Skills development for first and second 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 and applications
- apply concepts and processes in a variety of contexts
- select and apply appropriate strategies for completing a task or solving a problem
- recognise solutions to problems
Communicating and expressing
- listen to and discuss other children's mathematical descriptions and explanations
- discuss and explain mathematical activities
- discuss and record the results of mathematical activities using diagrams, pictures and symbols
- discuss problems presented 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
- understand the mathematical ideas behind the procedures he/she uses
Reasoning
- classify objects into logical categories
- make guesses and carry out experiments to test them
- recognise and create mathematical patterns and relationships
- justify the processes and results of mathematical activities
Implementing
- devise and use mental strategies and procedures for carrying out mathematical tasks
- use appropriate manipulatives to carry out mathematical tasks and procedures
- execute procedures efficiently
Understanding and recalling
- understand and recall terminology and facts.
Strand: Number
Strand Unit: Counting and numeration
Content for first class
The child should be enabled to
- count the number of objects in a set
count the same set several times, starting with a different object each time (regular and random arrays)
re-count rearranged sets and arrays to determine that number does not change - read, write and order numerals, 0-99
match a numeral to a set and vice versa
write numerals to correspond to sets
count on and back from a given number, using concrete materials, number line and hundred square
state the number that follows or precedes a number - estimate the number of objects in a set 0-20
compare a known set with other sets, check by counting
describe different sets of cubes as less than, more than or about the same as the known set.
Content for second class
The child should be enabled to
- count the number of objects in a set
estimate first and check by counting e.g. the number of marbles in a jar - read, write and order numerals 0-199
state the number that comes before and after a random number
fill in missing numbers on the hundred square - estimate the number of objects in a set 0-20.
Strand Unit: Comparing and ordering
Content for first class
The child should be enabled to
- compare equivalent and non-equivalent sets 0-20
name the inequality
I have 5 more than you; 7 is less than 10
6 is less than 9 by how many? - order sets of objects by number
- use the language of ordinal number, first to tenth
when ordering sets and numbers, describing patterns, taking turns.
Content for second class
The child should be enabled to
- compare equivalent and non-equivalent sets record using < > and =
- use the language of ordinal number e.g. using the calendar.
The treatment of content as suggested in the exemplars is common to both classes.
Strand Unit: Place value
Content for first class
The child should be enabled to
- explore, identify and record place value 0-99
group and count in tens and units using cubes, counters,lollipop sticks and coins (1p and 10p, 1 cent and 10 cents), base ten materials and notation boards
express groups of counters as units or as tens and units
record pictorially and on the abacus.
Content for second class
The child should be enabled to
- explore, identify and record place value 0-199
extend grouping and renaming activities to include the hundred, in tens
rename numbers as one hundred, tens and units
represent numbers using place value material: coins,number cards, word cards, number line.
The treatment of content as suggested in the exemplars is common to both classes.
Strand Unit: Operations
Content for first class
The child should be enabled to
Addition
- develop an understanding of addition by combining or partitioning sets, use concrete materials 0-20
find all the addition combinations to make up a given number:
11 + 1 = 12, 2 + 6 + 4 = 12
record addition: orally, pictorially, in number sentences, in jumps on the number line - explore, develop and apply the commutative, associative and zero properties of addition
commutative property: 6 + 2 = 8, 2 + 6 = 8
associative property: (2 + 3) + 5 =10, 2 + (3 + 5) =10
zero property: 7 + 0 = 7 - develop and/or recall mental strategies for addition facts within 20
use concrete materials to count on using commutative
property, zero property, counting in twos,
doubles and near doubles,
pairs of numbers that total 10 (6 + 4 = 10);
complement numbers to 10 (3 + n =10);
orally memorise addition facts using strategies - construct number sentences and number stories; solve problems involving addition within 20
construct and tell a number story, record pictorially, as a number sentence or as a written story
solve written problems; pupils can also devise problems for each other - add numbers without and with renaming within 99
estimate sum by adding the tens, check estimates using manipulatives
add numbers using concrete materials, notation boards, number lines and hundred squares
use mental calculations
record using number lines, number sentences and algorithm - explore and discuss repeated addition and group counting
counting in twos, fives, tens
count children in the line, 2, 4, 6, 8 ....
Content for second class
The child should be enabled to
Addition
- develop an understanding of addition by combining or partitioning sets
- explore, develop and apply the commutative, associative and zero properties of addition
- develop and recall mental strategies for addition facts within 20
discuss different strategies for combining numbers:
9 + 8 = 10 + 8 - 1 or 8 + 8 + 1 or 9 + 9 - 1
memorise and record addition facts using strategies - construct number sentences and number stories; solve problems involving addition within 99
- add numbers without and with renaming within 99
estimate simple sums within 99
use mental calculations
record using notation boards, number lines, number
sentences and algorithm
emphasise addition of 10 to multiples of 10, to other numbers (36 + 10)
add multiples of 10 to numbers (45 + 20) - explore and discuss repeated addition and group counting
in practical situations, e.g. buying a number of identical articles
10 sweets in a packet; how many in 5 packets?
10 + 10 + 10 + 10 + 10 = 50 sweets
Subtraction
Content for first class
develop an understanding of subtraction as deducting, as complementing and as difference 0-20
deducting:
I had 10 sweets, I ate 3. How many have I left?
complementing:
There are 10 stickers in a set. I have 4. How many more do I need to make a full set?
difference:
I have 12 crayons. Mary has 6 crayons. How many more have I? How many fewer has Mary?
focus on subtraction as the inverse of addition
record subtraction: concretely, orally, pictorially, in number sentences, in jumps on the number line, and on notation boards
- develop and/or recall mental strategies for subtraction 0-20
counting back/on, using doubles/near doubles, using zero, using knowledge of 10 facts, add to check results - construct number sentences and number stories;
solve problems involving subtraction 0-20
construct and tell a number story; record pictorially, as a number sentence, or as a written story
solve written problems; pupils can also devise problems for each other - estimate differences within 99
by subtracting the tens
check estimates using manipulatives - subtract numbers without renaming within 99
estimate difference
use concrete materials, number lines and hundred squares
use mental calculations
record using number lines, number sentences and algorithms - use the symbols +, - , =
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 - solve one-step problems involving addition or subtraction.
Content for second class
- develop an understanding of subtraction as deducting, as complementing and as difference
- develop and recall mental strategies for subtraction 0-20
discuss different strategies for subtracting numbers - construct number sentences involving subtraction of whole numbers; solve problems involving subtraction
- estimate differences within 99
use rounding strategies - subtract numbers without renaming within 99
estimate difference
use concrete materials, number lines and hundred squares
use mental calculations
record using number lines, number sentences and algorithms - use the symbols +, - , =
- solve one-step problems involving addition or subtraction.
Strand Unit: Fractions
The child should be enabled to
- establish and identify half of sets to 20
share sets of objects equally between two people record pictorially.
Content for second class
- establish and identify halves and quarters of sets to 20
discuss relationship between a half and a quarter.
Linkage
Shape and space: 2-D shapes
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Algebra
Strand Unit: Extending and using patterns
Content for first class
The child should be enabled to
- recognise pattern, including odd and even numbers
count in twos on the hundred square; colour each number you stop at
construct sets that increment in twos, starting with 0 (0, 2, 4, 6...), starting with 1 (1, 3, 5, 7 ...)
discuss and record pictorially
use two colours to identify odd and even numbers
on the hundred square; discuss results
extend activities to group counting with fives and tens - explore and use patterns in addition facts
notice patterns that make up tens
(9 + 1 = 10, 2 + 8 = 10, 18 + 2 = 20) and the effect
of adding 10 to a given number:
3 + 10 = 13, 13 + 10 = 23 - understand the use of a frame to show the presence of an unknown number
3 + 5 = _, 2 + _ = 6.
Content for second class
The child should be enabled to
- recognise patterns and predict subsequent numbers
counting on the hundred square:
start on 2, count on 5, 2 + 5 = 7
start on 12, count on 5, 12 + 5 = 17
explore other number patterns, including odd and even number patterns, on the hundred square
group count in threes, fours and sixes
discuss the results - explore and use patterns in addition facts
- understand the use of a frame to show the presence of an unknown number
24 + 6 = _ , 14 + _ = 20, 2 + 4 + _ = 12.
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Shape and space
Strand Unit: Spatial Awareness
Content for first class
The child should be enabled to
- explore, discuss, develop and use the vocabulary of spatial relations
between, underneath, on top of, around, through, left, right
explore closed shapes (e.g. circle), so that one walks from one point back to the same point without having to turn around
explore open shapes (e.g. V-shape), where one has to turn around to get back to the starting point make body shapes - give and follow simple directions within classroom and school settings
from desk to window
from classroom to school hall
from classroom to school yard
explore and solve practical problems.
Integration
Physical education: Dance; Gymnastics;
Outdoor and adventure activities
Content for second class
The child should be enabled to
- explore, discuss, develop and use the vocabulary of spatial relations
- give and follow simple directions within classroom and school settings, including turning directions using half and quarter turns
turning on the spot to face in different directions
take 2 steps forward, do a half turn, take 3 steps forward
pupils give instructions to other pupils
use mazes, grids, board games, computer
explore and solve practical problems.
Integration
Physical education: Dance; Gymnastics;
Outdoor and adventure activities
Strand Unit: 2-D shapes
Content for first class
The child should be enabled to
- sort, describe, compare and name 2-D shapes: square, rectangle, triangle, circle, semicircle
describe shapes, referring to size, corners, number and length of sides
sort shapes: 4-sided/not 4-sided, curved/not curved - construct and draw 2-D shapes
use templates, stencils, geostrips, geoboards - combine and partition 2-D shapes
combine shapes to make new shapes and patterns
make pictures and mosaic patterns by combining shapes
fit many examples of identical shapes together to cover surface - identify halves of 2-D shapes
fold paper shapes in half and cut to make new shapes - identify and discuss the use of 2-D shapes in the environment
in furniture, classroom objects, own possessions.
Linkage
Fractions
Integration
Music: Performing - Literacy
Content for second class
The child should be enabled to
- sort, describe, compare and name 2-D shapes:square, rectangle, triangle, circle, semicircle, oval
note similarities and differences between shapes - construct and draw 2-D shapes
- combine and partition 2-D shapes
- identify half and quar ter of shapes
discuss the relationship between halves and quarters - identify and discuss the use of 2-D shapes in the environment
look for examples of tiling in the environment.
Linkage
Fractions
Integration
Music: Performing - Literacy
The treatment of content as suggested in the exemplars is common to both classes.
Strand Unit: 3-D Shapes
Content for first class
The child should be enabled to
- describe, compare and name 3-D shapes, including cube, cuboid, cylinder and sphere
collect, sort and describe shapes, referring to number and shapes of faces, edges, vertices (corners on 3-D shape)
identify shapes that stack, roll or slide - discuss the use of 3-D shapes in the environment
boxes, packets, containers, fish-tank - solve and complete practical tasks and problems involving 2-D and 3-D shapes
use boxes, cardboard packs or containers in construction activities - explore the relationship between 2-D and 3-D shapes.
Integration:
Visual arts: Construction
Content for second class
The child should be enabled to
- describe, compare and name 3-D shapes, including cube, cuboid, cylinder, sphere and cone
make prints with the surfaces of 3-D shapes and discuss results
dismantle boxes and examine constituent shapes - discuss the use of 3-D shapes in the environment
- solve and complete practical tasks and problems involving 2-D and 3-D shapes
- explore the relationship between 2-D and 3-D shapes.
Integration:
Visual arts: Construction
Strand Unit: Symmetry
Content for second class
The child should be enabled to
- identify line symmetry in shapes and in the environment
fold shapes in half, blob and fold paintings
complete shapes or pictures symmetrically
collect and sort objects on the basis of symmetry.
Strand Unit: Angles
Content for second class
The child should be enabled to
- explore and recognise angles in the environment
investigate things that turn: door handles, wheels
make full, half and quarter turns in yard or hall
investigate angles as corners; use a right angle made from card to 'measure' corners on 2-D shapes; discuss relate square corner to quarter turn.
Integration
Visual arts: Print
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Measures
Strand Unit: Length
Content for first class
The child should be enabled to
- estimate, compare, measure and record length using non-standard units
lollipop sticks, pencils, spans, strides - select and use appropriate non-standard measuring units and instruments
choose a measuring unit from a selection available in the classroom
(e.g. selecting either a cube, lollipop stick or a stride to measure the room)
discuss which units are best for measuring long
objects and which are best for measuring short objects - estimate, measure and record length using standard unit (the metre)
length, width, height, measure, metre, nearly a metre, a bit more than/a bit less than a metre
discuss the need for standard units
collect sets of objects longer than, shorter than or the same length as a metre - solve and complete practical tasks and problems involving length
suggest ways of measuring around a tree-trunk or other irregular object
suggest ways of comparing objects at home - who has the widest gate?
measure with string and bring the string to school for comparison and discussion.
Content for second class
The child should be enabled to
- estimate, compare, measure and record length using non-standard units
- select and use appropriate non-standard measuring units/instruments
select and use units/instruments for measuring tasks
discuss which instrument is best for short objects and which is best for long objects - estimate, measure and record length using metre and centimetre
through counting and recording, explore relationship between metre and centimetre
measure using 10 cm rods, half-metre stick, metre stick, and trundle wheel
Integration:
Physical education: Athletics
- solve and complete practical tasks and problems involving length
find the height of each child in a group
who is the shortest/tallest?
graph results.
Linkage
Data: Representing and interpreting data
Strand Unit: Area
Content for second class
The child should be enabled to
- estimate and measure area using non-standard units
how many playing-cards, postcards or workbooks cover the table?
which shape is the most suitable?
measure the area of the same surface several times with different units
which surface has more wood, the table-top or the window-sill?
children suggest ways of finding out estimate, discuss, measure and record.
Linkage
Shape and space: 2-D shapes
The treatment of content as suggested in the exemplars is common to both classes.
Strand Unit: Weight
Content for first class
The child should be enabled to
- estimate, compare, measure and record weight using non-standard units
heavy, heavier, heaviest; light, lighter, lightest; balance
sort objects into heavy or light by hand
find objects that are lighter or heavier than given object
estimate comparative weight of two objects by sight
compare weights by hand weighing
check using balance - select and use appropriate non-standard measuring units and instruments
choose a measuring unit from a selection available in the classroom,
e.g. selecting either stones, cubes or beads to weigh school bag
discuss which units are best for weighing various objects - estimate, measure and record weight using standard unit (the kilogram) and solve simple problems
discuss the need for standard units
collect sets of objects lighter than, heavier than or the same weight as a kilogram
find the largest packet and the smallest packet that weighs a kilogram
make two objects (two balls of Plasticine) weigh the same.
Content for second class
The child should be enabled to
- estimate, compare, measure and record weight using non-standard units
- select and use appropriate non-standard measuring units and instruments
- estimate, measure and record weight using kilogram,
half kilogram and quarter kilogram and solve simple problems
measuring with pan balance, kitchen scales, bathroom scales
how many kilograms do you weigh?
graph the weights of a group of children - explore and discuss instances when objects or substances that weigh 1 kg vary greatly in size
fill bags or containers with 1 kg of sand, flour, polystyrene strips, beads.
Strand Unit: Capacity
Content for first class
The child should be enabled to
- estimate, compare, measure and record capacity using non-standard units
pour, fill, full, empty, holds more, less or the same amount as
find the capacity of a larger container by using teaspoons, egg-cups, cups
find containers that hold more or less than a given container; estimate, and check by measuring - select and use appropriate non-standard measuring units and instruments
choose a measuring unit from a selection
which container is best for filling the bucket? why? - estimate, measure and record capacity using standard unit (the litre) and solve simple problems
discuss the need for standard units
collect sets of containers that hold more than, less than or about the same as a litre
collect litre containers of different shapes and sizes; label; check capacity by pouring from one to the other
how many children could have a full cup of water from a litre bottle?
Content for second class
The child should be enabled to
- estimate, compare, meas u re and record the capacity of a wide variety of containers using non-standard units
estimate comparative capacity of two containers by sight; check by measuring and discuss results
fill several containers using the same unit and arrange in order of capacity; discuss
make a collection of different-shaped containers that hold the same amount - select and use appropriate non-standard measuring units and instruments
- estimate, measure and record capacity using litre, half-litre and quarter-litre bottles and solve simple problems
make collections of bottles of differing shapes but similar capacity
compare capacity of litre, half litre and quarter litre containers
ask the children to suggest reasons why some liquids are sold in a variety of different-sized or different-shaped cartons.
The treatment of content as suggested in the exemplars is common to both classes.
Strand Unit: Time
Content for first class
The child should be enabled to
- use the vocabulary of time to sequence events
sequence events associated with different times of the day, days of the week, months of the year
discuss characteristics of seasons, of months of the year, day before, day after - read and record time using simple devices
find how many times sand will pass through an egg-timer while a story is read
use candle clock or water clock to measure amount of time that passes by the end of a class activity, by roll call, by break time, by home time - read time in hours and half-hours on 12-hour analogue clock
become familiar with clock face, movement of hands
record positions at hours and half-hours
record activities at these times
examine television schedules to find programmes that begin on hour and half-hour
state what time it will be one hour later, half an hour later - read day, date and month using calendar
read today's day, date and month
discuss birthdays and other significant dates
identify from the calendar the day of the week on which a given date occurs
Content for second class
The child should be enabled to
- use the vocabulary of time to sequence events
- read and record time using simple devices
- read time in hours, half-hours and quarter-hours on 12-hour analogue clock
- read time in hours and half-hours on digital clock
- read day, date and month using calendar and identify the season
discuss the passing of time: 24 hours in a day,
7 days in a week, numbers of days in the month.
Strand Unit: Money (use up to introduction of the euro)
Content for first class
The child should be enabled to
- recognise, exchange and use coins up to the value of 50p
practise tendering and receiving amounts of money
calculate and give change
exchange a coin or coins for others of equal value - calculate how many items may be bought with a given sum.
Content for second class
The child should be enabled to
- recognise, exchange and use coins up to the value of £2
- write the value of a group of coins; record money amounts as pence
and later as pounds
135p may be written as £1.35.
Strand Unit: Money-euro
Content for first class
The child should be enabled to
- recognise, exchange and use coins up to the value of 50 cents
practise tendering and receiving amounts of money
calculate and give change
exchange a coin or coins for others of equal value - calculate how many items may be bought with a given sum.
Content for second class
The child should be enabled to
- recognise, exchange and use coins up to the value of €2
- write the value of a group of coins; record money amounts as cents and later as euro
135 cents may be written as €1.35.
Strand: Data
Strand Unit: Representing and interpreting data
Content for first class
The child should be enabled to
- sort and classify objects by two and three criteria
sort blocks according to colour, shape, size and thickness
identify a block in the collection from a description of its attributes - represent and interpret data in two, three or four rows or columns using real objects, models and pictures
represent concretely and pictorially the sets of children
who had an apple, an orange or a banana for lunch
identify the correspondence between the number of symbols (fruit pictures) and the people in the set progress to representing data using more abstract 3-D
forms, e.g. coloured blocks to represent people construct simple pictograms.
Integration
Geography: Natural environments
Content for second class
The child should be enabled to
- sort and classify objects by two and three criteria
- represent, read and interpret simple tables and charts (pictograms)
chart of cars passing school during a particular time
weather chart records - represent, read and interpret simple block graphs
construct by fixing coloured squares to large sheet of paper
progress to drawing on squared paper.
Integration
Geography: Natural environments
The treatment of content as suggested in the exemplars is common to both classes.