive, divisibles, divisors, common, square root,

Patterns and sequences:
Patterns, jump in twos/fives/tens, count in two/fives/tens, odd, even, hundred square, above, below, before, after, row column, order, describe.

Directed Numbers:
Positive, negative, temperatures, thermometer, increase, decrease, compare, balance.

Rules and Properties:
Frame, pattern, sequences, order, describe, predict, order, priority, symbols, signs, values, properties, brackets, terms.

Variables:
Variable, frame, pattern, sentences, describe, replace, substitute, symbols.

Equations:
Frame, pattern, sentences, order, describe, true, false, equation, symbols, variable, simple, complex.

Spatial Awareness: Describe, direction, underneath, on top of, around, through, left, right, right-hand side, left-hand side, half, quarter, next to, higher, lower, opposite, in front, straight, edge, forwards, backwards,

2-D Shapes: Square, rectangle, triangle, circle, semi-circle, oval, size, corners, sides, curved, flat, straight, edge, round, point, fit together, construct, design, rhombus, parallelogram, hexagon, trapezium, octagon, pentagon, equilateral, isosceles, scalene, right-angled, quadrilateral, polygon, regular, irregular, tessellate, tangrams.

3-D Shapes: Solid, cube, cuboid, cylinder, sphere, cone, square, circle, rectangle, circle, point, sides, faces, edges, vertices, roll, slide, straight, round, curved, prism, triangular prism, pyramid, construction, tessellate, parallelogram, polyhedron, tetrahedral, octahedron, template.

Symmetry: Fold, line, axis, symmetry, mirror, reflection, match, complete, half, fit, exactly,

Lines and Angles: Angle, corner, square corner, right-angle, fits exactly, moving, dymamic lines, vertical, oblique, horizontal, parallel, rotation, clockwise, anti-clockwise, greater than, less than, acute, obtuse, diagonal, strut, perpendicular, direction, reflex, sum, degrees, protractor, construct.

Length: Length, width, height, long,longer, longest, short, shorter,shortest, thick, thin, compare, estimate, measure, the same as, metre, metre stick, centimetre, about, longer than, shorter than, taller than, half, quarter, difference, kilometre, measurement, millimetre, perimeter, distances, area.

Area: Estimate, cover, surface, edge, flat, overlap, fit, space, gap, same area as, greater/smaller area than, compare, angles, squares, square units, regular, irregular, tessellate, compare, sets, hectare.

Weight: Weigh, weighs, weight, balance, heavy, heavier, heaviest, light, lighter, lighest, too many, too few, about, just over, just under, estimate , kilogram. Half, quarter, grammes, total, tonne.

Capacity: Full, empty, measure, compare, estimate, litre, nearly full, nearly empty, half, quarter, container, holds more, holds less, capacity, exactly, millilitre, graduated cylinder, volume.

Time: names of the days , months, seasons, hours, minutes, digital, next/last, early, earlier, earliest, late, later, latest, exactly, just before, just after, today, yesterday, tomorrow, date, o’clock, half-past, quarter to, quarter past, long, short hand, before , after, first, second ,third etc, counting in fives, rename, timetable, analogue, speed, distance, international time zones, convert,

Money: Coins, cent, price, spend, buy, sell, pay, change, cost, less, more, equals, exchange, cheap, cheaper, total cost, amount, altogether, same value as, how much, calculate, bill, value for money, unitary method, convert, currency, exchange rate charges.

Representing and Interpreting Data: Count, rows, columns, collect, collection, sets, construct, record, table, chart, information, more, fewer/less, fewest/least, difference, tally, total, estimate, how many, pictogram, block graph, bar chart, title, scale, bar line, data set, investigate, average.

Chance: Happen, occur, certain, possible, impossible, maybe, yes, no, perhaps, will, will not, might, might not, likelu, unlikely, definitely, toss, predict, occurrence, likelihood, random, uncertainty, experiment, investigate, actual, frequently, frequency, outcome,

Resources

Concrete Materials.
Infant Room
Links, clocks, teaching clock, beads, number jig-saws, pegs, straws, giant 3d shapes, blocks, number posters, teachers manual, selection of workbooks, workcards, 2D Shampes, height chart, number lines, cubes, lollipop sticks, weighing scales, plastic money.

First & Second Class
Clocks, abacus, large counters, set of addition table charts 2-12, rubber stamp number lines, beads and laces, dominoes, two colour spinners, 100 square, lollipop sticks, cubes, number lines, metre stick, height chart, Reference books, selection of workbooks, workcards

Third & Fourth Class
Mental Arithmetic (pegs and boards), 3-D shapes, hundred squares, Bingo games, 3 decimal sets , large protractor, metre stick, trundle wheel, Unifix cubes, Mathemagic posters and large compass. ( will use resources from senior room when necessary)

Fifth & Sixth Class
3 Weighing scales, rulers, calculators, fraction circles, fraction squares, tangrams, plastic shapes, protractor, clocks, fraction dominoes, relational attribute blocks, geometry fractions tangram activity kit, fraction tower, metre stick, protractor for blackboard, compass for blackboard, advanced card game, pentomino.

Resource Room
Cubes, counters, hundred squares/ number lines, multiplication boards (tables), base ten blocks, story of ten, wooden block sets, super duper sorting kit, Stile number books 1-12, CD roms – Number shark, number train, number plane, maths made easy 2, 2D and 3D shapes to sort, balance and weights, plastic clocks, toy money, metre stick.

Learning Support
Hundred squares, wooden number lines, number blocks, unifix cubes, Dienes blocks, links, fraction wall, fraction magnetic circles, maths CD – maths Blaster, number shark, games – Sum swamp, subtractions game, bus stop, auntie pastas pizza game (fractions), card games.

Use of the Environment
The childs own environment may be used in the teaching of maths. The school yard may be used when covering topics such as length, width, area and perimeter, Mathematical trails are particularly useful as they add a sense of fun and adventure to mathematical topics. Symmetry is all around us and is easy to incorporate into the childs own environment. Distance and number can also be integrated into the childs environment.

Parental Involvement
Parents can help their children informally by encouraging the correct use of mathematical language and the use of number, estimation and mental strategies in everyday life. Meetings with parents of Junior Classes to discuss uniformity of language, approaches and methodologies and how they can best help children are highly recommended.

Maths Games
Each teacher will use suitable maths games appropriate for the curriculum in their class.

Textbooks
The following textbooks are used in each class.
Junior and Senior Infants – Maths Aid
First Class – Action Maths
2 – 6 Class – Mathemagic and Shadow Book.
Teachers may chose to include a supplementary maths book such as Mental Maths.

Supplementary textbooks
The school has copies of various textbooks of parallel and above standards for each class. Pockets of graded worksheets can help in providing extension work for children who have mastered a concept.

Calculators
Calculators can enhance the implementation of the Maths Curriculum. They are part of the programme from 4 Class. In exceptional cases, some children may be allowed to use calculators for everyday use.

Thinking Strategies
Thinking Strategies and Addition Facts
Add 0, 1, 2
Counting on: Children can count on 1 or 2 without overloading their memory
2+3 = 3+2
Children need to understand the commutative property of addition
Adding 10
10 + 6, 10 +8 etc.
Subtraction is the inverse of addition
Doubles
5+5, 8+8, 4+4, etc. It is very important for children to know their doubles in order to allow work to be done on near doubles. This is also a good forerunner to multiplication.
Near doubles
This is any sum that is one away from being a double. 8+9, 4+3, etc.
Facts of Ten*
The numbers that add to 10: 6+4, 3+7, 9+1, etc.
Adding to 9*
One less than 10
Through 10*
Bridging the ten.
*The 10 Frame can be used to teach these three groups.

Thinking Strategies and Multiplication Facts

Repeated Addition
Get the children to make up 3 groups using 5 cubes. 5+5+5=15 or 3 groups of 5 is 15
Skip Counting
This can be done concretely on the number line or the 100 square before moving towards oral and written work.
4 x 6 = 6 x 4
Commutative property
Multiplying by 10
Doubles
Doubling the numbers (exponents). 6 x 6, 3 x 3, 7 x 7, etc.
One set more/less
This is a way to teach 4 and 6 times tables but the facts of 5 must be taught first. Therefore the 6 times tables are introduced as one set more than 5, i.e. 5 times 8 is 40 so 6 times 8 is 40 +8 = 48.
In the same way, 4 times tables are one set less.
Addition needs to be well known.
10s to teach 9s
9 groups of a numbers is one set less than 10 groups of that number
9 times tables on the fingers
Twice a known fact
4 x 7: 2 sevens is 14 so twice as much is 28. This can be a useful way of teaching parts of the 2,4,8 and 3,6 times tables.

Strategies for teaching Problem-Solving
Children should be taught a variety of strategies. Problem solving experiences should develop the ability to plan, take risks, learn from trial and error, check and evaluate solutions and think logically. The following strategies will be given to children to help them solve problems.

D – Decide what we have to do ( + – x etc.)
R – Reread the problem
A – Answer the problem
W – Write the answer properly, cent, metre, sweets, etc.

BOMDAS
Brackets, of, multiplication, division, addition, subtraction.

R A V E C C C
R – Read the problem carefully (x3)
A – Attend to key words (eg share)
V – Visualise problem ; use a picture/diagram
E – Estimate answer
C – Choose numbers to use
C – Calculate the answer
C – Check against your estimate.

Assessment
Record Keeping
Teacher Observation
Teacher Tests
Drumcondra Tests
Quest – Screening and Diagnostic test in reading and Maths
Homework – where the task is set in the home environment, ie. Weights/shapes/measures/timetable
Parent Teacher meetings: informative and informal

Linkage and Integration

Linkage is integration within the subject area itself. Strand content from one area supports learning in another one. Linkage in this way gives balance in the teaching of all strands.

It is very easy to link Mathematics with many other subjects, such as Geography, History, PE, Art, English, Irish, Outdoor Activities, Visual Arts, Study of the Environment, Music, Literacy, Print, Paint and Colour, Gymnastics, Dance and in many other aspects of our day to day living where we take chances and use our creativity.

Homework
Homework should be seen as reinforcement, as it offers an opportunity to widen experiences begun in the classroom , for example work with capacity or finding the area of a room. It encourages organisational skills and the ability to work independently.
Also see Homework Policy.

Children with Special Needs
Children with learning difficulties. (See learning support policy)
It is also important to consider the child who may be particularly good at mathematics. He/She can be given more difficult or taxing problems to solve rather than prematurely pushing him/her forward. Problems with two or three steps or open-ended problems are more difficult and provide a challenge. Once a concept is well understood it is better to use it in problem-solving activities than to overused rote computational exercises. Sequences of graded work-cards allow children to work at their own pace and to undertake extension activities.

Methodologies

Guided Discussion:
Guided Discussion is a very practical way of reinforcing mathematical concepts.
For it to be successful, however it is necessary that
all children are given the opportunity to speak.
The teacher and other children listen and respond positively.
Each child is encouraged to have the confidence to put forward his/her opinion.
The children are helped to explain clearly their points of view.

Hands on approach:
From infants to sixth class, children need to have “hands ons” experience with concrete materials. It helps them to understand concepts. This calls for a a lot of equipment and storage space.

Estimation:
Real life situations call on us to estimate many times every day. If we go shopping or measuring or calculating how long it will take to go on a journey we need to be able to estimate. Young children have to be taught to guess, then measure and calculate what the difference is. When we use calculators, it is good to have some idea what the answer should be. Estimation plays a big part in all strands of the mathematics programme.

Problem-Solving
Being able to solve problems is a very important factor in the study of mathematics. It is here that all the skills and concepts, already learned, can be applied. It is a vital link between the theory and the practice. It helps to develop the child’s reasoning powers and builds up self-esteem. It encourages curiosity and perseverance. Solving problems based on the environment of the child highlights the use of mathematics in a constructive and enjoyable way.

DEIS Initiatives that compliment and enhance the teaching of maths in our school:

Maths Recovery.
Maths Recovery is offered to qualifying pupils from First Class. The Resource teacher Ms. Gallagher has completed the training for Maths Recovery and works with children who are in need of this programme. For each participant a profile based on individual assessment is used to develop an individual teaching framework. In this school M.R. is individualised but after Easter the Resource teacher joins the class teacher in the classroom to work with Senior Infants in preparation for first class.

Ready,Set,Go,Maths
Ready, Set, Go, Maths is a DEIS initiative that provides guidance for infant teachers on a range of teaching and learning approaches to the key concepts and skills in early number. This programme is offered to the infant classes in our school and was introduced to us in the school year 2007/2008.
It centres on the substrands of:
Sorting
Counting and Recognition
Understanding Number
Relationships and Operations
Each year our school will add to the recommended resource list for this initiative. See Appendix 2 for existing Resources.

 

Success Criteria

It will be apparent that our policy is working if the children approach the mathematical concepts with an air of confidence and can complete the assessments for their age without too much difficulty. Also children who attend resource and learning support should make significant progress at their own level. (See NCCA Guidelines of Children with Special Difficulties)
Also feedback from parents and other staff members will be useful in assessing the success of our policy.

Roles and Responsibilities
All staff to support the plan.
Board of Management to ratify plan.
Parent to support the work of the school.

Timeframe and Implementation
Plan to implemented immediately and to be reviewed when deemed necessary.

Responsibility for Review
Post holder for Maths Equipment (Ms Gordon) to co-ordinate review when deemed necessary.

Ratification and Communication
Ratification by Board of Management.
It will be communicated to all staff on ratification .
Meeting with parents of Junior and Senior Infants to be held in early September.

The updated Maths Whole School Plan was ratified by the Board of Management.

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Appendix 1 to Maths Policy

Guidelines for Devising Questions and Tasks in a Maths Trail

??Items should be specific to the location and to the pupils for whom the trail is
prepared. Forumulaic or traditional textbook-type items are best avoided!
??Children should be encouraged to observe during the trail and then to focus on the
maths in the environment.
??It is good if items are grounded in a rich context. Narrative can also help to make
tasks more interesting for pupils.
??Pre-trail preparation and post-trail follow-up should be built into a maths trail.
??Some trails will focus on a specific strand whereas others may cover a number of
strands.
??A variety of tasks should be included.
??Items should be open-ended.
??Less items in a trail can be better if the mathematical content is interesting.
??Items should involve problem solving and estimation.
??New maths ideas should be introduced to children through the trail.
??Ask pupils how/why they arrived at a particular answer.
??Children should get the chance to look for maths in their environment and to
devise their own trails.
??The language of the trail is very important. The level, amount, reading level and
the clarity need to be carefully considered.
??One approach is to explain items to children first and then to use pictures as
prompts for the children while doing the trail. A book, Differentiation through
Maths Trails was recommended for having the same trail page for all pupils but
with different questions for each level.
??Stations/places on the trail might be marked with signs or paint.

Some ideas for creating mathematical trails
These ideas are to be used as a stimulus to developing maths trails at school level. They
constitute ideas only and will have to be adapted to class levels and appropriate content
inserted. Maths trails take a little time to develop but can then be used over and over again. It
is important to keep a balance over the strands and not always concentrated on the Number
strand.

MEASURES
??Name three things that are longer/shorter/heavier than the___________.
??Put the following objects in order starting with the shortest:
??How many pencils long is the bench?
??Which do you think is longer, the bench or you lying down?
??What day was it yesterday etc.?
??If you want to use the ________ what do you have to do?
??How much is the ______? If you have _________ how much more money do you need?
??How many centimetres long is the ___________?
??How many ________ would it take to cover the ____________?
??How heavy is the ____________ in grammes?
??Estimate how many _______ of water will fit in the ___________. Check
your answer.
??On what date was the _________ opened? How long ago is that in days,
months, years?
??How many ____________ can be bought with ___.
??How long is the ___________. Give your answer in metres (using
decimals or fractions, if necessary).
??If the train leaves the station at ______ and arrives in _________ at
________ how long will the journey take?
??Draw an analogue clock face showing the time on the ______________.
??How many pennies/cents does the _______ cost?
??How long is the perimeter of the ________ ?
??Find the area of the __________?
??What is the exchange rate today for buying US dollars? How many
dollars would I get for €100?
??How long does it take to _________?
SHAPE AND SPACE
??Where is the ___________? (over/under/beside etc.)
??Walk towards/away from the _________.
??How many corners on the _________?
??What shape is the ______________?
??Draw a __________ in the sand.
??What shapes can you see in this area?
??Find one example of symmetry in the area.

??Face the ________. Make one complete turn. Where are you facing?
Now make one half turn. Where are you facing?
??Why, do you think, is the _____ in the shape of a ___________?
??Use marla to make a model of the __________.
??Find lines that are parallel/vertical/horizontal.
??Face the ______. Turn one right angle to the right. What are you facing
now?
??Find an example of a right angle in the area. Find an angle that is
less/more than a right angle.
??What shape is the sign?
??How would someone in a wheelchair enter the building?
NUMBER
??How many ____________ are there?
??Are there more ________ or _________?
??How many more _____________than __________?
??Add the _______ and the _________.
??How many more ____ would you need to make 10?
??Write down the number on the _________.
??Estimate how many __________there are.
??Run from __ to __. Write down the order in which you came using these
words: first, second, third, fourth.
??Add the numbers on the _________.
??If each bench has four legs, how many legs in total in the park?
??If someone ate ¼ of the apples in the basket how many would they eat?
??What number is on the ________? Is the number greater than or less than
______. Round this number to the nearest thousand.
??Add the number on the ___ to the number on the ___.
??What do you get if you multiply all the digits in the number by each
other?
??How many seats are in this room? If the room were full of people and
each person paid 50c to enter how much money would be paid in total?
??How many sweets are in the box. If they were divided among ____
children how many would each child get?
??If one bun costs ___ and you can buy 4 for €1, what is the percentage
saving?
??What will this coat cost in the sale if 15% is taken from all items?
??What temperature is it here today. In winter the mean temperature is –2.
What is the difference between the two?
??There is a number written in Roman numerals on the grave stone. What
is the number in Hindu-Arabic numerals?
ALGEBRA
??If the pattern on the ________ was continued what colour would be next?
??Write down 3 interesting things about the number on the _________.
??What number would you take from 400 to give you the number on the
_________?

DATA
??If you had a choice would you buy a _________ or a ______________?
??Stand at the school gate. How many cars, lorries, vans, tractors pass in 15
minutes. Show this on a graph. Why do more lorries than cars pass at
this time?
??How likely is it that ___________ will happen here today?
??Put these statements in order of likeliness to happen.
??What is the average price of __________?