Mathematics

Introduction
Roles and Responsibilities
Preparation of Scheme of Work
Objectives for Junior Infants
Objectives for Senior Infants
Objectives for First Class
Objectives for Second Class

Objectives for Third Class
Objectives for Fourth Class
Objectives for Fifth Class
Objectives for Sixth Class
Note on Informal Assessment / Teaching Strategies
Methodology and Policy Issues

Introduction

The school plan in Mathematics reflects the particular needs of the school community in St Colmcille's BNS, Swords, and it is based on a comprehensive review of the previous school plan. The review was undertaken with specific reference to the two headings, curriculum planning and organisational planning, which were examined separately, but are linked inextricably in practice.

Curriculum Planning

Teaching Materials

Teaching materials are required at all class levels, and it is important that the pupils experience a variety of materials which enables them to explore particular mathematical tasks.

Equipment

There is a plentiful supply of Mathematical equipment and it may be obtaining by requisitioning it from the appropriate post holder. (See list of post holders in Part 1 of School Plan)

Textbooks

The main series in use in the junior classes is Mothemogic, and there is also a range of ancillary Mathematical material such as Busy at Maths, Moths Mastery and Figure It Out. Computer generated material is available on the school intranet.

Calculators and computers

A set of calculators has been purchased and may be requisitioned from the post holder. Each class has a PC, and access to the IT room is time-tabled.

Mathematical Language and methodologies

These issues are addressed at a later stage in this document.

Assessment and Record Keeping

This topic is addressed at a later stage in this document.

Organisational Planning

Roles and Responsibilities

Board of Management

It is the responsibility of the Board of Management to support and facilitate the school approach to Mathematics, and to approve this approach within context of the school plan

Parents

Communication between the parents and teachers about the content of the mathematics programme is undertaken through discussion, notes and formal parent teacher meetings. Parents are advised with regard to the importance of play and exploration, the methodologies being used to teach the various elements of the programme, approaches to homework and test results.

Principal

Oversees the development of the school plan in Mathematics
Consults with the Board of Management and parents with regard to the provision of resources
Ensures that sufficient time is made available for Mathematics
Identifies a teacher with sufficient expertise and interest in Mathematics to lead staff discussion and to draw up a policy document on the place, purpose and content of Mathematics

Special Duties Teacher

Encourages teachers to participate in the formulation of the Mathematics plan
Devises a written plan in consultation with the school staff
Organises the necessary resources to implement the plan
Presents draft documents to the staff at meetings
Supports colleagues as they prepare schemes of work and implement the plan
Informs new members of the teaching staff about the school plan
Organises assessment of mathematical attainment of the pupils, and reports on the results to colleagues

Other Teachers

Devise balanced programmes in line with the school plan which cater for the needs of each child
Provide information for the parents about the programme being taught in Mathematics
Mark scripts and provide results for the Principal, Special Duties and Resource teachers
Devise appropriate Mathematical activities for the pupils

Notes re Preparation of Mathematics Scheme

Introduction should include a general comment with regard to the approach to the teaching of Maths that you are going to adopt. e.g. The Mathematics curriculum provides opportunities for the child to explore the nature of maths as well as to acquire the knowledge, concepts and skills required for everyday living and for use in other subject areas. The curriculum comprises the following strands – number, shape and space, measures, data and for the senior pupils, algebra. These strands although presented in separate sections are not isolated areas, They are seen as inter-related areas and will be taught accordingly.

Pupils in this class show a wide range of ability and provision will be made for individual differences throughout the teaching of the programme. Continuous assessment (formal and informal) will focus on the identification of pupils’ existing knowledge.

My role will be to guide pupils to construct meaning, to develop mathematical structures for solving problems and to develop self-motivation in mathematical activity. The pupils will be given structured opportunities to engage in exploratory activity and they will not be pushed to achieve premature mechanical mastery of computational facts and procedures.

An important aim of the mathematics programme is to enable the pupils to use mathematical language effectively. This includes the ability to listen, question, discuss, read and record. A list of the mathematical terms and language to be taught is included at a later stage of this scheme.

Mathematical development requires a substantial amount of practical experience to establish, to reinforce concepts and to develop a facility for their every day use. The experience of manipulating and using objects and equipment is an essential element of the programme.

An emphasis will be placed on mental calculation, estimation and problem solving skills. Problem solving provides a context in which skills and concepts can be learned. The solving of problems based on the environment of the children is an important element of this programme.

The aims of the programme are to:

Develop a positive attitude towards maths and an appreciation of its practical use
Enable children to use mathematical language effectively and accurately
Enable children to acquire an understanding of mathematical concepts and processesEnable children to acquire proficiency in fundamental mathematical skills and to recall basic number facts
Develop problem solving abilities and a facility for the application of maths to every day life

Broad Objectives

Apply mathematical concepts and process in a variety of contexts
Communicate and express mathematical ideas, processes and results in oral and written form
Implement suitable standard and non-standard procedures
Recall and understand mathematical terminology, facts, definitions and formulae
Understand, develop and apply place value
Understand and use the properties of number
Understand the nature of the four operations and apply them
Approximate, estimate, calculate mentally and recall basic number facts
Understand the links between fractions, percentages and decimals
Identify positive and negative integers on the number line
Translate verbal problems into algebraic expressions
Solve simple linear equations
Acquire an understanding of properties and rules concerning algebraic expressions
Use acquired concepts, skills and processes in problem-solving
Develop a sense of spatial awareness
Investigate, recognise, classify and describe she properties of lines, angles, 2D and 3D shapes
Draw, construct and manipulate 2S and 3D shapes
Know, select and use appropriate instruments of measurement
Estimate, measure and calculate length, area, weight, capacity and average speed using non-standard and standard appropriate metric units
Estimate, measure and calculate angles, time, money and scale
Recognise and appreciate measures in everyday use
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 charts and bar graphs
Estimate and calculate using examples of chance
Use acquired concepts, skills and process in problem-solving

Additional Notes

1.	Introduction should include a comment on the results of the Objective Tests. (Second to Sixth Class). Were there general areas in which the children were weak. What amount of specific remediation is required? Which children were very weak?
2.	Write out names of text book and ancillary texts
3.	Write out objectives in the order in which you intend to teach them.
	N.B. There is no necessity to follow the order of the book. Ensure that the children encounter a blend of computational and practical work.
4.	Write a note on each objective, and give an example : the pupil can subtract numbers of not more than 2 digits where renaming is necessary –

- 27

Write out the list of aids, resources and work cards which are necessary to teach the programme.

Write out the system of recording which you intend to use. The most efficient method is the copybook method.

Name of Pupil	1	2	3	4

If you use objectives to test mastery, 2 out of 3 correct means that the pupil has attained this objective.

Write out the system of testing which you intend to use. How often?

End of year test is a minimal competency test. If teachers wish, they may examine other elements of the programme.

Suggested Allocation of Time

	Oral Instruction	Activities	Written Work
Infants	45%	45%	10%
First and Second	40%	30%	30%
Third and Fourth	35%	30%	35%
Fifth and Sixth	35%	20%	45%

10.

Problem Areas:
Second Class: Subtraction with renaming
Fourth Class: Long multiplication
Middle and Senior Classes: Problem solving

11.

Policy matters

Place an emphasis on oral work
Use immediate environment to teach mathematics
Use practical apparatus to teach place value
Place value should receive emphasis in all standards
Teach a blend of computation and practical maths. Do not leave measurement etc until the last month of the school year
The memorisation of addition tables should be taught in First Class
The memorisation of multiplication tables should be taught in Third Class
Other matters regarding methodology should be checked out with the post holder with responsibility for Mathematics

Objectives for Junior Infants

Strand Unit: Classifying

The child should be enabled to:

Classify objects on the basis of one attribute such as colour, shape, texture or size

sort collections of objects
add similar objects to a clearly defined set

Identify the complement of a set (elements not in a set)

categorise objects such as things I like /don’t like
red things / things that are not red

Matching

3.	Match equivalent and non-equivalent sets using one to one correspondence match pairs of identical objects match pairs of related objects match equivalent and non-equivalent sets to establish the concepts of more than, less than, enough, as many as

Comparing

4.	Compare objects according to length, width, height, quantity, thickness or size introduce concepts long, short, longer, shorter
5.	Compare sets without counting

Ordering

6.	Order objects according to length or height
7.	Order sets without counting

Counting

8.	Count the numbers of objects in a set, 1 – 10

Comparing and ordering

9.	Compare equivalent and non-equivalent sets 1 –5 by matching without using symbols – more than, less than, the same as
10.	Order sets of objects by number, 1-5
11.	Use the language of ordinal number: first, last

Analysis of number

Combining

12.	Explore the components of number, 1-5 identify the ways in which the numbers can be modelled using concrete objects: 4 and 1 identify pairs of related facts: 1 and 2 is the same as 2 and 1
13.	Combine sets of objects, totals to 5

Partitioning

14.

Partition sets of objects, 1-5

partition sets of objects with a pencil or straw to show component parts
record pictorially

Numeration

15.	Develop an understanding of the conservation of numbers, 1 –5
16.	Read, write and order numerals, 1 –5
17.	Identify the empty set and the numeral 0
18.	Tell at a glance the number of objects in a set, 1-5
19.	Solve simple oral problems, 0 –5

Extending patterns

20.

Identify, copy and extend patterns in colour, shape and size

Spatial awareness

21.	Explore, discuss, develop and use the vocabulary of spatial awareness – over, under, up, down, on, beside, in
22.	Moving in straight / curved lines, in a circle, finding own space

3-D shapes

23.	Sort 3-D shapes, regular and irregular
24.	Solve tasks and problems involving shape

2-D shapes

25.	Sort and name 2-D shapes: circle, square, triangle, rectangle
26.	Directed sorting of 2-D shapes on the basis of different criteria – round /not round; thick / thin
27.	Use suitable structured materials to create pictures
28.	Solve problems involving shape

Length

29.	Develop an understanding of the concept of length
30.	Discuss objects in the environment: long/short / tall / wide / narrow / longer / shorter / wider than
31.	Compare and order objects according to length or height

Weight

32.	Develop an understanding of the concept of weight through exploration and use of appropriate vocabulary: heavy /light ; heavier /lighter ; balance /weigh
33.	Compare objects according to weight

Capacity

34.	Develop an understanding of the concept of capacity through exploration and the use of appropriate language: full / nearly full; empty/ holds more /holds less/ holds as much as
35.	Compare containers according to capacity

Time

36.	Develop an understanding of the concept of time through exploration and the use of appropriate language: morning/evening/night / day / lunchtime /bedtime / early /late/ days of the week /school days /weekends
37.	Sequence daily events or stages in a story

Money

38.	Recognise and use coins up to 5c
39.	Solve practical tasks and problems using money

Data

40.	Sort and classify sets of objects by one criterion – shape, colour, size, texture and function
41.	Match sets, equal and unequal – enough / more / as many as / less
42.	Represent and interpret a set of simple mathematical data using real objects, models and pictures

Objectives for Senior Infants

Strand Unit: Classifying

The child should be enabled to:

Classify objects on the basis of one attribute such as colour, shape, texture or size

sort collections of objects
add similar objects to a clearly defined set

Identify the complement of a set (elements not in a set)

categorise objects such as things I like /don’t like
red things / things that are not red

Matching

3.	Match equivalent and non-equivalent sets using one to one correspondence match pairs of identical objects match pairs of related objects match equivalent and non-equivalent sets to establish the concepts of more than, less than, enough, as many as

Comparing

4.	Compare objects according to length, width, height, quantity, thickness or size introduce concepts long, short, longer, shorter
5.	Compare sets without counting

Ordering

6.	Order objects according to length or height
7.	Order sets without counting

Counting

8.	Count the numbers of objects in a set, 1 – 10
9.	Count the objects in a set, 0 -20

Comparing and ordering

10.	Compare equivalent and non-equivalent sets 1 –5 by matching without using symbols – more than, less than, the same as
11.	Compare equivalent and non-equivalent sets 0- 10 by matching
12.	Name the inequality: I have 2 more than you; 3 is less than 5
13.	Order sets of objects by number, 1-5
14.	Order sets of objects by number 0 -10
15.	Use the language of ordinal number: first, last
16.	Use the language of ordinal number: first, second, third, last

Analysis of number

Combining

17.	Explore the components of number, 1-5 identify the ways in which the numbers can be modelled using concrete objects: 4 and 1 identify pairs of related facts: 1 and 2 is the same as 2 and 1
18.	Explore the components o number, 1 -10
19.	Combine sets of objects, totals to 5
20.	Combine sets of objects, totals to 10

Partitioning

21.	Partition sets of objects, 1-5 partition sets of objects with a pencil or straw to show component parts record pictorially
22.	Partition sets of objects, 0 –10
23.	Use the symbols + and = to construct word sentences involving addition

Numeration

24.	Develop an understanding of the conservation of numbers, 1 –5
25.	Develop an understanding of the conservation of numbers 0 -10
26.	Read, write and order numerals, 1 –5
27.	Read, write and order numerals, 0 -10
28.	Identify the empty set and the numeral 0
29.	Tell at a glance the number of objects in a set, 1-5
30.	Tell at a glance the number of objects in a set 2-10
31.	Solve simple oral problems, 0 –5
32.	Solve simple oral and pictorial problems, 0 -10

Extending patterns

33.	Identify, copy and extend patterns in colour, shape and size
34.	Identify, copy and extend patterns in colour, shape, size and number (3 – 4 elements)
35.	Discover different arrays of the same number – how many different patterns of 10 can you make?
36.	Recognise patterns and predict subsequent numbers – 2,3,4,___, 6, 7; 10, 9, __, __, 6.

Spatial awareness

37.	Explore, discuss, develop and use the vocabulary of spatial awareness – over, under, up, down, on, beside, in
38.	Explore, discuss, develop and use the vocabulary of spatial awareness – above, below, bear, far, right, left
39.	Moving in straight / curved lines, in a circle, finding own space

3-D shapes

40.	Sort 3-D shapes, regular and irregular
41.	Sort, describe and name 3-D shapes: cube, cuboid, sphere and cylinder; edge, corner, face, straight, curved, round and flat
42.	Combine 3-D shapes to make other shapes
43.	Solve tasks and problems involving shape

2-D shapes

44.	Sort and name 2-D shapes: circle, square, triangle, rectangle
45.	Directed sorting of 2-D shapes on the basis of different criteria – round /not round; thick / thin, side
46.	Make shapes with art straws
47.	Use suitable structured materials to create pictures
48.	Combine and divide 2-D shapes to make larger or smaller shapes
49.	Draw shapes found in environment
50.	Solve problems involving shape
51.	Give simple moving and turning directions

Length

52.	Develop an understanding of the concept of length
53.	Discuss objects in the environment: long/short / tall / wide / narrow / longer / shorter / wider than
54.	Compare and order objects according to length or height
55.	Identify: as long as / as wide as / longest / shortest
56.	Estimate and measure length in non-standard units
57.	Select and use appropriate non-standard units to measure length, width and height
58.	Present simple problems

Weight

59.	Develop an understanding of the concept of weight through exploration and use of appropriate vocabulary: heavy /light ; heavier /lighter ; balance /weigh
60.	Compare objects according to weight
61.	Estimate and weigh in non-standard units
62.	Select and use appropriate non-standard units to weigh objects
63.	Present simple problems

Capacity

64.	Develop an understanding of the concept of capacity through exploration and the use of appropriate language: full / nearly full; empty/ holds more /holds less/ holds as much as
65.	Compare containers according to capacity
66.	Estimate and measure capacity in non-standard units
67.	Select and use appropriate non-standard units to measure capacity
68.	Present simple problems

Time

69.	Develop an understanding of the concept of time through exploration and the use of appropriate language: morning/evening/night / day / lunchtime /bedtime / early /late/ days of the week /school days /weekends
70.	Use yesterday / today / seasons /soon / not yet /birthday
71.	Discuss significant events, festivals and holidays
72.	Sequence daily events or stages in a story
73.	Make scrapbooks of `My Day’
74.	Read time in one-hour intervals

Money

75.	Recognise and use coins up to 5 cent
76.	Recognise coins up to 20 cent and use coins up to 10 cent
77.	Use correct vocabulary: cost /price /cheap / expensive /change /too much /too little
78.	Solve practical tasks and problems using money

Data

79.	Sort and classify sets of objects by one criterion – shape, colour, size, texture and function
80.	Sort and classify sets of objects by two criteria
81.	Match sets, equal and unequal – enough / more / as many as / less
82.	Represent and interpret a set of simple mathematical data using real objects, models and pictures
83.	Represent and interpret data in two rows or columns using real objects, models or pictures
84.	Discuss the need for a common baseline

First Class

Strand Unit

Counting and Numeration

The child should be enabled to:

1.	Count the number of objects in a set
2.	Read, write and order numerals 0 – 99
3.	Estimate the number of objects in a set 0-20
4.	Compare equivalent and non-equivalent sets 0 – 20
5.	Order sets of objects by number
6.	Use the language of ordinal number, first to tenth

Place Value

7.	Explore, identify and record place value 0 – 99 Use of concrete objects very important

Operations

Addition

8.	Develop an understanding of addition by combining sets
9.	Explore, develop and apply the commutative property of addition 6 + 2 = ? + 6 = ?
10.	Explore, develop and apply the associative property of addition (2 +4) + 5 = 2 + (? + 5) = ?
11.	Explore, develop and apply the zero property. 7 + 0 = ?
12.	Develop and recall addition strategies for addition facts within 20.
13.	Construct number sentences and stories.
14.	Solve problems involving addition within 20
15.	Add numbers without renaming within 99
16.	Add numbers with renaming within 99
17.	Explore and discuss repeated addition and group counting.

Subtraction

18.	Develop an understanding of subtraction as deducting, as complementing and as difference, 0 – 20. Focus on subtraction as the inverse of addition Examples of deducting Example of complementing Example of difference
19.	Develop and recall strategies for subtraction, 0 – 20
20.	Construct number sentences and number stories involving subtraction
21.	Solve problems involving subtraction, 0 – 20.
22.	Subtract numbers without renaming, 0 – 99.
23.	Use the symbols +, -, =.
24.	Solve one step problems involving subtraction

Fractions

25.

Establish and identify half of sets to 20

Algebra

26.

Recognise patterns – odd and even numbers

27.

Explore and use patterns in addition facts

28.

Understand the use of a frame to show the presence of an unknown number.
Example: 3 + 6 = ? ; Example: 2 + ? = 8.

Spatial Awareness

29.	Explore, discuss, develop and use the vocabulary of spatial awareness – between, underneath, on top of, around, through, left and right.
30.	Give and follow simple directions

2D Shapes

31.	Sort, describe, compare and name square, rectangle, triangle, circle and semi-circle
32.	Construct and draw 2D shapes
33.	Identify halves of 2D shapes
34.	Identify and discuss the shape of 2D shapes in environment

3D Shapes

35.	Describe, compare and name cube, cuboid, cylinder and sphere
36.	Discuss the use of 3D shapes in the environment
37.	Solve practical problems involving 2D and 3D shapes
38.	Explore the relationship between 2D and 3D shapes

Length

39.	Estimate, compare and record length using non-standard units
40.	Select appropriate non-standard measuring units
41.	Estimate, measure and record length using standard unit – metre
42.	Solve and complete practical tasks involving length

Weight

43.	Estimate, compare, measure and record weight using non-standard units
44.	Select appropriate non-standard measuring units
45.	Estimate, measure and record weight using standard unit (kg)
46.	Solve and complete practical tasks involving weight.

Capacity

47.	Estimate, compare, measure and record capacity using non-standard units
48.	Select appropriate non-standard measuring units
49.	Estimate, measure and record capacity using standard unit (litre)
50.	Solve and complete practical tasks involving capacity.

Time

51.	Use the vocabulary of time to sequence events
52.	Read and record time
53.	Read time in hours and half hours on 12 hour analogue clock
54.	Read day, date and month using calendar

Money

55.	Recognise, exchange and use coins up to the value of 50 cent
56.	Calculate how many items can be bought with a given sum

Data

57.	Sort and classify objects by one or two criteria
58.	Represent and interpret data in two, three or four rows or columns

Second Class

Strand Unit

Counting and Numeration

The child should be enabled to :

1.	Count the number of objects in a set
2.	Read, write and order numerals 0 – 99
3.	Read, write and order numerals 0 -199
4.	Estimate the number of objects in a set 0-20
5.	Compare equivalent and non-equivalent sets 0 – 20
6.	Compare equivalent and non-equivalent sets and record using < , > and =
7.	Order sets of objects by number
8.	Use the language of ordinal number, first to tenth

Place Value

9.	Explore, identify and record place value 0 – 99 Use of concrete objects very important
10.	Explore, identify and record place value 0 - 199

Operations

Addition

11.	Develop an understanding of addition by combining sets
12.	Explore, develop and apply the commutative property of addition 6 + 2 = ? + 6 = ?
13.	Explore, develop and apply the associative property of addition (2 +4) + 5 = 2 + (? + 5) = ?
14.	Explore, develop and apply the zero property. 7 + 0 = ?
15.	Develop and recall addition strategies for addition facts within 20.
16.	Construct number sentences and stories.
17.	Solve problems involving addition within 20
18.	Add numbers without renaming within 99
19.	Add numbers with renaming within 99
20.	Explore and discuss repeated addition and group counting.

Subtraction

21.	Develop an understanding of subtraction as deducting, as complementing and as difference, 0 – 20. Focus on subtraction as the inverse of addition Examples of deducting Example of complementing Example of difference
22.	Develop and recall strategies for subtraction, 0 – 20
23.	Construct number sentences and number stories involving subtraction
24.	Solve problems involving subtraction, 0 – 20.
25.	Subtract numbers without renaming, 0 – 99.
26.	Subtract numbers with renaming, 0 – 99.
27.	Use the symbols +, -, =
28.	Use the symbols <, >
29.	Solve one step problems involving subtraction
30.	Solve two step problems involving subtraction

Fractions

31.	Establish and identify half of sets to 20
32.	Establish and identify quarters of sets to 20

Algebra

33.	Recognise patterns – odd and even numbers
34.	Count on 100 square
35.	Explore and use patterns in addition facts
36.	Understand the use of a frame to show the presence of an unknown number. Example: 3 + 6 = ? ; Example: 2 + ? = 8.

Spatial Awareness

37.	Explore, discuss, develop and use the vocabulary of spatial awareness – between, underneath, on top of, around, through, left and right.
38.	Give and follow simple directions

2D Shapes

39.	Sort, describe, compare and name square, rectangle, triangle, circle , semi-circle and oval.
40.	Construct and draw 2D shapes
41.	Identify halves and quarters of 2D shapes
42.	Identify and discuss the shape of 2D shapes in environment

3D Shapes

43.	Describe, compare and name cube, cuboid, cylinder, sphere and cone.
44.	Discuss the use of 3D shapes in the environment
45.	Solve practical problems involving 2D and 3D shapes
46.	Explore the relationship between 2D and 3D shapes

Symmetry

47.

Identify line symmetry in shapes and in the environment

Angles

48.

Explore and recognise angles in the environment

Length

49.	Estimate, compare and record length using non-standard units
50.	Select appropriate non-standard measuring units
51.	Estimate, measure and record length using standard unit – metre and centimetre
52.	Solve and complete practical tasks involving length

Area

53.

Estimate and measure area using non-standard units

Weight

54.	Estimate, compare, measure and record weight using non-standard units
55.	Select appropriate non-standard measuring units
56.	Estimate, measure and record weight using kg, ½ kg, ¼ kg.
57.	Solve and complete practical tasks involving weight.

Capacity

58.	Estimate, compare, measure and record capacity using non-standard units
59.	Select appropriate non-standard measuring units
60.	Estimate, measure and record capacity using litre, ½ litre, ¼ litre
61.	Solve and complete practical tasks involving capacity.

Time

62.	Use the vocabulary of time to sequence events
63.	Read and record time
64.	Read time in hours, half hours and quarter hours on 12 hour analogue clock
65.	Read time in hours and half hours on digital clock
66.	Read day, date and month using calendar; identify season

Money

67.	Recognise, exchange and use coins up to the value of 50 cent
68.	Recognise, exchange and use coins up to the value of €2
69.	Calculate how many items can be bought with a given sum
70.	Write the value of a group of coins; record money amounts as cent and later as euro

Data

71.	Sort and classify objects by one or two criteria
72.	Represent and interpret data in two, three or four rows or columns
73.	Represent, read and interpret simple block graphs

Third Class

Objective

Number

1.	Place value. To explore and identify place value in whole numbers from 0 – 999. Example 1: 342 Example 2: 913
2.	To read, write and order three digit numbers. Example 1: What is the next number after 499? ; Example 2: Put these numbers in ascending order – 421, 241, 142 and 214
3.	To round whole numbers to the nearest 10 or nearest hundred. Example 1: 26, 13, 35; Example 2: 342, 258 and 850
4.	To explore and identify place value in decimals to one place of decimals. Example 1: 0.3 ; Example 2: 496.7

Operations

1.	Add and subtract without and with renaming within 999. Example 1: 946 – 225; 400 + 120 + 366; Example 2: 401 – 234 ; 713 + 94 + 109
2.	Know and recall addition and subtraction facts Addition and subtraction tables to be taught; drills and patterns to be taught as oral work
3.	Solve word problems involving addition and subtraction (single step and multi-step) Example 1: A farmer had 104 sheep. He bought 69 sheep. How many has he then? Example 2: A farmer had 230 hectares. He sold 95 hectares. How many hectares has he then? Example 3: There are 157 boys attending a school. There are 16 more girls. How many pupils in the school? Example 4: A milkman has 402 cartons, He sold 27 to one shop and 16 to another shop. How many has he left? Teaching strategies for problem solving
4.	Develop an understanding of multiplication as repeated addition and vice versa. Example 1: 2 +2 +2 = ; Example 2: 3 x 2 =
5.	Explore, understand and apply the zero, commutative and distributive properties of multiplication. Example 1: Tick the correct answer : 5 x 0 = 5, 1, 5. Example 2: 5 x 2 = x 5 Example 3: 5 x 4 = (3 x 4) + (___ x 4) Example 4: 7 x 14 = (3 x 14) + ( ____ x 14)
6.	Develop and / or recall multiplication facts within 1000 counting in 2’s, 3’s, 4’s etc
7.	Multiply a one digit or two digit number by 0 – 10. Example 1: 13 x 3; Example 2: 25 x 6; Example 3: 24 x 7; Example 4 : 99 x 9 (this is the greatest level of demand at this standard)
8.	Solve and complete practical tasks and problems involving multiplication of whole numbers. Example 1: How many days in 9 weeks. Example 2: There are 47 crayons in a box. How many in 8 boxes? Example 3: A farmer has 52 sheep. Another farmer has 4 times as many. How many sheep have they altogether?

Division

9.	To develop an understanding of division as sharing and as repeated subtraction, without and with remainders.
10.	To develop and / or recall division facts within 100
11.	To divide a one digit number or two digit number by a one digit number, with or without remainders. Example 1: 20 ÷ 4; Example 2: 35 ÷ 5; Example 3: 28 ÷ 3 Example 4: 85 ÷ 4; Example 5: 97 ÷ 5; Example 6: 61 ÷ 3
12.	Solve and complete practical tasks and problems involving division of whole numbers. Example 1: 81 marbles were shared equally among 9 children. How many did each get? Example 2: How many boxes each containing 6 eggs can be filled from a container that holds 5o eggs? How many eggs will be left over? Example 3: How many bags containing 7 balloons can be made from 43 red balloons and 41 green balloons?

Strand Unit

Fractions

Identify fractions and equivalent forms of fractions with denominators 2, 4, 8 and 10.
Example 1: What part is shaded ?

Example 2: Shade 1/10 of this figure.

Example 3: Shade 5/8 of this figure.

Example 4: What fraction is shaded ?

To compare and order fractions with appropriate denominators and position on the number line.

Example:

To calculate a fraction of a set using concrete materials

Shade ¼

To develop an understanding of the relationship between fractions and division

Example 1: ¼ of 32 =

Example 2: 1/8 of 64 =

Example 3: 32 ÷ 4 =

Example 4: 64 ÷ 8 =

To calculate a unit fraction of a number and calculate a number, given a unit fraction of a number.

Example 1: ¼ of a number =3. What is the number?

Example 2: 1/10 of a number =9. What is the number?

To solve and complete practical tasks and problems involving fractions.
Resources needed for practical tasks.

Strand Unit

Decimals

Identify 1/10’s and express in decimal form
Example 1:

Order decimals on the number line
Example

Solve problems involving decimals

Algebra

Unit, Number Patterns and Squares

1.	Explore, recognise and record patterns in number
2.	To explore, extend and describe arithmetic and geometric sequences. Example 1: 1, 5, 9, 13, __, ___. Example 2: 81, 27, 9, __
3.	Use patterns as an aid in the memorisation of number facts.

Resources: Excel number patterns; 100 squares

Assessment: Informal

Strand Unit

Number Sentences

1.	Translate an addition or subtraction number sentence with a frame into a word problem. Example 1: 3 + 7 = . Mary has three sweets. She gets seven more. How many has she now? Example 2: 900 - ______ = 460. Make up a problem.
2.	Solve one step number sentences. Example 1: 400 - _______ = 350 Example 2: 810 + 23 =

Strand Unit

Shape and Space

1.	Identify, describe and classify 2d shapes (square, rectangle, triangle, hexagon, circle, semi-circle, oval and irregular shapes. Informal assessment – match word to shape
2.	Explore, describe and compare the properties (sides, angles, parallel and non-parallel) of 2D shapes. Assessment: How many sides has a ______?
3.	Construct and draw 2D shapes using templates, stencils, geo-strips and geo-boards
4.	Combine, tessellate and make patterns with 2D shapes Use computer software
5.	Identify the use of 2D shapes in the environment. Assessment: Draw house / signs
6.	Solve and complete practical tasks and problems involving 2D shapes.

Strand Unit

3D Shapes

1.	Identify, describe and classify 3D shapes, including cube, cuboid, cylinder, cone, sphere, triangular prism and pyramid.
2.	Explore, describe and compare the properties of 3D shapes
3.	Explore and describe the relationship of 3D shapes with constituent 2D shapes.
4.	Construct 3D shapes
5.	Solve and complete practical tasks and problems using 2D and 3D shapes.

Strand Unit

Symmetry

1.	Identify line symmetry
2.	Identify and draw lines of symmetry in 2 D shapes

Strand Unit

Lines and Angles

1.	Identify, describe and classify vertical, horizontal and parallel lines
2.	Recognise an angle in terms of rotation
3.	Classify angles as greater than, less than or equal to a right angle
4.	Solve problems involving lines and angles

Strand Unit

Length

1.	Estimate, compare, measure and record lengths of a wide variety of objects using appropriate metric units
2.	Re-name units of length in metres and centimetres Example 1: 125 cm = 1m 25cm Example 2: 2m 3 cm = 203 cms
3.	Solve and complete practical tasks and problems involving the addition and subtraction of units of length (m and cm)

Strand Unit

Area

1.	Estimate, compare and measure the area of regular and irregular shapes

Strand Unit

Weight

1.	Estimate, compare, measure and record the weight of a wide variety of objects using appropriate metric units (kg and g) Need to know: 1000g = 1kg
2.	Solve and combine practical tasks and problems involving the addition and subtraction of units of weight (kg and g) Do not combine kg and g in same sum

Strand Unit

Capacity

1.	Estimate, compare, measure and record the capacity of a wide variety of objects using appropriate metric units (litres, 250ml and 500ml).
2.	Solve and complete practical tasks and problem involving the addition and subtraction of units of capacity, Do not combine litres and ml

Strand Unit

Time

1.	Consolidate and develop a sense of time passing
2.	Read time in five minute intervals on analogue and digital clocks
3.	Read time in analogue and digital forms
4.	Read and interpret simple time tables
5.	Rename minutes as hours and minutes Example: 70 minutes = ? Restrict to 1 hr 55 minutes
6.	Read dates from calendars and express weeks as days and vice versa
7.	Solve and complete practical tasks and problems involving time.

Money

1.	Rename amounts of money as pounds or pence and record using p or £ symbol and decimal point.
2.	Solve and complete one step problems and tasks involving the addition and subtraction of money.

Representing and interpreting data

Data

1.	Collect, organise and represent data using pictograms, block graphs and bar charts
2.	Read and interpret tables, pictograms, block graphs and bar charts
3.	Use data sets to solve and complete practical tasks and problems

Chance

1.	Use vocabulary of uncertainty and chance: possible, impossible, might, certain, not sure.
2.	Order events in terms of likelihood of occurrence.
3.	Identify and record outcomes of simple random processes.

Note on Informal Assessment / Teaching Strategies

1.	Estimate when doing addition and subtraction
2.	Drills in addition and subtraction – 3+ 6; 3 +16; 3 + 26;
3.	Orally solve word problems – single step, multi-step
4.	Evaluate and review problem solving strategies Read each problem three times – there are 402 cattle in 3 fields. 86 in field 1, 86 in field 2, how many in field 3? Draw and discuss
5.	Teach concept of multiplication as continuous addition 2+2 +2 +2 = 2 x 4
6.	Know number facts to 100
7.	Work involving 0
8.	Develop concept of division as repeated subtraction

Fourth Class

Objective

Number

1.	Place value. To explore and identify place value in whole numbers from 0 – 999. Example 1: 342 Example 2: 913
2.	To explore and identify place value in whole numbers, 0 – 9999 Example 1: 1078 ; Example 2: 6,789
3.	To read, write and order three digit numbers. Example 1: What is the next number after 499? ; Example 2: Put these numbers in ascending order – 421, 241, 142 and 214
4.	To read, write and order four digit numbers and solve simple problems Example 1: What is the largest number that can be made from 3,7, 0 6 ? Example 2: Write 5683 in expanded form. (5,000 + 600 + 80 +3)
5.	To round whole numbers to the nearest 10 or nearest hundred. Example 1: 26, 13, 35; Example 2: 342, 258 and 850
6.	Round whole numbers to the nearest thousand. Example 1: Which number is nearer to 5,000 ? 4328 or 5675? Example 2: Which number is nearer to 1,000 ? 576 or 1564?
7.	To explore and identify place value in decimals to one place of decimals. Example 1: 0.3 ; Example 2: 496.7
8.	To explore and identify place value in decimals to two places of decimals Example 1: Value of 7 in 503.76 ; Example 2: Value of 9 in 500.09

Operations

9.	Add and subtract without and with renaming within 999. Example 1: 946 – 225; 400 + 120 + 366; Example 2: 401 – 234 ; 713 + 94 + 109
10.	Add and subtract without and with renaming within 9999 Example 1: 5,289 + 252 + 758 Example 2: 5,002 – 4,976 Importance of estimation, check answers with calculator
11.	Know and recall addition and subtraction facts Addition and subtraction tables to be taught; drills and patterns to be taught as oral work
12.	Solve word problems involving addition and subtraction (single step and multi-step) Example 1: A farmer had 104 sheep. He bought 69 sheep. How many has he then? Example 2: A farmer had 230 hectares. He sold 95 hectares. How many hectares has he then? Example 3: There are 157 boys attending a school. There are 16 more girls. How many pupils in the school? Example 4: A milkman has 402 cartons, He sold 27 to one shop and 16 to another shop. How many has he left? Teaching strategies for problem solving
13.	Develop an understanding of multiplication as repeated addition and vice versa. Example 1: 2 +2 +2 = ; Example 2: 3 x 2 =
14.	Explore, understand and apply the zero, commutative and distributive properties of multiplication. Example 1: Tick the correct answer : 5 x 0 = 5, 1, 5. Example 2: 5 x 2 = ? x 5 Example 3: 5 x 4 = (3 x 4) + (___ x 4) Example 4: 7 x 14 = (3 x 14) + ( ____ x 14)
15.	Develop and / or recall multiplication facts within 1000 counting in 2’s, 3’s, 4’s etc Assessment: Informal
16.	Multiply a one digit or two digit number by 0 – 10. Example 1: 13 x 3; Example 2: 25 x 6; Example 3: 24 x 7; Example 4 : 99 x 9
17.	Multiply a two digit number or three digit number by a one or two digit number Example 1: 25 x 36 ; Example 2: 127 x 27
18.	Solve and complete practical tasks and problems involving multiplication of whole numbers. Example 1: How many days in 9 weeks. Example 2: There are 47 crayons in a box. How many in 8 boxes? Example 3: A farmer has 52 sheep. Another farmer has 4 times as many. How many sheep have they altogether?
19.	35 children buy 1 packet of sweets each per day. How many packets will they buy during the month of March

Division

20.	To develop an understanding of division as sharing and as repeated subtraction, without and with remainders. Informal assessment
21.	To develop and / or recall division facts within 100 Informal assessment
22.	To divide a one digit number or two digit number by a one digit number, with or without remainders. Example 1: 20 ÷ 4; Example 2: 35 ÷ 5; Example 3: 28 ÷ 3 Example 4: 85 ÷ 4; Example 5: 97 ÷ 5; Example 6: 61 ÷ 3
23.	To divide a three digit number by a one digit number with and without renaming. Example 1: 396 ÷ 9; Example 2: 409 ÷ 8
24.	Explore and apply the distributive property of division. Example 1: 96 ÷ 8 = (80 ÷ 8) + (? ÷ 8)
25.	Solve and complete practical tasks and problems involving division of whole numbers. Example 1: 81 marbles were shared equally among 9 children. How many did each get? Example 2: How many boxes each containing 6 eggs can be filled from a container that holds 5o eggs? How many eggs will be left over? Example 3: How many bags containing 7 balloons can be made from 43 red balloons and 41 green balloons?

Strand Unit

Fractions

26.

Identify fractions and equivalent forms of fractions with denominators 2, 4, 8 and 10.

27.

Identify fractions and equivalent forms of fractions with denominators, 3, 5, 6. 9 and 12

Example 1: What part is shaded ?

Example 2: Shade 1/10 of this figure.

Example 3: Shade 5/8 of this figure.

Example 4: What fraction is shaded ?

Example 5: What fraction is shaded ?

28.

To compare and order fractions with appropriate denominators and position on the number line.

29.

To calculate a fraction of a set using concrete materials

30.

To develop an understanding of the relationship between fractions and division
Example 1: ¼ of 32 =
Example 2: 1/8 of 64 =
Example 3: 32 ÷ 4 =
Example 4: 64 ÷ 8 =

31.

To calculate a unit fraction of a number and calculate a number, given a unit fraction of a number.
Example 1: ¼ of a number =3. What is the number?
Example 2: 1/10 of a number = 9. What is the number?

32.

Calculate a number, given a multiple fraction of the number
Example 1: 4/5 of a number is 16. What is the number?
Example 2: 5/9 of a number is 45. What is the number?

33.

Express one number as a fraction of another number.
Example 1: 4 = ? of 16.

34.

To solve and complete practical tasks and problems involving fractions.
Example 1: Find 1/5 of 2,500 metres.
Example 2: Find ¾ of 1 metre
Resources needed for practical tasks.

Strand Unit

Decimals

35.

Identify 1/10’s and express in decimal form

36.

Express hundredths as decimals and fractions
Example 1: 7/100 =
Example 2: ¼ = ?/100 =

37.

Order decimals on the number line

Example

38.

Identify place value of whole numbers and decimals to two places and write in expanded form.
Example: 3.45 = 3 + ? + ? = 3 ? /100

39.

Identify the number with the greatest value.
Example 1: 0.57, 0.10, 0.72, 0,25
Example 2: What value has the 6 in each of the following? 4.65, 2.76, 6.05

40.

Add whole numbers and decimals up to two places.
Example 1: 2.56 + 2.4 + 3
Example 2: 5.98 + 7 + 0.3

41.

Subtract whole numbers and decimals up to two places.
Example 1: 6.91 – 4. 75Example 2: 5.00 – 2.56

42.

Multiply a decimal number up to two places by a single digit whole number.
Example 1: 4.5 x 9
Example 2: 4.67 x 4

43.

Divide a decimal number up to two places by a single digit whole number.
Example 1: 2.5 ÷ 5
Example 2: 15.47 ÷ 7

44.

Solve problems involving decimals
Example 1: 2 pieces of pipe were joined . One pipe was 15.4m and the other pipe was 16.7m. What was the length of the two pipes together?
Example 2: A bag of apples weighs 2.86kg. What is the weight of 8 bags?

Algebra

Unit, Number Patterns and Squares

45.	Explore, recognise and record patterns in number, 0 – 999
46.	Explore, recognise and record patterns in number, 0 - 9999
47.	To explore, extend and describe arithmetic and geometric sequences. Example 1: 1, 5, 9, 13, __, ___. Example 2: 81, 27, 9, __
48.	Use patterns as an aid in the memorisation of number facts. Resources: Excel number patterns; 100 squares Assessment: Informal

Strand Unit

Number Sentences

49.	Translate an addition or subtraction number sentence with a frame into a word problem. Example 1: 3 + 7 = . Mary has three sweets. She gets seven more. How many has she now? Example 2: 900 - ______ = 460. Make up a problem.
50.	Translate a one step problem into a number sentence Example: John has 24 cars. He wants to arrange them in rows of 8. Write the number sentence
51.	Solve one step number sentences. Example 1: 400 - _______ = 350 Example 2: 810 + 23 =
52.	Discuss and record solutions for open number sentences. Example 1: 3 + ? < 9. Example 2: 5 + ? > 8

Strand Unit

Shape and Space

53.	Identify, describe and classify 2D shapes (square, rectangle, triangle, hexagon, circle, semi-circle, oval and irregular shapes. Informal assessment – match word to shape
54.	Identify, describe and classify 2 D shapes: Equilateral, isosceles, scalene triangles; parallelogram, rhombus, pentagon and octagon
55.	Explore, describe and compare the properties (sides, angles, parallel and non-parallel) of 2D shapes. Assessment: How many sides has a ______?
56.	Construct and draw 2D shapes using templates, stencils, geo-strips and geo-boards
57.	Construct and draw 2D shapes using ruler and set square
58.	Combine, tessellate and make patterns with 2D shapes Use computer software
59.	Identify the use of 2D shapes in the environment. Assessment: Draw house / signs
60.	Solve and complete practical tasks and problems involving 2D shapes.

Strand Unit

3D Shapes

61.	Identify, describe and classify 3D shapes, including cube, cuboid, cylinder, cone, sphere, triangular prism and pyramid.
62.	Explore, describe and compare the properties of 3D shapes
63.	Establish and appreciate that when prisms are sliced through each face in equal in shape and size. Practical work using plasticine, food packages.
64.	Explore and describe the relationship of 3D shapes with constituent 2D shapes.
65.	Construct 3D shapes – trace around nets
66.	Construct 3 D shapes from 2D shapes
67.	Solve and complete practical tasks and problems using 2D and 3D shapes.
68.	Identify the use of 3D shapes in the environment

Strand Unit

Symmetry

69.	Identify line symmetry in the environment
70.	Identify and draw lines of symmetry in 2 D shapes
71.	Identify lines of symmetry as horizontal, vertical or diagonal. Use examples from the environment – open book, window, gates
72.	Use understanding of line symmetry to complete missing half of a shape, picture or picture.

Strand Unit

Lines and Angles

73.	Identify, describe and classify vertical, horizontal and parallel lines
74.	Identify, describe and classify oblique and perpendicular lines
75.	Recognise an angle in terms of rotation
76.	Draw, discuss and describe intersecting lines and angles – perpendicular and oblique lines; obtuse, acute and right angles. Example 1: Which of these angles is obtuse? Example 2: Which of these angles is acute?
77.	Classify angles as greater than, less than or equal to a right angle
78.	Solve problems involving lines and angles Example 1: What is the smallest angle formed by the hands of the clock at 3.00 ? Example 2: What is the smallest angle formed by the hands of the clock at twenty to three?

Strand Unit

Length

79.	Estimate, compare, measure and record lengths of a wide variety of objects using appropriate metric units
80.	Estimate, compare, measure and record lengths of doors, corridors, school yard, playing field and drives - use trundle wheel, tape measures
81.	Re-name units of length in metres and centimetres Example 1: 125 cm = 1m 25cm Example 2: 2m 3 cm = 203 cms
82.	Rename units of length using decimal or fraction form. Example 1: 25 cm = 0.25m = ¼ m Example 2: 2km 150m = 2150m = 2.15 km
83.	Understand, estimate and measure the perimeter of regular 2D shapes
84.	Solve and complete practical tasks and problems involving the addition and subtraction of units of length (m and cm)
85.	Solve and complete practical tasks and problems involving the addition, subtraction, multiplication and simple division of units (m, cm and km)

Strand Unit

Area

86.	Estimate, compare and measure the area of regular and irregular shapes
87.	Use standard square units : sq cm, sq m (m and cm)

Strand Unit

Weight

88.	Estimate, compare, measure and record the weight of a wide variety of objects using appropriate metric units (kg and g) Need to know: 1000g = 1kg
89.	Become familiar with major and minor markings on scales – 100g, ½ kg, ¼ kg.
90.	Rename units of weight in kg and g. Example 1: 2kg 250 g = 2250g
91.	Rename units of weight using decimal or fraction form. Example 1: 500g = ½ kg = 0.5 kg Confine examples to 2 places of decimals
92.	Solve and complete practical tasks and problems involving the addition and subtraction of units of weight (kg and g) Do not combine kg and g in same sum in 3rd Class
93.	Solve and complete practical tasks and problems involving the addition, subtraction, multiplication and simple division of units of weight (kg and g)

Strand Unit

Capacity

94.	Estimate, compare, measure and record the capacity of a wide variety of objects using appropriate metric units (litres, 250ml and 500ml).
95.	Become familiar with the major and minor markings on measuring containers – 100ml, ½ l, ¾ l, ¼ l.
96.	Rename units of capacity in litres and ml Example 1: 1250ml = 1l 250m
97.	Rename units of capacity using fraction and decimal form. (Confine to 2 places of decimals) Example: 2 ¼ l = 2. 25 l = 2250 ml
98.	Solve and complete practical tasks and problem involving the addition and subtraction of units of capacity, Do not combine litres and ml in 3rd Class.
99.	Solve and complete practical tasks and problems involving multiplication and simple division of units of capacity. (l and ml)

Strand Unit

Time

100.

Consolidate and develop a sense of time passing

101.

Read time in five minute intervals on analogue and digital clocks

102.

Read time in one minute intervals on analogue and digital clocks

103.

Read time in analogue and digital forms

104.

Express digital time as analogue time and vice versa.

105.

Read and interpret simple time tables

106.

Rename minutes as hours and minutes
Example: 70 minutes = ?
Restrict to 1 hr 55 minutes in 3rd Class

107.

Read dates from calendars and express weeks as days and vice versa

108.

Solve and complete practical tasks and problems involving time

109.

Solve and complete practical tasks and problems involving time and dates and the addition and subtraction of hours and minutes
Add hours and minutes separately

2 hours 40 minutes

+ 3 hours 30 minutes

5 hours 70 minutes

= 6 hours 10 minutes

Rename before subtraction

5 hours 20 minutes	=	4 hours 80 minutes
- 1 hour 40 minutes	=	- 1 hour 40 minutes
		3 hours 40 minutes

Money

110.	Rename amounts of money as euro and cent using € symbol and decimal point.
111.	Solve and complete one step problems and tasks involving the addition and subtraction of money.
112.	Solve and complete one step and two step problems involving the addition, subtraction, multiplication and division of money.

Representing and interpreting data

Data

113.	Collect, organise and represent data using pictograms, block graphs and bar charts
114.	Incorporate the scales 1:2, 1:5, 1:10 and 1: 100
115.	Read and interpret tables, pictograms, block graphs and bar charts
116.	Read pie charts using ½, 1/3 and ¼.
117.	Use data sets to solve and complete practical tasks and problems

Chance

118.	Use vocabulary of uncertainty and chance: possible, impossible, might, certain, not sure.
119.	Use vocabulary of uncertainty and chance: chance, unlikely, likely, never and definitely.
120.	Order events in terms of likelihood of occurrence.
121.	Identify and record outcomes of simple random processes.

Fifth Class

Strand Unit

Place Value

The child should be enabled to:

Read, write and order whole numbers and decimals

Examples: Number line with whole numbers only
Order numbers, beginning with the smallest
Number line with decimals

Identify place value in whole numbers and decimals

8,345 – value of 8? Value of 3?
269.045 – value of 2? Value of 4? Value of 5?

Round whole numbers to nearest ten, hundred and thousand; round decimals to nearest whole number.

Examples: 46 ~ 50; 389 ~ 400 ; 48.7 ~ 49

Strand Unit

Operations

1.	Estimate sums, differences, products and quotients of whole numbers. Example: 450 x 9 = 4500 Estimate first – based on 450 x 10, then use calculator.
2.	Add and subtract whole numbers and decimals (to 3 decimal places) with and without a calculator Example 1: 56 +3.092 + 2.14 Example 2: 250 +58.004 +0.16
3.	Multiply a decimal (up to 3 places) by a whole number, with and without a calculator Example 1: 8.125 x 9 Example 2: 3.004 x 6
4.	Divide a 3 digit number by a 2 digit number (with and without calculator) Example 1: 269 – 27 Example 2: 304 -80
5.	Divide a decimal number by a whole number Example 1: 75.6 – 4 Example 2: 80.3 – 9

Strand Unit

Fractions

1.	Compare and order fractions and identify equivalent forms of fractions with denominators 2 –12. Make fraction wall Paper folding
2.	Express improper fractions as mixed numbers and vice versa and position on number line Example 1: 22/5 = ? Example 2: 1 8/9 = ?
3.	Add simple fractions and simple mixed numbers Example 1: ½ + 1/8 = Example 2: 2 ¾ + 1 5/8 =
4.	Subtract simple fractions and simple mixed numbers Example 1: 6/9 – ½ Example 2: 3 ½ - 1 2/3
5.	Multiply a fraction by a whole number Example 1: ¾ x 5 Example 2: ½ x 8
6.	Express tenths, hundredths and thousandths in decimal form Example 1: 0.2 = Example 2: 456/1000 =

Strand

Decimals and Percentages

1.	Develop an understanding of simple percentages and relate to fractions and decimals Example 1: 90% = fraction = decimal Example 2: 25% = fraction = decimal
2.	Compare and order fractions and decimals Order diagrammatically or on number line Example 1: .3, .26, .09 (begin with the smallest) Example 2: ¼, 3/5, 2/3 (begin with biggest)
3.	Solve problems involving operations with whole numbers, fractions, decimals and simple percentages. Use diagrams; estimate and compute answers with a calculator Example 1: Sean had £3.85. He spent ¼ of it. How much had he left? Example 2: Paul had £4.20. He spent 15% of it. How much did he spend?

Strand Unit

Number Theory

1.	Identify simple prime and composite numbers. A prime number is a number greater than 1 with only 2 divisors, itself and 1. Use Sieve of Eratosthenes to identify prime numbers Example 1: Pick out prime numbers in this set: 3, 6, 9, 11, 15. Example 2: Pick out composite numbers in this set: 5, 8, 12, 14.
2.	Investigate relationship between odd and even numbers. 0dd + 0dd = ? Even + Even = ? Odd + Even = ?
3.	Identify square and rectangular numbers Construct diagrams on geo-boards, peg-boards and squared paper to illustrate square and rectangular numbers Explore, compare and record these numbers
4.	Identify factors and multiples Example 1: List the multiples of 10 Example 2: List the factors of 39

Strand Unit

Algebra

Directed Numbers

1.	Identify positive and negative numbers in context Discuss the idea of owing money, below par in golf, temperature, sea level Refer to positive numbers as positive 7 and negative numbers as negative 8 etc Record numbers with signs - +2 , - 4 etc Rewind a video tape

Strand Unit

Rules and Properties

1.	Explore and discuss simple properties and rules about brackets and priority of operation Example 1: 10 + (4 +4) = Example 2: (3 x 4) + 5 = Example 3: 4 + 3 x 5 = Example 4: 96 – 8 –12 =
2.	Identify relationships and record verbal and simple symbolic rules for number patterns. Example 1: 2.0, 3.5, 5.0, 6.5, _, __ Example 2: 81, 27, 9, _ , _

Strand Unit

Equations

1.	Translate number sentences with a frame into a word problem and vice versa Example 1: How many teams of 4 can be made from a class of 28 children? 28 – 4 =
2.	Solve one step number sentences and equations Example 1: 75 – 43 = Example 2: 3.5 x ______ = 14 Example 3: 25% of ____ = 15.

Shape and Space

Strand Unit

2 D Shapes

1.	Name, explore and compare a wide variety of three and four side figures in terms of size and number of angles, type and number of sides (Trapezium, scalene triangle and regular hexagon).
2.	Identify the properties of the circle. Examine area of circle by counting square units.
3.	Construct a circle of given radius or diameter
4.	Tessellate combinations of 2D shapes
5.	Classify shapes according to their lines of symmetry
6.	Use 2D shapes and properties to solve problems Make a specified shape with Tangram shapes

Strand Unit

3 D Shapes

1.	Identify and examine 3D shapes Compare and record number of faces of 3D shapes Identify number of edges and vertices of 3D shapes Name the shape of faces Deconstruct 3D shapes into nets Draw the nets of 3D shapes Construct 3D shapes from nets

Strand Unit

Lines and Angles

1.	Recognise, classify and describe angles and relate angles to shape and the environment
2.	Measure and record angles as acute, reflex or right angles and determine the number of such angles in relation to common regular shapes
3.	Recognise angles in terms of rotation
4.	Examine, measure and record the angles formed by the hands of a clock at a variety of different times
5.	Estimate, measure and construct angles in degrees
6.	Explore the sum of angles in a triangle

Strand Unit

Measures

Length

1.	Select and use appropriate instruments of measurement
2.	Estimate and measure length using appropriate metric units
3.	Estimate and measure the perimeter of regular and irregular shapes

Area

1.	Discover the area of a rectangle is length by breadth
2.	Estimate and measure the area of regular and irregular 2D shapes
3.	Calculate area using square centimetres and metres Find area of square of side 9 cm Find area of rectangle of length 9 cm and width 5 cm
4.	Compare visually square metres and square centimetres

Strand Unit

Weight

1.	Select and use appropriate instruments of measurement
2.	Estimate and measure weight using appropriate metric units

Strand Unit

Capacity

1.	Select and use appropriate instruments of measurement
2.	Estimate and measure capacity using appropriate metric units

Strand Unit

Time

1.	Read and interpret timetables and 24 clock (digital and analogue)
2.	Interpret and convert between times in 12 hour and 24 hour format 10.30 p.m. = ? 07.50 =

Strand Unit

Money

1.	Compare value for money using unitary method Example: Which is better value for money? 6 apples for 72 cent or 4 apples for 40 cent ?

Strand Unit

Data

1.	Collect, organise and represent data using pictograms, single and multiple bar charts and simple pie charts
2.	Read and interpret pictograms, single and multiple bar charts and pie charts
3.	Compare and use simple data sets Personal data such as heights, ages, sports results
4.	Explore and calculate averages of simple data sets
5.	Use data sets to solve problems

Strand Unit

Chance

1.	Identify and list all possible outcomes of simple random processes
2.	Estimate the likelihood of occurrence of events
3.	Construct and use frequency charts and tables

Sixth Class

The topics for 5th Class have been repeated in this list.

Strand Unit

Place Value

The child should be enabled to:

1.	Read, write and order whole numbers and decimals Examples: Number line with whole numbers only Order numbers, beginning with the smallest Number line with decimals
2.	Identify place value in whole numbers and decimals 8,345 – value of 8? Value of 3? 269.045 – value of 2? Value of 4? Value of 5?
3.	Round whole numbers to nearest ten, hundred and thousand; round decimals to nearest whole number. Examples: 46 ~ 50; 389 ~ 400 ; 48.7 ~ 49 Round decimals to one, two or three decimal places Examples: 2.6247 = 2. ? (1 place); = 2.6 ? (2 places); 2.62? (3 places)

Strand Unit

Operations

1.	Estimate sums, differences, products and quotients of whole numbers. Example: 450 x 9 = 4500 Estimate first – based on 450 x 10, then use calculator.
2.	Estimate sums, differences, products and quotients of decimals Example: 4.5 x 9 = ? (based on 4.5 x 10)
3.	Add and subtract whole numbers and decimals (to 3 decimal places) with and without a calculator Example 1: 56 +3.092 + 2.14 Example 2: 250 +58.004 +0.16
4.	Multiply a decimal (up to 3 places) by a whole number, with and without a calculator Example 1: 8.125 x 9 Example 2: 3.004 x 6
5.	Multiply a decimal by a decimal with and without a calculator Example 1: 7.25 x 1.5 Example 2: 13.2 x 0.75
6.	Divide a 3 digit number by a 2 digit number (with and without calculator) Example 1: 269 ÷ 27 Example 2: 304 ÷ 80
7.	Divide a 4 digit number by a 2 digit number Example 1: 3150 ÷ 25 Example 2: 6228 ÷ 29
8.	Divide a decimal number by a whole number Example 1: 75.6 ÷ 4 Example 2: 80.3 ÷ 9
9.	Divide a decimal number by a decimal, with and without a calculator Example 1: 36.9 ÷ 2.6 Example 2: 27.6 ÷ 0.2

Strand Unit

Fractions

1.	Compare and order fractions and identify equivalent forms of fractions with denominators 2 –12. Make fraction wall Paper folding
2.	Compare and order fractions and identify equivalent forms of fractions
3.	Express improper fractions as mixed numbers and vice versa and position on number line Example 1: 22/5 = ? Example 2: 1 8/9 = ?
4.	Add simple fractions and simple mixed numbers Example 1: ½ + 1/8 = Example 2: 2 ¾ + 1 5/8 = Use equivalent fractions to simplify calculations Common denominator should be got by listing multiples
5.	Subtract simple fractions and simple mixed numbers Example 1: 6/9 – ½ Example 2: 3 ½ - 1 2/3
6.	Multiply a fraction by a whole number Example 1: ¾ x 5 Example 2: ½ x 8
7.	Multiply a fraction by a fraction Example 1: ½ x 1/3 Example 2: 3/5 x 1/6
8.	Express tenths, hundredths and thousandths in decimal form Example 1: 0.2 = Example 2: 456/1000 =
9.	Divide a whole number by a unit fraction Example 1: 2- ¼ Example 2: 15 – 1/3
10.	Understand and use simple ratios Example 1: 2:5 = 4:? Example 2: 6:9 = ? :3

Strand

Decimals and Percentages

	1. Develop an understanding of simple percentages and relate to fractions and decimals Example 1: 90% = fraction = decimal Example 2: 25% = fraction = decimal
2.	Use percentages and relate to fractions and decimals Example 1: 7/10 = ? Example 2: 15/20 = ? Example 3: 0.65 = ?%
3.	Compare and order fractions and decimals Order diagrammatically or on number line Example 1: .3, .26, .09 (begin with the smallest) Example 2: ¼, 3/5, 2/3 (begin with biggest)
4.	Compare and order percentages of numbers Example 1: Which is bigger – 25% of 150 or 15% of 250 ? Example 2: What percentage is 15 minutes of 1 ½ hours?
5.	Solve problems involving operations with whole numbers, fractions, decimals and simple percentages. Use diagrams; estimate and compute answers with a calculator Example 1: Sean had £3.85. He spent ¼ of it. How much had he left? Example 2: Paul had £4.20. He spent 15% of it. How much did he spend?
6.	Solve problems relating to profit and loss, discount, VAT, interest, increases and decreases Example 1: A radio was bought for £50 and sold at a profit of 20%. What was the selling price? Example 2: What was the selling price of an article bought for £66 and sold at a profit of 33 1/3% Example 3: An article was bought for £200 and sold for £235. What was the percentage profit? Example 4: Calculate the sale price of an article which cost £30 and is now being sold at a discount of 15%.

Strand Unit

Number Theory

1.	Identify simple prime and composite numbers. A prime number is a number greater than 1 with only 2 divisors, itself and 1. Use Sieve of Eratosthenes to identify prime numbers Example 1: Pick out prime numbers in this set . 3, 6, 9, 11, 15. Example 2: Pick out composite numbers in this set: 5, 8, 12, 14.
2.	Investigate relationship between odd and even numbers. 0dd + 0dd = ? Even + Even = ? Odd + Even = ?
3.	Identify square and rectangular numbers Construct diagrams on geo-boards, peg-boards and squared paper to illustrate square and rectangular numbers Explore, compare and record these numbers
4.	Identify and explore square numbers Example 1: 5 x 5 = 25 = 52 Example 2: 9 x 9 = 81 = ?
5.	Explore and identify simple square roots Example 1: square root of 81 = ? Example 2: square root of 64 = ?
6.	Identify factors and multiples Example 1: List the multiples of 10 Example 2: List the factors of 39
7.	Explore and record factors and multiples to identify common factors and multiples Example 1: Find common factors of 25 and 35. Example 2: List the common multiples of 8 and 10 (stop at 80)
8.	Write whole numbers in exponential form Example 1: 1,000 = 10 x10 x 10 = 103 Example 2: 16 = 2 x 2 x 2 x 2 = ?

Strand Unit

Algebra

Directed Numbers

Identify positive and negative numbers in context

Discuss the idea of owing money, below par in golf, temperature, sea level
Refer to positive numbers as positive 7 and negative numbers as negative 8 etc
Record numbers with signs - +2 , - 4 etc
Rewind a video tape
Walk the number line to experience positive and negative numbers
Identify and mark positive and negative numbers on personal and class number lines

Example 1: The night temperature was –7 and the day temperature was +6. How many degrees hotter was it by day?
Example 2: What is the difference between –8 and +4 ?

Strand Unit

Rules and Properties

1.	Explore and discuss simple properties and rules about brackets and priority of operation Example 1: 10 + (4 +4) = Example 2: (3 x 4) + 5 = Example 3: 4 + 3 x 5 = Example 4: 96 – 8 –12 =
2.	Know simple properties and rules about brackets and priority of operations
3.	Use calculator to find missing numbers and missing operator. Example 1: 37 ? 21 ? 23 = 800 Example 2: 27 ? (36 ? 11) = 675
4.	Identify relationships and record verbal and simple symbolic rules for number patterns. Example 1: 2.0, 3.5, 5.0, 6.5, _, __ Example 2: 81, 27, 9, _ , _
5.	Deduce and record rules for given number patterns. Example 1: 2,6,12,20, 30, _, _. Example 2: 4.1, 8.2, 16.4, _,_.

Strand Unit

Variables

1.	Explore the concept of a variable in the context of simple patterns, tables and simple formulae and substitute values for variables. Example 1: d = 2r (Find d, if r = 4) Example 2: a = l x w. (Find a, if l =5, and w =6)

Equations

1.	Translate number sentences with a frame into a word problem and vice versa Example 1: How many teams of 4 can be made from a class of 28 children? 28 – 4 =
2.	Translate word problems with a variable into a number sentence. Example 1: Peter thought of a number, multiplied it by 7, and added 6 to the answer. The result was 41. What was the number? Example 2: If Brian was 3 times his present age, he would be 6 years younger than his mother who is 39. How old is Brian?
3.	Solve one step number sentences and equations Example 1: 75 – 43 = Example 2: 3.5 x ______ = 14 Example 3: 25% of ____ = 15. Example 4: y + 7 =13. Find y Example 5: 8a – 7 = 33. Find a

Shape and Space

Strand Unit

2 D Shapes

1.	Name, explore and compare a wide variety of three and four side figures in terms of size and number of angles, type and number of sides (Trapezium, scalene triangle and regular hexagon).
2.	Construct triangles from given sides or angles
3.	Identify the properties of the circle. Examine area of circle by counting square units.
4.	Relate the diameter of a circle to its circumference by measurement.
5.	Measure the circumference of circle using a piece of string.
6.	Construct a circle of given radius or diameter
7.	Tessellate combinations of 2D shapes
8.	Classify shapes according to their lines of symmetry
9.	Plot simple co-ordinates and apply where appropriate. Use squared paper.
10.	Use 2D shapes and properties to solve problems Make a specified shape with Tangram shapes

Strand Unit

3 D Shapes

1.	Identify and examine 3D shapes Compare and record number of faces of 3D shapes Identify number of edges and vertices of 3D shapes Name the shape of faces Deconstruct 3D shapes into nets Draw the nets of 3D shapes Construct 3D shapes from nets

Strand Unit

Lines and Angles

1.	Recognise, classify and describe angles and relate angles to shape and the environment
2.	Identify types of angles in environment
3.	Measure and record angles as acute, reflex and right angles and determine the number of such angles in relation to common regular shapes
4.	Recognise angles in terms of rotation
5.	Examine, measure and record the angles formed by the hands of a clock at a variety of different times
6.	Estimate, measure and construct angles in degrees
7.	Explore the sum of angles in a triangle
8.	Explore the sum of the angles in a quadrilateral

Strand Unit

Measures

Length

1.	Select and use appropriate instruments of measurement
2.	Estimate and measure length using appropriate metric units
3.	Rename measures of length Example 1: 233m = 233/1000 = 0.233km Example 2: 1 m 11 cm = 1 11/100m = 1.11m
4.	Estimate and measure the perimeter of regular and irregular shapes
5.	Use and interpret scales on maps and plans

Area

1.	Discover the area of a rectangle is length by breadth
2.	Recognise that the length of the perimeter of a rectangle does not determine the area of the shape
3.	Construct rectangles of constant perimeter with varying areas
4.	Estimate and measure the area of regular and irregular 2D shapes
5.	Calculate the area of regular and irregular 2D shapes Check area of shape by measuring with square centimetre units Calculate area of circle by counting squares only
6.	Calculate area using square centimetres and metres Find area of square of side 9 cm Find area of rectangle of length 9 cm and width 5 cm
7.	Calculate area using ares and hectares Fields, playground, car parks
8.	Compare visually square metres and square centimetres
9.	Identify the relationship between square metres and square centimetres
10.	Find the area of a room from a scale plan

Strand Unit

Weight

1.	Select and use appropriate instruments of measurement
2.	Estimate and measure weight using appropriate metric units
3.	Rename measures of weight using appropriate metric units Example 1: 759g = ¾ kg = 0.75kg Example 2: 4kg 45g = 4 45 /1000 = 4.045kg

Strand Unit

Capacity

1.	Select and use appropriate instruments of measurement
2.	Estimate and measure capacity using appropriate metric units
3.	Rename measures of capacity using appropriate metric measures Example 1: 625ml = 5/8l = 0.625l Example 2: 8 L 253 ml = 8 253 /1000 = 8.253 L
4.	Find the volume of a cuboid experimentally

Strand Unit

Time

1.	Read and interpret timetables and 24 clock (digital and analogue)
2.	Explore international time zones
3.	Interpret and convert between times in 12 hour and 24 hour format 10.30 p.m. = ? 07.50 =
4.	Explore the relationship between time, distance and speed

Strand Unit

Money

1.	Compare value for money using unitary method Example: Which is better value for money? 6 apples for 72p or 4 apples for 40p?
2.	Calculate sale prices. Example 1: Find the price of an article which originally cost £200 and is reduced by 25% in a sale Example 2: The price of an article without VAT is £160. How much will it cost if VAT is added at 12 ½ %?
3.	Convert foreign currencies to Irish pounds and vice versa Example 1: Change £28 to francs. (£1 = 8 francs) Example 2: Change £28 Irish pounds to sterling. (£1 = 75p sterling)

Strand Unit

Data

1.	Collect, organise and represent data using pictograms, single and multiple bar charts and simple pie charts
2.	Read and interpret pictograms, single and multiple bar charts and pie charts
3.	Read and interpret trend graphs
4.	Compare and use simple data sets Personal data such as heights, ages, sports results
5.	Explore and calculate averages of simple data sets
6.	Use data sets to solve problems

Strand Unit

Chance

1.	Identify and list all possible outcomes of simple random processes
2.	Select two numbers at random from the numbers 1,2,3,4,5
3.	Estimate the likelihood of occurrence of events
4.	Construct and use frequency charts and tables

Note on Informal Assessment / Teaching Strategies

1.	Estimate when doing addition and subtraction
2.	Drills in addition and subtraction – 3+ 6; 3 +16; 3 + 26;
3.	Orally solve word problems – single step, multi-step
4.	Evaluate and review problem solving strategies Read each problem three times – there are 402 cattle in 3 fields. 86 in field 1, 86 in field 2, how many in field 3? Draw and discuss
5.	Teach concept of multiplication as continuous addition 2+2 +2 +2 = 2 x 4
6.	Know number facts to 100
7.	Work involving 0
8.	Develop concept of division as repeated subtraction

Methodology

Policy Issues

Work on the concepts is vital. The children should encounter as much practical work as possible. This will assist their understanding, and avoid some of the problems caused by an unduly abstract approach to the teaching of Mathematics
Emphasise the importance of place value
Emphasise the place which the environment plays in the teaching of Mathematics

It is important that there is consistency with regard to methods.

Subtraction

Second Class Programme

3 types of subtraction

Deduction: If I take 3 from 10, how many are left?
Complementary: 3 and what makes ten?
Difference: What is the difference between 3 and 10.

Regrouping (Re-naming) is used throughout the texts to teach subtraction of whole numbers, time and subtraction of fractions. Previously, the equal addends method (borrowing and pay back) was recommended because of the difficulties with large numbers when doing division, but the reduced level of demand with regard to division means that it is now opportune to recommend decomposition of number as a method for doing subtraction. However, if the pupils have already learned the equal addends method, there is no necessity to change methods. It is recommended that time and addition and subtraction of fractions be taught by using decomposition.

Regrouping : Examples

33 is 3 tens and 3 units; 33 is 2 tens and 13 units
43 is 4 tens and 3 units; 43 is 3 tens and 13 units

Subtraction

24		You cannot take 8 from 4.
- 8		Open a bundle of 10. Regroup. Now you have 1 ten and 14 units

114
- 8

Ensure that lots of examples are done involving 0

Long Division

Use repeated subtraction to introduce concept
Teach 13 times tables so that the pupils are facilitated with doing estimations
Introductory phase is 2 digits divided by 2 digits
Encourage pupils to make estimates
Teach rounding off to the nearest 10

Problem Solving

Read the problem 3 times
Tell the main idea in your own words
Find the question sentence
Pick out the important facts
How do the facts (numbers) relate to each other?
Form the number sentences
Estimate
Calculate and form an answer sentence

Fractions

To reduce the level of difficulty involved, children will need activity of a concrete nature so that when each fractions is recorded in abstract form, it will be associated with a concrete activity.

Sequence of ideas

Place an emphasis on equivalent fractions
The idea of a fraction as a shape divided into equal parts
Revise the idea of ½ in the environment : half –hour, half moon
Identify shapes divided into halves
Divide shapes into halves and colour each half in different colour
Begin a fraction wall showing 1 unit and ½
Introduce concept of ¼
Fraction wall with ½ and ¼
Renaming fractions : ½ = 2/4
Addition of fractions
Subtraction of fractions
Writing mixed numbers: 2½ using concrete apparatus to show 2½
Express mixed numbers in fractions : 2 ¼ = 9 quarters
Introduce idea of numerator and denominator
Rename fractions in lowest terms using HCF
Rename fractions through cancelling

Addition of mixed numbers:

a)		2	1	+	1	1
		2	2	+	1	3
	=	3	+	3	+	2
	=	3	+	6	+	6
	=	3	5
	=	3	6


b)		3	1	+	4	7
		3	2	+	4	12
	=	7	+	6	+	7
	=	7	+	12	+	12
	=	7	+	13
	=	7	+	12
	=	8	1
	=	8	12

Subtraction of mixed numbers

a)		2	5	-	1	7
		2	6	-	1	12
	Subtract whole numbers first: 2 – 1 = 1
	=	1	+	10	-	7
	=	1	+	12	-	12
	=	1	3
	=	1	12
	=	1	1
	=	1	4

b)		5	1	-	1	2
		5	2	-	1	3
	=	4	1	-	2
	=	4	2	-	3
	=	4	3	-	4
	=	4	6	-	6
	We cannot subtract 4/6 from 3/6 so we change 1 into sixths
	=	3	6	+	3	-	4
	=	3	6	+	6	-	6
	=	3	5
	=	3	6

Decimals

The most important concept in working with decimals is that of place value.

Use place value grid

Tens	Units	Tenths	Hundredths
1	4	5	6

Unit strip divided into ten equal parts
Write fractions as decimal fractions and vice versa
Identify decimal fractions shaded in shapes
Write units and fractions in decimal form
Sequences involving decimals
Writing decimals on the abacus
Use notation board to represent numbers

H	T	U	1/10
O O OO	OOO OOO	OO	OOOO OOO

Relate decimals to money
Introduce hundredths. Use 100 square
Recording tenths as hundredths
Writing hundredths as tenths and hundredths
When multiplying / dividing by 10, 100, 1000, do not advise the pupils that the decimal point moves to the left or to the right. It is the digits that move to the left or right.

Time

Add hours and minutes separately

=	2 hours 40 minutes 3 Hours 30 minutes 5 hours 70 minutes 6 hours 10 minutes

Rename before subtraction

5 hours 20 minutes
1 hour 40 minutes

=
=

4 hours 80 minutes
1 hour 40 minutes
3 hours 40 minutes

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