## Mathematics Plan - Kilnadeema National School

**Introductory Statement**

This document is a statement of the aims and the objectives, principles and strategies for teaching and learning

**Mathematics**at Kilnadeema National School. It was developed during the school years 2003-2005 through a process of consultation, discussion, workshops, staff planning days and In-service Training Days. The plan has been updated as part of the school’s Self Evaluation Process.

**Rationale**

This document has been drawn up in response to the principles outlined in the Revised Curriculum. We as a staff believe that Mathematics permeates most areas of children’s lives. To really understand Mathematics, they must see it in context. The child learns from the people and materials around him/her. It is experience of the social and physical world that is the source of concepts, ideas, facts and skills. Integration of these experiences is the vital ingredient. Elements of this programme will be reviewed regularly at staff meetings. The success criteria by which this policy will be judged include the following:

- Teacher observation.
- Classroom assessment including evaluation of assignments.
- Standardised tests will be averaged and compared with a pre-policy base line.

- Parent(s)/Guardian(s)/Pupil/Community feedback.

**Mathematics In Our School**

We in Kilnadeema N.S. see mathematics education as providing the child with a wide range of knowledge, skills, and related activities that will help him/her develop an understanding of the physical world and of social interactions. It endeavours to give the child a language and a system to communicate confidently through the medium of mathematics. We see the mathematics programme as catering for the needs of each individual child.

Discovery learning is made more effective through guidance and language development thus enabling the child to formulate ideas and theories about what he/she is discovering.

We regard a Constructivist approach as central to this mathematics curriculum. To learn mathematics, children must construct their own internal structures. Through our mathematics programme we endeavour to enable each child to develop the following skills:

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

We will follow procedure similar to the one outlined below:

- Children discuss the problem.
- Try a possible approach.
- Discuss further.
- Make modifications arising from interaction.
- Construct concepts from deductions.
- Arrive at a solution or solutions.
- Discuss results.
- Record.

**Aims**

We endorse the aims of the Mathematics curriculum as articulated in the Revised curriculum.

The aims of our Mathematics programme, therefore, are as follows:

- To develop a positive attitude towards Mathematics.
- To develop an appreciation of both the practical and aesthetic aspects of mathematics.
- To develop problem-solving abilities.
- To enable the child to apply mathematical concepts in everyday life.
- To enable the child to use mathematical language effectively and accurately.
- To enable the child reach his/her full potential in understanding of mathematical concepts and processes.
- To enable the child to acquire proficiency in fundamental mathematical skills and in recalling basic number facts.

**The Strands of the mathematics curriculum are:**

- Early mathematical activity (Junior Infants)
- Number
- Algebra
- Shape and Space
- Measure
- Data

**Broad Objectives**

We endorse the Broad Objectives of the Mathematics Curriculum as articulated in the Revised Curriculum.

**Skills development**

The mathematics curriculum should enable the child to:

- Apply mathematical concepts and processes, plan and implement solutions to problems, in a variety of contexts.
- Communicate and express mathematical ideas, processes and results in oral and written form.
- Make mathematical connections within mathematics itself, throughout other subjects, and in applications of mathematics in practical everyday contexts.
- Reason, investigate and hypothesise with patterns and relationships in mathematics.
- Implement suitable standard and non-standard procedures with a variety of tools and manipulatives.
- Recall and understand mathematical terminology, facts, definitions and formulae.
- Identify symmetry in shapes and identify shape and symmetry in the envirnonment.
- Describe direction and location using body-centred (left/right, forward/back) and simple co-ordinate geometry.
- Use acquired concepts, skills and processes in problem-solving.

**Number**

The mathematics curriculum should enable the child to:

- Understand, develop and apply place value in the denary system (including decimals).
- Understand and use the properties of number.
- Understand the nature of the four operations and apply them appropriately.
- Approximate, estimate, calculate mentally and recall basic number facts.
- Understand the links between fractions, percentages and decimals and state equivalent forms.
- Use acquired concepts, skills and processes in problem-solving.

**Algebra**

The mathematics curriculum should enable the child to:

- Explore, perceive, use and appreciate patterns and relationships in numbers.
- Identify positive and negative integers on the number line.
- Understand the concept of a variable, and substitute values for variables in simple formulae, expressions and equations.
- Translate verbal problems into algebraic expressions.
- Acquire an understanding of properties and rules concerning algebraic expressions.
- Solve simple linear equations.
- Use acquired concepts, skills and processes in problem solving.

**Shape and Space**

The mathematics curriculum should enable the child to:

- Develop a sense of spatial awareness.
- Investigate, recognise, classify and describe the properties of lines, angles, and two-dimensional and three-dimensional shapes.
- Deduce informally relationships and rules about shape.
- Combine, tessellate and partition two-dimensional shapes and combine and partition three-dimensional shapes.
- Draw, construct and manipulate two-dimensional and three-dimensional shapes.

**Measures**

The mathematics curriculum should enable the child to:

- Know, select and use appropriate instruments of measurement.
- Estimate, measure and calculate length, area, weight, capacity and average speed using non-standard and appropriate units of measurement.
- Recognise and appreciate measures in everyday use.
- Use acquired concepts, skills and processes in problem-solving.

**Data**

The mathematics curriculum should enable the child to:

- Collect, classify, organise and represent data using concrete materials and diagrammatic, graphical and pictorial representation.
- Read, interpret and analyse tables, diagrams, bar-charts, pictograms, line-graphs and pie-charts.
- Appreciate, recognise and express the outcomes of simple random processes.
- Estimate and calculate using examples of chance.
- Use acquired concepts, skills and processes in problem-solving.

**Principles**

The importance of integration and of enabling children to see mathematics as practical and relevant has been given careful consideration in the drawing up of this programme.

This integrated learning experience is being facilitated by due consideration of the following points:

- The six strands.
- Integration and linkage
- Continuity and progression
- Revision of concepts and skills.
- Use of relevant equipment.
- Discussion.
- Assessment.
- Planning to cater for individual difference.

**Specific Objectives**

The following is a class list of objectives that children will, in as far as possible, be enabled to attain.

**APPROACHES AND METHODOLOGIES**

The approaches and methodologies to be adopted in the mathematics curriculum in Kilnadeema National School include the following:

- Guided discussion – child/child or teacher/child.
- Discussion skills.
- Hands-on approach using appropriate equipment.
- Accurate use of mathematical language.
- Estimating.
- Problem-solving.
- Working with concrete materials.
- Linkage within the mathematical programme.
- Integration of Maths with other subjects, e.g. P.E. (length, height..) Geography (scale etc.), History (time, money...), Science (problem-solving)
- Calculators are used where appropriate from 4th class on.
- Children with special needs and varying abilities will be catered for and included, where appropriate, in the Mathematics Curriculum in our school.

**hands-on approach**as essential right through to sixth class if children are to understand mathematical concepts. To facilitate this we will provide adequate

**equipment**for the children to work individually, in pairs or in groups.

**Mathematics Equipment in Kilnadeema N.S.**

An annual audit of our maths equipment is carried out, as one of the duties of our posts of responsibility. Equipment is itemised according to strand/strand unit and its location is noted. A copy of this list is circulated to all staff members.

**(See attached list)**

**INTEGRATION IN MATHEMATICS**

Mathematics pervades most areas of children’s lives, whether they are ‘looking at and responding to’ structural forms in the visual arts curriculum or calculating how to spend their pocket money. For children to really understand mathematics they must see it in context, and this can be done through drawing attention to the various ways in which we use mathematics within other subjects in the curriculum.

This

**integration of mathematics**with other subjects is an important factor in broadening the child’s education. Integration adds to the child’s enjoyment of mathematics, gives him/her added interest in the subject and encourages transfer of learning.

**Examples of how we integrate mathematics in our school are:**

**S.E.S.E.**

- Recording results of experiments in science (Strand: Data)
- Creating & reading maps in geography.
- Interpreting weather, climate etc. (Strand Unit: Directed numbers)
- Collecting data for analysis.
- Sense of time and chronology in history (Strand Unit: Time)
- Methods of payment of ‘early peoples and ancient societies’ (Strand unit: Money)

**Physical Education**

- Measuring lengths of jumps, races etc.
- Creating symmetrical and asymmetrical shapes in gymnastics.

**Music**

- Maths language of ‘long/short notes’
- Improvising and creativity (Strand Unit: Chance)

**Visual Arts**

- Correct words to describe shapes
- Making/constructing 2-D and 3-D shapes
- Print symmetrical shapes

**Parental Involvement in the Mathematics Programme**

In Kilnadeema N.S. we encourage and welcome the involvement of parent(s)/guardian(s) in their children’s education. Such partnership is exemplified in:

- Our initial meeting for parent(s)/guardian(s) of the incoming Junior Infants at which the importance of involving the young child in the language of maths around him/her is discussed. Parent(s)/guardian(s) are given information sheets with ideas re: number, matching, time, exploring space etc. (see sheet attached to plan)
- Annual Parent(s)/guardian(s)/Teacher meetings which allow for a discussion of individual children’s progress.
- Informal Parent(s)/guardian(s)/Teacher meetings convened at the request of the parent(s)/guardian(s) or teacher.
- Written communications via the child’s homework journal.
- Organisation of Shared Maths Games aimed at improving children’s numeracy skills. Games are brought home weekly, to be played with parent(s)/guardian(s) (Duration – approx. 6 weeks)
- Involvement with the child’s mathematics homework. Such homework is merely a reinforcement of work done in class, and parent(s)/guardian(s) are made aware of terminology and methods being used when necessary, e.g. subtraction with renaming – sheet sent out explaining new approach.

**Help Your child with Maths**

Just as children learn a lot about reading and writing before they go to school, they also learn a lot about maths. By seeing their parent(s )/guardian(s) use numbers and by hearing them talk about numbers, children quickly learn that numbers have meaning and purpose. Here are some suggestions for helping your child with maths:

**Use numbers**

He /She will need lots of practise with counting before he really develops a sense of numbers.

- Point out the numbers that are all around him/her: - clocks, calendars, signs etc.
- Take a ‘number walk’ or car ride and look for numbers in order, one to ten.
- Count, count and count again: - ‘How many legos do you have?’ ‘How many sweets did you get?’ ‘Can you get me three apples?’
- Do simple adding: - ‘Let’s see, I put one biscuit in your lunchbox and now I’m giving you another one. How many do you have now?’
- Do simple subtraction: - ‘There are three sausages in the fridge, but I’m going to take one for your tea. How many will be left?’

**Look at patterns, matching, sorting**

- Point out patterns to your child: - ‘The stripes on your shirt make a nice pattern – red, blue, green, red, blue, green.’
- Put away the washing together. Let your child match the socks.
- Let him sort each family member’s clothes into a pile.
- Help him to sort the food shopping by putting it into the right press.

**Explore space**

Encourage him to explore how things fit together.

- Give him big and small containers to play with in the bath.
- Provide simple jigsaw puzzles.
- Give your child things for building and making things: - blocks, boxes, paper, scissors and marla or playdough.
- Talk about left and right.

**Talk about maths**

- Let your child hear you use numbers: - ‘I need a cup and a half of sugar.’

- Use words to compare things: - ‘Which tomato is bigger?’ ‘Which box of cereal is taller?’
- Sing songs that have numbers in them: - ‘Baa, Baa Black Sheep.’ ‘This Old Man’
- Say number rhymes: - ‘Five little monkeys jumping on the bed’, ‘One, two, buckle my shoe’.
- Read books about numbers: - ‘The Three Little Pigs’, ‘The Hungry Caterpillar’.

**Talk about time**

- Put up a calendar in a place where your child can easily see it. Use it to talk about days of the week. Mark time by crossing off days until birthdays and special days.
- Introduce your child to time by pointing out the numbers and time on the clock.
- Point out the difference between a digital clock and a regular clock.
- Use the television guide to look up favourite programmes.
- Use a kitchen timer or an egg timer to time different activities like getting dressed or brushing teeth.

**Use Money**

- Let your child see the prices of things when you shop.
- Talk about how much things cost. Make comparisons: ‘The apples cost 25 cent each and the oranges are 15 cent each. I think we should buy oranges.’
- Count back the change together. Explain the value of the different coins and notes.
- Set up a play shop with your child. Collect some empty packets and tins and carrier bags. Make play money or use real money.

**ASSESSMENT AND RECORD KEEPING**

Assessment provides information that can be used in decision-making about how the teacher can realistically answer the needs of the child. It is an integral part of the educational process and should not become an end in itself. We consciously keep a balance between time spent on assessment and time spent on teaching and learning. Assessment should be a positive experience for the child as this makes his/her learning more effective.

**Why Assess?**We regard assessment as having a formative role. It enhances the child’s learning by providing accurate feedback for the child and the teacher. It informs the teacher of the child’s strengths and weaknesses. It assists the teacher in planning and pacing the mathematics programme. It also has an evaluative role in directing the teacher in relation to curricular content and methodologies for his/her particular group.

**WHAT DO WE ASSESS?**

**Conceptual knowledge and understanding****–**to assess if the child can understand and can apply the concepts.**Problem-Solving ability**- to assess the child’s ability to approach process and solve mathematical tasks.**Computational proficiency**– the teacher will assess if the child uses number, applies the 4 number operations appropriately and computes efficiently both mentally and in writing.**Recall Skills**– to assess if the child can recall number facts, terminology, definitions and formulae. This will be particularly important in the case of estimation.**Mastery of specific content areas**– focussing on the specific strand areas.**Ability to communicate and express****–**mathematical ideas and processes by observation, discussion and recording.**Attitudes****–**we need to assess children’s attitudes towards mathematics including confidence, interest and willingness to take risks.

**HOW DO WE ASSESS?**

We use a variety of assessment tools including:

**Teacher Observation**– we assess children everyday by observing them at work, correcting work and engaging in discussion.**Teacher-designed tasks and tests**– these include such activities as oral tests of recall skills (tables, number patterns etc.), written tests of numerical competence; problem-solving exercises; projects that require compilation of data, construction, diagrams...

**Work Samples, Portfolios and Projects**– we keep systematic collections of the children’s work in folders and these provide tangible records of development over the year. We use them as a source of reference in communicating with parent(s)/guardian(s) and colleagues.**Standardised Testing**– each teacher from 1st – 6th class uses the relevant**Drumcondra Primary****Mathematics Tests**on an agreed date in the last term. These norm-referenced tests compare pupils with other pupils and with national standards. They can be analysed and used as a means of identifying children’s strengths/weaknesses and their readiness for further learning. The results are also used as a means of determining children who may need supplementary teaching from the Learning-Support teacher.**Diagnostic Testing**– is carried out by a) the class teacher to analyse and identify persistent errors in a child’s work, and b) by the learning-support/resource teachers to analyse and identify specific difficulties in order to provide appropriate remediation.

**RECORDING AND COMMUNICATING**

Test results are held by the class teacher and used in communicating with parents/support teachers. They are also used with colleagues in order to assess progress, planning, strengths/weaknesses throughout the school.

**MATHEMATICAL LANGUAGE**

Our mathematical programme, in Kilnadeema N.S., seeks to enable the child to use mathematical language effectively and accurately. This includes the ability to listen, question and discuss as well as to read and record.

One of the causes of failure in mathematics is poor comprehension of the words and phrases used. Some of the language will be encountered only in the mathematics lesson, and children will need many opportunities to use it before it becomes part of their vocabulary. While the average and above average student will have few problems dealing with a variety of methodologies and language, the weaker pupil will greatly benefit from a single, whole-school approach to sums, language, tables and problems.

Our mathematical programme will have a

**common approach to the terms used and proper use of symbol names.**

Discussion rather than questioning will be the basis of the interaction between teacher and child. The process will be supported by the development of the following skills.

- Turn taking.
- Active listening.
- Positive response to the opinions of others.
- Confidence in putting forward opinions.
- Ability to explain clearly their point of view.

**agreed language and approaches**are outlined in the following pages.

**Thinking Strategies**

**Thinking Strategies & Addition Facts**

**Add 0, 1, 2**

**2 + 3 = 3+2**

**Adding 10**

**Subtraction is the inverse of addition**.**Doubles.**

**Near doubles**

**Facts of ten**

**i.**e. the numbers that make 10: 6 + 4, 3 + 7, 9 + 1 etc.

**Adding to 9**(one less than 10)**Through 10**(also called bridging the ten) 10 +2 = 12, 10 + 4 = 14 etc.

**Thinking Strategies & Multiplication Facts**

**Repeated Addition****Skip Counting**

**4 X 6 = 6 X 4**(commutative property)**Doubles**2 X 2, 3 X 3, 4 X 4 etc.**One set more/less**

**10’s tables to teach 9’s**

i.e. 9 X 8 is the same as 80 - 8

**Twice a known Fact**

**PROBLEM SOLVING/TALK AND DISCUSSIONS:**It is school policy that the children be given opportunities to have the confidence and competence to use mathematical language correctly. Without the correct language and knowledge of the basic facts (tables) children will not be able to solve problems.

- Problem solving begins in Junior Infants/Senior Infants with all problems solved orally. In 1st and 2nd Classes great emphasis will be placed on knowing the correct operation to be performed. See following sheet of problems.
- At least once a week 6 problems will be solved orally with emphasis put on the operation.
- More able children will solve the problems on paper.
- From 3rd to 6th classes the following rubric

**E + D**

**M. S.**

**Q**

**R + R**

- 3 problems per week will be solved orally in each class using the above rubric. This lesson should last no more than 5 minutes.
- The teacher can use a problem of his/her own or one may be taken from any Maths book.
- Problem solving in Maths requires many skills. The child should develop the ability to plan, take risks, learn from trial and error, check and evaluate solutions.

A problem written in Mathematical form can look easy for the child, but in written form can cause many problems.

e.g. written form:

*There were 271 people on a train going from Dublin to Cork. At Naas station in Kildare 96 people got off and 48 got on. How many people were on the train then?*

*Mathematical form: (271 – 96) + 48*

As you can see from the example above the written form looks more difficult to solve.

**R + R:**Children are to read the question for approximately 10-15 seconds, then read again. The second time however, the children are asked to look out for words which they do not understand (this is integration with English).**Q:**Children are asked what questions are we being asked in the sum.**MS :**We make great use of talk and discussion to draw from the children the meaning of greater than, less than etc. as associated with the question. We reduce the question to a simple Mathematical Sentence.**E + D:****E**stimate and**D**o.- If this is carried out regularly in all classes children will be exposed to the language and solving process of up to 100 problems per year.