Mathematics/Mhatamaitic

Title

Mathematics School Plan

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 Lisaniskey NS. It was formulated by the school staff and informed by the Curriculum Statements and Curriculum Guidelines, needs of the children and the expertise and experience of the staff.

Rationale

Pupil and teacher learning is enhanced;
Shared view of school’s philosophy regarding maths;
Children will benefit from structured approach regarding content and methodology;
To increase the standard of maths in our school
Teacher’s workload is shared;
Self esteem of staff and pupils is enhanced;
Most effective approaches are shared;
Resources are researched and shared;
It is the most effective instrument by which efforts and strengths of both teachers and pupils are harmonised and co-ordinated;
That revision and assessment form an essential part of our maths teaching
Guide for coping with change/ future action

Eg. Due to maths in-service we decided to review the teaching of maths throughout the school to conform to principles outlined in the revised curriculum.

To ensure that each teacher meets the learning needs of each pupil. Continuity is maintained without overlap; and there is uniformity of attitude and approach on certain issues.

Vision and Aims

Vision:

To aid the children in achieving their true potential in maths
To give all pupils an opportunity to succeed regardless of ability
To foster in them a love of maths
To provide the child with the necessary skills to live a full life as a child and later as an adult
To emphasise the practical aspects of maths using problem solving and social maths
That maths is fun and can be enjoyed by all members of the school community.

Eg. We see maths as being very important in relation to our school and very necessary in the development of all our pupils. It is a subject, which has many values including practical and aesthetic and can benefit all our pupils.

Aims: (PG 12-14 of Content statement)

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.

Content of Plan

Curriculum:

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)

In order to ensure that all teachers are familiar with the curriculum for their class level, we will consult our Curriculum Handbooks, and our Maths at a Glance cards.

In order to ensure that this familiarity is maintained if teachers change classes or if new teachers join the staff, we will have a Staff meeting as early in the school year as possible, (or before the school year starts if possible); regular formal and informal review and planning between teachers of same level classes.
With regard to multi class situations, at the middle and senior levels of the school, topics/themes will be introduced to the whole class at the same time, with development and differentiated teaching as a follow on. This will also be done in the Junior room, as far as possible, but, there is little scope for this. Generally, lessons will be on a class basis, as opposed to a whole room activity.
When there is a split class within the school, it is envisaged that the relevant class teachers will plan each week what content and methodologies will be used in the following week.

Integration

A cross curricular approach will help the child to make connections between different curricular areas, add to the child’s enjoyment of mathematics and encourage the transfer of learning.

Linkage

All the strands of the mathematics programme will be seen and taught as interrelated units in which understanding in one area is dependent on and supportive of ideas and concepts in other strands.

Approaches and Methodologies: SEE APPENDIX 2 “USE OF MATHS LANGUAGE IN THE SCHOOL”

General

Tables

Schematic Teaching of Addition Tables

Addition Tables

+ 0 When I add 0 I make no change

+ 1 When I add 1 I “jump on 1 place on the number line”.

+ 2 Using a number line (e.g. magnetic counters/peg boards).and I “jump on 2 places on the number line.”

3 + 2 = 5 Language: “3 and 2 makes/is equal to/is the same as 5”

Doubles one to one correspondence e.g. using counters.

* * * *

4 + 4 = 8

Near doubles 4 + 5 = 4 + 4 + 1 or 5 + 5 – 1

5 + 6 = 5 + 5 + 1 or 6 + 6 – 1

* * * * *

* * * *

Commutative Law Buy one get one free.

4 + 3 is the same as 3 + 4.

Ten Facts 1 + 9, 2 + 8, 3 + 7, 4 + 6. Use the ten frame. NUMBER STORIES

Through ten 10 + 2 = 12 ; 10 + 4 = 14 etc. Use the ten frame.

Do addition practically first (e.g. using counters, number lines, 100 square,) and then abstractly.

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

Activities for tables

Use of games e.g. Snakes and ladders, Dominoes, Playing cards
Use of dice
Loop games: Marbles card game, Basic Doubles card game
Competitions eg. Knockout, Buzz, Beat the clock
Videos, computer software, cassette tapes, web-sites

– Talk and Discussion

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. This policy will be communicated to parents so they can help children constructively with homework. The school as a whole will encourage the accurate and effective use of mathematical language.

Language of tables

3 + 0=3 eg. Three and zero equals three

5 – 5=0 eg. Five take away five equals zero

0 x 2=0 eg. Zero times two, zero multiplied by two, two zeroes ( senior room)

10 ÷ 5=2 eg. Ten divided by five equals 2, five into ten goes twice/two times.

Language and the number operations

Addition with regrouping

1. We introduce the addition of 3 addends horizontally but this must lead to addition vertically.

In senior infants and 1st class 4 + 3 + 2= is the same as: 4

+ 2

Always start adding from the bottom. When the children have mastered this process, they can then apply the commutative property of addition, ie start with the biggest number and add on the next one; look for the tens and add on the other number.

Introduce addition with regrouping using Dien’s Blocks,

T U

1 8

+ ₁ 4

2 2

four and eight is twelve.
Twelve is too big for the Unit house, so I swap ten units for a stick of ten, and he goes over to the ten house. The two units stay in the unit house.
How many tens in the tens house now? Two.
Now I have two tens left in the Ten house and two units in the unit House. That makes twenty two “22”.
Demonstrate this first using Dien’s Blocks and then introduce the actual sum as well.

Subtraction with regrouping

Introduce subtraction with regrouping using Dien’s blocks:

	T		U
²	3	¹³	3
			9
	2		4

3 take away 9 you cannot do. Where could we get some more units from? We’ll borrow a stick of ten from the ten house. To come into the unit house, he has to change back to ten units.
Now we have 13 units in the units house. 13 take 9, we can do. We have 2 tens left and 4 units left and that makes 24.
Demonstrate this using only Dien’s Blocks first and then introduce the actual sum as well.

When the children are comfortable with the procedure you can suggest writing the sum like this to save time:

T		U
² 3		¹ 3
		9
2		4

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.

Subtraction: From 2nd class on we should use the decomposition method throughout the school as shown for 2nd class.

Long Multiplication: 54

x 23

162 —– 54 x 3

1080 —– 54 x20

1242

Always remember the zero for the 2nd line (multiplying by the ten)

Long Division:

0214 EMSD strategy (Estimate, Multiply, Subtract, bring Down)

28 5992

-56

-28

112

-112

Time Calculations:

1 hr 35 mins.

+ 2 hrs 45 mins.

3 hrs 80 mins. (1hr. 20 mins.)

= 4 hrs 20 mins.

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

x 3

³/₈ = 27

(b) of = multiply

Find ³/₈ of 72 3 x 72

8 1

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 (42 ÷ 7)

⁹/₉ = 6 x 9 = 54

⁹/₉ = 54

Fractions: Addition of Mixed Numbers.

2 ⁵/₆ + 3 ¾ add the units first; 2+3=5 LCD = 12

= ¹⁰/₁₂ + ⁹/₁₂

= ¹⁹/₁₂(1 + ⁷/₁₂) go back for your units

= 5 + 1⁷/₁₂ = 6⁷/₁₂

Subtraction of mixed numbers:

3 ¹/₅ – 2 ⁷/₁₀ Subtract the units first 3-2=1 LCD = 10

= ²/₁₀ – ⁷/₁₀ ²/₁₀ is too small, borrow one unit. That leaves me with no units.

That becomes ¹⁰/₁₀, and add it to the ²/₁₀ . That makes ¹²/₁₀

= ¹²/₁₀ – ⁷/₁₀

= ⁵/₁₀ = ¹/₂

DECIMALS: 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.

Fractions: Fractions will be introduced by using Fraction walls and Fraction Circles:

e.g.

○ ○ ○

1 unit = 2 halves = 4 quarters

Paper folding will also be used to explain the equivalence of fractions:

²/₈ = ¼ ⁴/₈ = ½ ⁶/₈ = ¾

Decimals: The decimal point never moves:

e.g. 2.4 + 3.76 + 1.957 2.4

3.76 Snowman effect/ Buttons on your shirt.

+ 1.957

Estimation

Estimation skills are developed in all strands and at all levels.

In teaching Measures at all levels we take every opportunity to have the children practise estimation of

*Lengths *heights

*widths *distances

*weights *volume

*capacity

Key strategies for Measures

Estimate
Discuss or consider
Measure or do
Record or report

In teaching Number we develop estimation skills by practising a

variety of strategies including:

Front-ended strategy,
Clustering strategy,
Rounding strategy
Special numbers strategy

Estimation Procedure for number:

Estimate first
Write down your estimate
Solve the problem
Compare your estimate with the actual result

Calculators

Children from Third & Fourth Class using calculators are encouraged to estimate first what the answer to a problem should be. Calculators are generally used for correcting sums. They are also used by some children with special needs, having been shown how to use them properly, to facilitate speed and proficiency, thus developing confidence and self-esteem.

Mental Maths

It is school policy that mental arithmetic is a feature of regular mathematical activity.

Resources used:

Bingo Boards
Target Boards
Number fans
Tables

– Active Learning and Guided Discovery

It is school policy to use materials at all levels and appropriately because …..

Concrete materials play an important role in concept development. They provide a link to connect the operational to real world problem-solving situations.
Experience with concrete materials also facilitates the development of appropriate language as children communicate about what they are doing and what they see happening.
As they use models children should also begin to understand the symbolism related to the operation.
Models can then be used to help children learn new thinking strategies.

Discussion skills

Turn-taking
Active-listening
Responding positively to the opinions of others
Confidence in putting forward an opinion
Ability to explain clearly their point of view

– Problem-Solving

The focus is on real life problem solving.

Types of problems

Word problems
Practical tasks
Open-ended investigations
Puzzles
Games
Projects
Mathematical trails
Missing Contradictory Surplus Data

Strategies used

The Rose Approach
RUDE
RAVE CCC

– Using the Environment

The children are learning all the time from the people and materials around them .In our teaching we look to the environment of the classroom, the school grounds, the locality of the school, the children’s homes and the wider world for opportunities to make maths more real, more interesting and more fun.

Creating a maths rich environment

Benchmarks e.g.card marking ‘1 metre’ on wall
Special box or shelf for maths books
Puzzle of the day/week on flipchart
Maths games
Maths trails
Number rich environment in Infant rooms
Playground markings

– Skills through Content

Applying and problem-solving
Communicating and expressing
Integrating and connecting
Reasoning
Implementing
Understanding and recalling

The skills “span the content” and the methodologies to develop them are modelled by the teacher.

Assessment and Record Keeping:

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

The teacher observes the child’s activity, written work, discussion and questioning during class or group work.

Interview Method[talking to children formally and informally ]

Error Analysis

Home work/Parental feedback

Work samples, projects.

A systematic collection of children’s work is kept in a folder and they provide a tangible record of development over a year, the child can play a part in the compilation of his/her own portfolio by choosing a piece of work for inclusion.

Mastery Records

Teacher designed tasks and tests

Oral tests of recall skills [tables, counting in groups, number patterns continued]

Written tests

Criterion Referenced tests

Standardised Tests

Sigma-T tests will be administered in May each year. Records will be kept safely in the filing cabinet. They will be available to parents on request. They can also be used to determine children who need learning support/resource hours. = or <10%. These results will form the basis of Individual Teacher Planning.

DiagnosticTests

Our Sigma results will be used as our Diagnostic tests.

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
Peer Tutoring
More concrete approach
Emphasising maths language
Maths games
Maths software
Resources
Learning support guidelines

Suggested strategies for challenging the better abled mathematical child

Problem solving books/Brain Teaser Books
Maths Facts Book
Maths games
Maths software
Additional class appropriate work-books.

Organisation:

Timetable:

Maths will be allocated – 3 hours per week in Classes 1 – 6

2 hrs 15 minutes for Infants

Discretionary time can be allocated, at the teacher’s and at the school’s discretion, to any of the six curriculum areas including Maths.

Homework:

Maths homework will generally be given every day, Monday to Thursday. 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

Resources and ICT:

Teaching materials will be provided at all class levels and in every strand. Children will experience a variety of materials and will have the freedom to choose from these when exploring a mathematical task. A variety of teacher designed worksheets, photocopiable master books, teacher reference books and textbooks will be used in order to present work to the children in a variety of ways. Calculators,(3rd to 6th), and computers will enhance the implementation of the curriculum.

Maths Equipment

Inventory: See Appendix 1

Calculators

Pupils in Third, Fourth, Fifth and Sixth Class learn to use calculators for some maths activities. *** See Section on calculator use and Special Needs Children. Children will always be encouraged to estimate first before calculating exact result on the calculator.

Using a calculator

The first reason for using a calculator is for checking answers.
If problem solving is the main objective of the exercise, use a calculator.
Use a calculator for teaching place – value: g. 7846 – change to 7046
(800 has to be subtracted, not 8) 7846 – change to 7806

Use a calculator for teaching tables in 3rd Class.
For repeated addition: press the number, then press +, and finally press = as often as required. g. Press 6: Press + Press = Press = Press etc.
(The display should read 6, then 12, then 18, then 24, then 30 ….. etc)
For repeated subtraction: press the number being subtracted from, then press = as often as required. g. Press 60: press -, press 7, press =, press = etc.
(The display should read 60, then 53, then 46, then 39 …. Etc.)
For directed numbers: press a number, then press – , and finally press = as often as required. The calculator will show minus numbers below zero.
g. Press 31: press – 8 , press =, press =, press= etc.
The display should read 31, then 23, then 15, then 7, then –1, then –9 etc.,
Mental Strategies: 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).

Maths and ICT

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
adventure programs (See appendix)
data bases
spreadsheets
using the internet to access materials and information

Textbooks

Textbooks will be evaluated by the Staff, and will include a balanced treatment of all strands, varied presentation of problems and an emphasis on the use of manipulatives.

A variety of textbooks could be made available to the children based on the quality of their content in particular strands e.g. Mathemagic, Action Maths, Ready Steady Maths, Figure it Out.

Also having a selection of different mathematic books or graded workcards will help provide extension work for children who have mastered a concept. Supplementary Maths workbooks, BrainTeasers, New Wave Mental Maths, Sum Detective, Maths Challenge.

MATHEMATIC TEXT BOOKS IN USE:

Each class grouping will work from a core textbook, but a variety of supplementary books will also be used for reinforcement.

Parental Involvement – Home School Links:

Communicating with parents about the correct terminology/language and methods being used

Advisory notes as the need arises
Write language of tables in the table book
Parent -teacher meetings
Open door policy

Other ways Parents can be encouraged to help their children

Paired maths, encourage parents to buy maths games at Christmas/Birthday times, etc.

Parents and maths information leaflet

Mathematics/Mhatamaitic

Useful Links