# Skills development for infant classes

Through completing the strand units of the mathematics curriculum the child should be enabled to

##### Applying and problem-solving
• select appropriate materials and processes for mathematical tasks
• select and apply appropriate strategies for completing a task or solving a problem
• recognise solutions to problems
##### Communicating and expressing
• discuss and explain mathematical activities
• record the results of mathematical activities concretely and using diagrams, pictures and numbers
• discuss problems presented concretely, pictorially or orally
##### Integrating and connecting
• connect informally acquired mathematical ideas with formal mathematical ideas
• recognise mathematics in the environment
• recognise the relationship between verbal, concrete, pictorial and symbolic modes of representing numbers
• carry out mathematical activities that involve other areas of the curriculum
##### Reasoning
• classify objects into logical categories
• recognise and create sensory patterns
• justify the processes or results of activities
##### Implementing
• devise and use mental strategies and procedures for carrying out mathematical tasks
• use appropriate manipulatives to carry out mathematical tasks and procedures
##### Understanding and recalling
• recall and understand terminology.

## Strand: Early mathematical activities

Content for junior infant class

### 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 (i.e. elements not in a set)
categorise objects such as things I like/donÕt like,
red things/things that are not red.

### Strand unit: Matching

The child should be enabled to

• match equivalent and non-equivalent sets using one-to-one correspondence
match pairs of identical objects in one-to-one correspondence:
lollipop sticks, Unifix cubes
match pairs of related objects in one-to-one correspondence:
putting out knives and forks, buttoning coats, putting lids on pans

match equivalent and non-equivalent sets to establish the concept of more than, less than, enough, as many as.

### Strand unit: Comparing

The child should be enabled to

• compare objects according to length, width, height, weight, quantity, thickness or size
compare pairs of identical objects that differ in length, noting the need for a baseline or common starting point
compare pairs of pencils
how does each differ from the next?

long/short, longer/shorter
• compare sets without counting
more than and less than.

### Strand unit: Ordering

The child should be enabled to

• order objects according to length or height
examine three objects and describe how each object differs from the preceding one
order objects by length or height, starting with a different object each time
order new objects to make a set like a given one
• order sets without counting.

## Strand: Number

### Strand unit: Counting

Content for junior infant classes

The child should be enabled to

• count the number of objects in a set, 1-10
count objects, pushing them aside while counting
count regular arrays or rows before random groups
use number rhymes and stories.

Content for senior infant classes

The child should be enabled to

• count the number of objects in a set, 0-20
count the same set several times, starting with a different object each time
present different patterns and arrays of the same number.

### Strand unit: Comparing and ordering

Content for junior infant classes

The child should be enabled to

• compare equivalent and non-equivalent sets 1-5 by matching without using symbols
use one-to-one matching to determine equality and inequality (more than/less than/same as)
record by drawing
• order sets of objects by number, 1-5
arrange sets of objects in ascending order
order rods and number strips by length
order number cards; match them with sets and number patterns
• use the language of ordinal number: first, last
who is first/last in the line?
the first colour is red, the last colour is blue.

Content for senior infant classes

The child should be enabled to

• compare equivalent and non-equivalent sets 0-10 by matching
name the inequality: I have 2 more than you; 3 is less than 5
• order sets of objects by number, 0-10
• use the language of ordinal number: first, second, third, last
use ordinal numbers to describe position in a line
use this language when ordering numbers.

### Strand unit: Analysis of number - Combining

Content for junior infant classes

The child should be enabled to

• explore the components of number, 1-5
identify the ways in which the numbers can be modelled using concrete objects:
4 and 1, 2 and 2, 1 and 2 and 1
identify pairs of related facts: 1 and 2 is the same as 2 and 1
• combine sets of objects, totals to 5
add one more to a given set
combine two sets, state total
record pictorially

Content for senior infant classes

The child should be enabled to

• explore the components of number, 1-10
• combine sets of objects, totals to 10
use appropriate strategies: counting all, counting on
counting on on the number strip
start at 5, count on 3, where am I?
oral counting without the number strip
combine two or more sets, state total
record

### Strand unit: Analysis of number - Partitioning

Content for junior infant classes

• partition sets of objects, 1-5
partition sets of objects with a pencil or straw to show component parts
record pictorially.

Content for senior infant classes

• partition sets of objects, 0-10
8 people are on my team. 6 are girls, how many are boys?
record pictorially
• use the symbols + and = to construct word sentences involving addition
formal introduction of the symbols should occur only after sufficient oral and exploratory work has been completed
the meaning of the symbols will have to be discussed frequently
the equals sign does not signal 'the answer comes next':
equals means 'the same' or equivalent; explore using a number balance.

### Strand unit: Analysis of number - Numeration

Content for junior infant classes

• develop an understanding of the conservation of number, 1-5
count rearranged number arrays and observe thatthe number does not change
• read, write and order numerals, 1-5
present sets to match a numeral and vice versa
use counters or objects to form number patterns
trace numerals cut out of sandpaper or carpet
draw numerals in sand or with thick crayon
• identify the empty set and the numeral zero
show an empty basket; how many apples in it?
remove pencils from a jar until none is left
show the numeral
count down to zero
counting back number rhymes
• subitise (tell at a glance) the number of objects in a set, 1-5
tell at a glance how many objects are in a set
estimate using a known set
without counting, classify the other sets as less
than/about the same as/more than the given set
• solve simple oral problems, 0-5
you have 3 sandwiches for lunch, you eat 2, how many are left? Zero can be used when there are none left.
Joan has 2 crayons, Sean has 3 crayons, how many altogether?
teacher presents a problem orally, pupils use counters to solve it.

Content for senior infant classes
• develop an understanding of the conservation of number, 0-10
• read, write and order numerals, 0-10
• identify the empty set and the numeral zero
• estimate the number of objects in a set, 1-10
check estimate by counting
• solve simple oral and pictorial problems, 0-10
problems can include story problems and open-ended
exploratory questions
how many different ways can you make a pattern with 6 counters?

The treatment of content as suggested in the exemplars is common to both classes.

## Strand: Algebra

### Strand unit: Extending patterns

Content for junior infant class

The child should be enabled to

• identify, copy and extend patterns in colour, shape and size using a range of objects, e.g. cubes or threading beads continue the pattern, what comes next?
pupils make their own patterns using gummed paper shapes; two colours, two shapes, two sizes
computer software can be used where appropriate discuss results.

Integration
Visual arts: Making prints

Content for senior infant class

The child should be enabled to

• identify, copy and extend patterns in colour, shape, size and number (3-4 elements)
copy and extend patterns using beads and blocks, by drawing and colouring
e.g. 2 blue, 3 red; 3 circles, 1 square; 2 big beads, 1 small bead; red, blue, yellow
discuss
• discover different arrays of the same number teacher makes a pattern (array) using a number of counters; child creates a different array using the same number of counters
how many different patterns of 10 can you make?
how many numbers can you arrange in pairs?
• recognise patterns and predict subsequent numbers find the missing numbers: 2, 3, 4, _, 6, 7 10, 9, _, _, 6, 5, 4, 3, _ , _ .

Integration
Visual arts: Making prints

## Strand: Shape and space

### Strand unit:Spatial awareness

Content for junior infant class

The child should be enabled to

• explore, discuss, develop and use the vocabulary of spatial relations
position: over, under, up, down, on, beside, in
directions: moving in straight/curved lines, in a circle,
finding own space.

Content for senior infant class

The child should be enabled to

• explore, discuss, develop and use the vocabulary of spatial relations
position: above, below, near, far, right, left
direction: through the hoop, behind the mat

### Strand unit: 3-D shapes

Content for junior infant class

The child should be enabled to

• sort 3-D shapes, regular and irregular
things that do/do not roll, do/do not fit together
make constructions with 3-D shapes and discuss them
• solve tasks and problems involving shape.

Content for senior infant class

The child should be enabled to

• sort, describe and name 3-D shapes: cube, cuboid, sphere and cylinder
edge, corner, face, straight, curved, round and flat
sort shapes according to rules, e.g. objects with four
sides, objects that roll
• combine 3-D shapes to make other shapes
• solve tasks and problems involving shape.

### Strand unit:2-D shapes

Content for junior infant class

The child should be enabled to

• sort and name 2-D shapes: square, circle, triangle, rectangle
directed sorting of 2-D shapes with different criteria, e.g. round/not round, thick/thin
• use suitable structured materials to create pictures
• solve problems involving shape
which two shapes go together to cover a square?

Content for senior infant class

The child should be enabled to

• sort, describe and name 2-D shapes: square, circle, triangle, rectangle
collect and sort different shapes
e.g. straight, curved, flat, side, corner
make shapes with art straws, on geoboard
draw shapes found in the environment
• combine and divide 2-D shapes to make larger or smaller shapes
cut paper shapes into 2 or 4 pieces and discuss the results
• solve problems involving shape and space
make a shape with 7 blocks
how many different shapes can you make with 5 blocks?
• give simple moving and turning directions.

Integration
Physical education: Dance; Gymnastics;
Visual arts: Construction

The treatment of content as suggested in the exemplars is common to both classes.

## Strand: Measures

### Strand unit: Length

Content for junior infant class

The child should be enabled to

• develop an understanding of the concept of length through exploration, discussion, and use of appropriate vocabulary
discuss objects in the environment: long/short, tall/short, wide/narrow, longer,shorter, wider than sort objects according to length
• compare and order objects according to length or height.

Integration
Music:Developing a sense of duration; Early literacy

Content for senior infant class

The child should be enabled to

• develop an understanding of the concept of lengt through exploration, discussion, and use of appropriate vocabulary
• compare and order objects according to length or height
identify: as long as/as wide as/longest/shortest
• estimate and measure length in non-standard units
estimate, and check by measuring
how many lollipop sticks do you think will fit along
the length of the table? Guess, check and discuss
• select and use appropriate non-standard units to measure length, width or height. Discuss reasons for choice.
present simple problems:
How can we find out which is wider, the door or the
table? Which unit will we use (stick or pencil)?

Integration
Music:Developing a sense of duration; Early literacy

### Strand unit: Weight

Content for junior infant class

The child should be enabled to

• develop an understanding of the concept of weight through exploration, handling of objects, and use of appropriate vocabulary
heavy/light, heavier/lighter, balance, weigh
sort objects into heavy or light sets
handle and describe objects using the vocabulary of weight
• compare objects according to weight
present simple problems, e.g. pupils estimate (guess) by handling
which object is heavier or lighter?
check using balance; discuss
compare pairs of objects that look alike but are different in weight, e.g. golf ball and plastic squash ball.

Content for senior infant class

The child should be enabled to

• develop an understanding of the concept of weight through exploration, handling of objects and use of appropriate vocabulary
• compare and order objects according to weight compare objects that differ in size, shape and weight by handling
check using balance; discuss
compare an object with a collection of objects
compare a collection of objects with another collection of objects
order three objects according to weight by handling;
check using balance; discuss
• estimate and weigh in non-standard units
check using balance
present simple problems:
how many apples do you think will balance your lunchbox?
• select and use appropriate non-standard units to weigh objects
present simple problems:
How can we find the weight of a stone?
Which unit will we use (matchsticks or conkers)?
discuss reasons for choice.

Integration
Geography: Human environments

The treatment of content as suggested in the exemplars is common to both classes.

### Strand unit: Capacity

Content for junior infant class

The child should be enabled to

• develop an understanding of the concept of capacity through exploration and the use of appropriate vocabulary
full/nearly full/empty/holds more/holds less/holds as much as fill and empty containers of various sizes, discuss
use smaller containers to fill larger containers
• compare containers according to capacity
use a variety of containers; discuss
emphasise that full means full to the top
present simple problems:
do you think the jar holds more sand than the cup?
will all the water from the jug go into the glass?

Content for senior infant class

The child should be enabled to

• develop an understanding of the concept of capacity through exploration and the use of appropriate vocabulary
• compare and order containers according to capacity
fill one container and pour contents into another
compare the capacity of two very different containers, noting that both can hold the same amount
compare three containers; arrange in order of capacity; label, e.g. holds more/holds most
• estimate and measure capacity in non-standard units
present simple problems:
estimate (guess) how many spoons or egg-cups of sand or dried peas will fill the cup
how many jugs of water will fill the bucket?
use the same unit to fill two different containers; check by measuring
record results using one counter for each cup or jug
poured children work in pairs
• select and use appropriate non-standard units to measure capacity
present simple problems:
How can we find the capacity of the bucket?
Which unit will we use (teaspoons or cups)?
discuss reasons for choice.

### Strand unit: Time

The child should be enabled to

• develop an understanding of the concept of time through the use of appropriate vocabulary
morning/evening, night/day, lunchtime, bedtime, early/late, days of the week, school days, weekends
use the language of time to discuss events
record weather for each day on a chart
• sequence daily events or stages in a story
pupils state the order of familiar events
order pictures in correct time sequence
sequence events in familiar stories and rhymes.

Integration
History: Myself and my family
Geography: The physical world

Content for senior infant class

The child should be enabled to

• develop an understanding of the concept of time through the use of appropriate vocabulary
yesterday/today/tomorrow/seasons/soon/not yet/birthday
significant events, festivals, holidays
• sequence daily and weekly events or stages in a story
discuss significant times in the day
record orally and pictorially the time sequence of four events in the school day
make scrapbooks of 'My Day'
sequence pictures representing stages of development
pupils identify errors in a sequence; discuss
• read time in one-hour intervals.

Integration
History: Myself and my family
Geography: The physical world

### Strand unit:Money

Content for junior infant class

The child should be enabled to

• recognise and use coins (up to 5p) sort and name 1p, 2p and 5p coins
select appropriate coins in simple shopping activities,
use correct vocabulary: buy, sell, spend, coins,
pence, how much?
• solve practical tasks and problems using money.

Content for senior infant class

The child should be enabled to

• recognise coins up to 20p and use coins up to 10p
exchange a number of coins for a single coin of equal value and vice versa
use coins in shopping activities, tender appropriate coins, calculate change
use correct vocabulary: cost, price, cheap/expensive,change, too much/too little
• solve practical tasks and problems using money
which items can be bought with a given coin?
spend the same amount of money in two different ways.

### Strand unit:Money - Euro

Content for junior infant class

The child should be enabled to

• recognise and use coins (up to 5 cents)
sort and name coins up to 5 cents
select appropriate coins in simple shopping activities,
use correct vocabulary: buy, sell, spend, coins, cents,how much?
• solve practical tasks and problems using money.

Content for senior infant class

The child should be enabled to

• recognise coins up to 20 cents and use coins up to 10 cents
exchange a number of coins for a single coin of equal value and vice versa
use coins in shopping activities, tender appropriate coins, calculate change
use correct vocabulary: cost, price, cheap/expensive, change, too much/too little
• solve practical tasks and problems using money
which items can be bought with a given coin?
spend the same amount of money in two different ways.

## Strand: Data

### Strand unit:Recognising and interpreting data

Content for junior infant class

The child should be enabled to

• sort and classify sets of objects by one criterion
sort collections on the basis of colour, shape, size,texture and function
• match sets, equal and unequal
enough/more/as many as/less
• represent and interpret a set of simple mathematical data using real objects, models and pictures
children represent the chosen set concretely and pictorially
children identify the numerical correspondence between the pictures and the objects, e.g. the set of children who had an apple for lunch.

Content for senior infant class

The child should be enabled to

• sort and classify sets of objects by one and two criteria
sort into two groups by one criterion: with/without wheels, red/not red shapes
sort by two criteria: red toys with wheels
• represent and interpret data in two rows or columns
using real objects, models and pictures
pupils choose between two types of pet
pupil is given picture or model of a pet
pictures or models are arranged in columns or rows in one-to-one correspondence
discuss and compare results
discuss the need for a common baseline.

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