Skills development for third and fourth classes
Through completing the strand units of the mathematics curriculum the child should be enabled to
Applying and problem-solving
- select appropriate materials, concepts and processes for mathematical tasks and applications
- apply concepts and processes in a variety of contexts
- analyse problems and plan an approach to solving them
- select and apply a variety of strategies to complete tasks and projects or to solve problems
- evaluate solutions to problems
Communicating and expressing
- discuss and explain the processes used and the results of mathematical activities, problems, and projects
- listen to and discuss other children's mathematical descriptions and explanations
- discuss and record the processes and results of work using a variety of methods
- discuss problems presented verbally or diagrammatically and carry out analyses
Integrating and connecting
- connect informally acquired mathematical ideas and processes with formal mathematical ideas and processes
- understand the connections between mathematical procedures and the concepts he/she uses
- recognise mathematics in the environment
- represent mathematical ideas and processes in different modes: verbal, pictorial, diagrammatic, and symbolic
- recognise and apply mathematical ideas and processes in other areas of the curriculum
Reasoning
- make hypotheses and carry out experiments to test them
- make informal deductions involving a small number of steps
- explore and investigate mathematical patterns and relationships
- reason systematically in a mathematical context
- justify processes and results of mathematical activities, problems and projects
Implementing
- devise and use mental strategies and procedures for carrying out mathematical tasks
- use appropriate manipulatives to carry out mathematical procedures
- execute standard procedures efficiently with a variety of tools
Understanding and recalling
- understand and recall terminology, facts and definitions.
Strand: Number
Strand unit: Place value
Content for third class
The child should be enabled to
- explore and identify place value in whole numbers, 0-999
grouping and swapping activities involving units, tens, hundreds using concrete materials, e.g. lollipop sticks, abacus, notation boards, base ten materials, money
significance of zero: 208, 420 - read, write and order three-digit numbers
identify and record numbers represented by money and abacus
identify and express numbers in expanded form
246 = 2 hundreds + 4 tens + 6 units
order numbers on the number line or hundred square
247: what is the value of 4 in this number?
which digit has the greatest value?
what is the next number after 499? - round whole numbers to the nearest ten or hundred
which number is nearer to 40: 29 or 79?
which number is nearer to 500: 432 or 567? - explore and identify place value in decimal numbers to one place of decimals.
Content for fourth class
The child should be enabled to
- explore and identify place value in whole numbers, 0-9999
grouping and swapping activities involving units, tens, hundreds and thousands using concrete materials and notation boards
significance of zero: 1078, 2005, 3620 - read, write and order four-digit numbers and solve simple problems
write 5683 in expanded form
5000 + 600 + 80 + 3
what is the value of the underlined 7 in 777_7?
make as many numbers as you can from 3, 7, 0, 6
place in order, starting with the largest - round whole numbers to the nearest thousand
which number is nearer to 5000: 4328 or 5675? - explore and identify place value in decimal numbers to two places of decimals.
Strand unit: Operations
Addition and subtraction
Content for third class
The child should be enabled to
- add and subtract, without and with renaming, within 999
estimate sums and differences (rounding where necessary)
check estimates
record using horizontal and vertical presentation - know and recall addition and subtraction facts
- solve word problems involving addition and subtraction
Content for fourth class
The child should be enabled to
- add and subtract, without and with renaming, within 9999
estimate sums and differences
check estimates without and with a calculator - know and recall addition and subtraction facts
- solve word problems involving addition and subtraction
use a calculator to develop problem-solving strategies and verify estimations
Multiplication
Content for third class
The child should be enabled to
- develop an understanding of multiplication as repeated addition and vice versa
count sets of objects in twos, threes, fours etc. to tens
count in steps on the number line or hundred square
construct number sentences with concrete materials and record diagrammatically
** ** ** = ******
2 + 2 + 2 = 6
3 x 2 = 6
record number sentences as 6 + 6 + 6 - 3 x 6 - 18 - explore, understand and apply the zero, commutative and distributive properties of multiplication
use concrete materials, charts and illustrations to establish and record:
zero property, e.g. 5 x 0 = 0 and 0 x 7 = 0
commutative property, e.g. 3 x 4 = 4 x 3
distributive property, e.g. 5 x 4 = (3 x 4) + (2 x 4) - develop and/or recall multiplication facts within 100
counting in 2, 3, 5 and 10
doubles, trebles
2 x 9 = 18, 4 x 9 = 36, 8 x 9 = 72
3 x 4 = 12, 9 x 4 = 36 - multiply a one-digit or two-digit number by 0-10
use rounding to estimate products
rounding up/down, e.g. 6 x 28 is near to 6 x 30
represent in horizontal and vertical form
23 x 7 and 23
x 7
establish effect of multiplication by 1 and by 10
1 3 17 = 17, 10 3 53 = 530 - solve and complete practical tasks and problems involving multiplication of whole numbers
how many days in 9 full weeks?
Content for fourth class
The child should be enabled to
- develop an understanding of multiplication as repeated addition and vice versa.
- explore, understand and apply the zero, commutative, distributive and associative properties of multiplication
use concrete materials and charts to establish associative property,
e.g. (3 x 4) x 5 = 3 x (4 x 5) - develop and recall multiplication facts within 100
- multiply a two-digit or three-digit number by a one or two-digit number
estimate products
represent multiplication in expanded form
26 x 37 = (20 x 37) + (6 x 37)
record and calculate using long multiplication algorithm
37
26X
222 (37 x 6)
740 (37 x 20)
962 (total) - use a calculator to check estimates
- solve and complete practical tasks and problems involving multiplication of whole numbers
34 children buy one packet of sweets per child each day
how many packets altogether do they buy in a month?
Division
Content for third class
- develop an understanding of division as sharing and as repeated subtraction, without and with remainders
share a quantity in equal groups of 2, 3, ...
record using number sentences or vertically
20 - 4 - 4 - 4 - 4 - 4 = 0 - develop and/or recall division facts within 100
use inverse of multiplication facts
use halves
9 is half of 18 (2 x 9 = 18) - divide a one-digit or two-digit number by a one-digit number without and with remainders
represent division as repeated subtraction
represent division as number sentences
record using the division algorithm
use different strategies to estimate quotients and
check answers
rounding up or down, e.g. 44 divided by 12 is about 40 divided by 10 - solve and complete practical tasks and problems involving division of whole numbers
problems based on the environment
how many cars are needed to take 27 children
to a game if only 4 children are allowed in each car?
estimate, discuss and record.
Content for fourth class
- develop an understanding of division as sharing and as repeated subtraction, without and with remainders
- develop and/or recall division facts within 100
- divide a three-digit number by a one-digit number without and with remainders
using regrouping
using algorithm
explore, understand and apply the distributive property of division - use calculator to check estimates
using compatible numbers (i.e. numbers easily worked
with an extension of basic facts)
338 divided by 7 is compatible with 350 divided by 7 - solve and complete practical tasks and problems involving division of whole numbers
how many small boxes of eggs (6 per box) can be
filled from a crate containing 350 eggs?
estimate, discuss and record.
Strand unit: Fractions
Content for third class
The child should be enabled to
- identify fractions and equivalent forms of fractions with denominators 2, 4, 8 and 10
construct and cut out simple fractions of regular shapes
record using diagrams or fraction charts - compare and order fractions with appropriate denominators and position on the number line
- calculate a fraction of a set using concrete materials
- develop an understanding of the relationship between fractions and division
- calculate a unit fraction of a number and calculate a number,
given a unit fraction of the number - solve and complete practical tasks and problems involving fractions
what fraction of a chart is coloured yellow/is not green?
Content for fourth class
The child should be enabled to
- identify fractions and equivalent forms of fractions with denominators 2, 3, 4, 5, 6, 8, 9, 10 and 12
construct and cut out simple fractions of regular shapes
record using diagrams or fraction charts - compare and order fractions with appropriate denominators and position on the number line
- calculate a fraction of a set using concrete materials
- calculate a number, given a multiple fraction of the number
- express one number as a fraction of another number
- solve and complete practical tasks and problems involving fractions
Strand unit: Decimals
Content for third class
The child should be enabled to
- identify tenths and express in decimal form express one tenth as 0.1
cut out tenths and/or 0.1 of regular shapes
record using diagrams or charts
Linkage
Fractions
- order decimals on the number line
draw a circle around the number with the greatest
value: 0.5, 0.1, 0.7, 0.2 - solve problems involving decimals.
Content for fourth class
The child should be enabled to
- express tenths and hundredths as fractions and decimals
- identify place value of whole numbers and decimals to two places and write in expanded form
3.45 = 3 + 0.4 + 0.05 - order decimals on the number line
identify the number with the greatest value:
0.57, 0.01, 0.72, 0.25
add and subtract whole numbers and decimals up to two places - multiply and divide a decimal number up to two places by a single-digit whole number
- solve problems involving decimals.
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Algebra
Strand unit: Number patterns and sequences
Content for third class
The child should be enabled to
- explore, recognise and record patterns in number, 0-999
group and count in twos, threes, fours ... tens on number line and hundred square
recognise number bonds through grouping
17 + 3, 27 + 3, 37 + 3
recognise links within and between multiplication tables (e.g. links between 4 and 8 times tables)
patterns of odd and even numbers - explore, extend and describe (explain rule for) sequences
patterns or sequences of objects or shapes
whole-number sequences
(e.g. 54, 44, 34, or 1, 3, 9, 27) - use patterns as an aid in the memorisation of number facts
make patterns on the hundred square.
Content for fourth class
The child should be enabled to
- explore, recognise and record patterns in number, 0-9999
- explore, extend and describe sequences
- use patterns as an aid in the memorisation of number facts
make patterns on the hundred square.
Strand unit: Number sentences
Content for third class
The child should be enabled to
- translate an addition or subtraction number sentence with a frame into a word problem (frame not in initial position)
3 + 7 = __
Mary has three sweets, she gets seven more, how many has she now? - solve one-step number sentences
400 - _ = 350
810 + 23 = __ .
Content for fourth class
The child should be enabled to
- translate an addition, subtraction, multiplication or division number sentence with a frame into a word problem (frame not in initial position)
- translate a one-step word problem into a number sentence
Rita has 18 toy cars
She wants to arrange them in 3 rows
18 = 3 x _ - solve one-step number sentences
discuss and record solutions for open number sentences
3 + _ < 7 or 5 + _ > 8.
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Shape and space
Strand unit: 2-D shapes
Content for third class
The child should be enabled to
- identify, describe and classify 2-D shapes: square, rectangle, triangle, hexagon, circle, semicircle, oval and irregular shapes
- explore, describe and compare the properties (sides, angles, parallel and non-parallel lines) of 2-D shapes
- construct and draw 2-D shapes
use templates, stencils, geostrips, geoboards - combine, tessellate and make patterns with 2-D shapes
cover surfaces with 2-D shapes that tessellate or do not tessellate
identify properties that facilitate or hinder tessellation
combine shapes to make patterns - identify the use of 2-D shapes in the environment
buildings, road signs, printing, household objects - solve and complete practical tasks and problems involving 2-D shapes.
Linkage
Area
Integration
Visual arts:Drawing - An awareness of line, shape
Content for fourth class
The child should be enabled to
- identify, describe and classify 2-D shapes: equilateral, isosceles and scalene triangle, parallelogram,rhombus, pentagon, octagon
- explore, describe and compare the properties (sides, angles, parallel and non-parallel lines) of 2-D shapes
- construct and draw 2-D shapes
use ruler and set square - combine, tessellate and make patterns with 2-D shapes
combine shapes to make patterns and to make other shapes
create a tessellating pattern on squared paper - identify the use of 2-D shapes in the environment
hoardings, shop fronts, paving-stones - solve and complete practical tasks and problems involving 2-D shapes.
Linkage
Area
Integration
Visual arts:Drawing - An awareness of line, shape
Strand unit: 3-D shapes
Content for third class
The child should be enabled to
- identify, describe and classify 3-D shapes, including, cube, cuboid, cylinder, cone, sphere, triangular prism, pyramid
- explore, describe and compare the properties of 3-D shapes
number and shape of faces, number of edges and
corners, ability to roll, slide or stack - explore and describe the relationship of 3-D shapes with constituent 2-D shapes
identify constituent 2-D shapes by observation and
deconstruction and compile a table of results - construct 3-D shapes
trace around nets and cut out; use straws or pipe cleaners - solve and complete practical tasks and problems involving 2-D and 3-D shapes.
Content for fourth class
The child should be enabled to
- identify, describe and classify 3-D shapes, including cube, cuboid, cylinder, cone, sphere, triangular prism, pyramid
- establish and appreciate that when prisms are sliced through (in the same direction) each face is equal in shape and size
keep work exploratory and simple
e.g. use Plasticine, triangular prisms or suitable foods - explore and describe the relationship of 3-D shapes with constituent 2-D shapes
- construct 3-D shapes
construct from 2-D shapes - solve and complete practical tasks and problems involving 2-D and 3-D shapes
identify the use of 3-D shapes in the environment.
Integration
Visual arts: Construction; Paint and colour
Geography: Human environments
The treatment of content as suggested in the exemplars is common to both classes.
Strand unit: Symmetry
Content for third class
The child should be enabled to
- identify line symmetry in the environment
- identify and draw lines of symmetry in two dimensional shapes
fold paper shapes or use a mirror to identify lines of symmetry
use fold lines to draw and record lines of symmetry
classify 2-D shapes according to their number of lines of symmetry.
Linkage
Fractions
Content for fourth class
The child should be enabled to
- identify line symmetry in the environment
- identify lines of symmetry as horizontal, vertical or diagonal
using examples from the environment, e.g. an open book, windows, gates - use understanding of line symmetry to complete missing half of a shape, picture or pattern
in drawings, on geoboard or pegboard where the fold is vertical, horizontal or diagonal.
Linkage
Fractions
Strand unit: Lines and angles
Content for third class
The child should be enabled to
- identify, describe and classify vertical, horizontal and parallel lines
discuss and describe lines in the environment
draw and label lines
use geostrips to construct vertical and horizontal lines - recognise an angle in terms of a rotation
form angles by opening books and doors, by rotating
clock hands and geostrip arms, by physically turning
(clockwise/anti-clockwise), or on computer - classify angles as greater than, less than or equal to a right angle
construct and use a right-angle measure to identify
right angles in the environment and in
2-D and 3-D shapes
classify and record angles as >, < or = to a right angle - solve problems involving lines and angles.
Content for fourth class
The child should be enabled to
- identify, describe and classify oblique and perpendicular lines
use straws to construct oblique and perpendicular lines
and diagonals in a square - draw, discuss and describe intersecting lines and their angles
perpendicular and oblique lines,
acute, obtuse and right angles - classify angles as greater than, less than or equal to a right angle
- solve problems involving lines and angles.
Integration
Physical education: Dance; Gymnastics
Visual arts: Drawing; Construction
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Measures
Strand unit: Length
Content for third class
The child should be enabled to
- estimate, compare, measure and record lengths of a wide variety of objects using appropriate metric units (m, cm)
everyday objects, furniture, heights of children
estimate length and height without and with unit of measurement present measure to check estimates - rename units of length in m and cm - 125 cm = 1 m 25 cm
- solve and complete practical tasks and problems involving the addition and subtraction of units of length (m, cm)
confine to totals that can be readily checked by measuring.
Integration
Physical education: Athletics
Content for fourth class
The child should be enabled to
- estimate, compare, measure and record lengths of a wide variety of objects, using appropriate metric units, and selecting suitable instruments of measurement
lengths and heights of doors, corridors, school yard,paths, drives, playing-fields
instruments: rulers, tape measures, trundle wheel - rename units of length using decimal or fraction form
25 cm = 0.25 m = quarter m
2 km 150 m = 2150 m = 2.15 km - understand, estimate and measure the perimeter of regular 2-D shapes
- solve and complete practical tasks and problems involving the addition, subtraction, multiplication and simple division of units of length (m, cm, km).
Integration
Physical education: Athletics
Strand unit: Area
Content for third class
The child should be enabled to
- estimate, compare and measure the area of regular and irregular shapes
counting non-standard square units.
Content for fourth class
The child should be enabled to
- estimate, compare and measure the area of regular and irregular shapes
use standard square units: sq. cm, sq. m (cm2, m2).
Linkage
Shape and space: 2-D shapes
Strand unit: Weight
Content for third class
The child should be enabled to
- estimate, compare, measure and record the weight of a wide variety of objects using appropriate metric units (kg, g)
everyday objects, books, piles of copybooks lighter
and heavier than 1 kg
objects showing that there is no constant relationship between weight and size
handle and compare objects as an aid to estimation - solve and complete practical tasks and problems involving the addition and subtraction of units of weight (kg and g)
confine to totals which can be readily checked by weighing.
Content for fourth class
The child should be enabled to
- estimate, compare, measure and record the weight of a wide variety of objects using appropriate metric units (kg, g) and selecting suitable instruments of
measurement
use and select from bathroom scales, kitchen scales, spring balance become familiar with major and minor markings on scales (e.g. 100 g markings, half kg, quarter kg) - rename units of weight in kg and g
2 kg 250 g = 2250 g - rename units of weight using decimal or fraction form
250 g = 0.25 kg = quarter kg
confine to examples requiring only two places of decimals - solve and complete practical tasks and problems involving the addition, subtraction, multiplication and simple division of units of weight (kg and g).
The treatment of content as suggested in the exemplars is common to both classes.
Strand unit: Capacity
Content for third class
The child should be enabled to
- estimate, compare, measure and record the capacity of a wide variety of objects using appropriate metric units (l, ml)
use cartons, spoons, cups, jugs, plastic bottles and other common containers
use litre, 250 ml and 500 ml measuring containers
use tall, low, wide and narrow containers - solve and complete practical tasks and problems involving the addition and subtraction of units ofcapacity (l, ml)
confine to totals that can be readily checked by measuring.
Content for fourth class
The child should be enabled to
- estimate, compare, measure and record capacity using appropriate metric units (l, ml) and selecting suitable instruments of measurement
become familiar with major and minor markings on measuring containers
(e.g. 100 ml markings, half l, quarter l ) - rename units of capacity in l and ml 1500 ml = 1 l 500 ml
- rename units of capacity using decimal and fraction form
250 ml = 0.25 l = quarter litrel
2 l 150 ml = 2150 ml = 2.15 l
confine to examples requiring only two places of decimals - solve and complete practical tasks and problems involving the addition, subtraction, multiplication and simple division of units of capacity (l, ml).
Strand unit: Time
Content for third class
The child should be enabled to
- consolidate and develop further a sense of time passing
place daily, weekly, monthly and annual events in sequence
discuss movement of hands of clock or sand in hourglass as indicating passing of time
refine and develop vocabulary of time
before/after, a long time ago, last year, last month, yesterday, immediately, soon, tomorrow, in a week's time, for a short/long time
Integration
Geography: The physical world
- read time in five-minute intervals on analogue and digital clock (12-hour)
count in fives up and down number line, hundred square and clock face
construct simple clock face and relate intervals
quarter hour = 15 min = 3 x 5 min
discuss and record times of a variety of common events, school and home activities, television programmes - record time in analogue and digital forms
- read and interpret simple timetables
school, bus, train, television schedules. - rename minutes as hours and hours as minutes
confine work to five-minute intervals
70 min = 1 hour 10 min - read dates from calendars and express weeks as days and vice versa
collect and record significant personal dates and dates in life of school and family - solve and complete practical tasks and problems involving times and dates
practical problems that can be readily checked by measurement.
Content for fourth class
The child should be enabled to
- consolidate and develop further a sense of time passing
Integration
Geography: The physical world
- read time in one-minute intervals on analogue and digital clock (12-hour)
- express digital time as analogue time and vice versa
- read and interpret simple timetables.
The treatment of content as suggested in the exemplars is common to both classes.
- rename minutes as hours and hours as minutes
- read dates from calendars and express weeks as days and vice versa
- solve and complete practical tasks and problems involving times and dates and the addition and subtraction of hours and minutes
practical problems that can be readily checked by measurement
add hours and minutes separately
4 hours 45 minutes + 3 hours 25 minutes = 7 hours 70 min
Integration
Physical education: Athletics
Strand unit: Money - Euro
Content for third class
The child should be enabled to
- rename amounts of euro or cents and record using symbols and decimal point
- solve and complete one-step problems and tasks involving the addition and subtraction of money.
Content for fourth class
The child should be enabled to
- rename amounts of money as euro or cents and record using e symbol and decimal point
125 cents = €1.25 and €3.56 = 356 cents - solve and complete practical one-step and two-step problems and tasks involving the addition, subtraction, multiplication and simple division of money.
Integration
History: Early peoples and ancient societies
The treatment of content as suggested in the exemplars is common to both classes.
Strand: Data
Strand unit: Representing and interpreting data
Content for third class
The child should be enabled to
- collect, organise and represent data using pictograms, block graphs and bar charts
collect data from the environment and record in tabular form
represent data in appropriate format
discuss strengths and limitations of the format used
use simple scale in block graphs and bar charts
use computer applications if available to organise and represent data - read and interpret tables, pictograms, block graphs and bar charts
- use data sets to solve and complete practical tasks and problems
solve simple problems using data collected from own environment.
Linkage
Shape and space: Lines and angles
Integration
Geography: Natural environments
Science: Energy and forces
Content for fourth class
The child should be enabled to
- collect, organise and represent data using pictograms, block graphs, bar charts and bar-line graphs incorporating the scales 1:2, 1:5, 1:10, and 1:100
use scales appropriate to the range of numbers for this level - read and interpret bar-line graphs and simple pie charts
involving use of halves, thrids and quarters - use data sets to solve and complete practical tasks and problems.
Linkage
Shape and space: Lines and angles
Integration
Geography: Natural environments
Science: Energy and forces
Strand unit: Chance
Content for third class
The child should be enabled to
- use vocabulary of uncertainty and chance: possible, impossible, might, certain, not sure
- order events in terms of likelihood of occurrence
examine and discuss the likelihood of occurrence of simple events and order from least likely to most likely
Our school will be closed next Monday
The sun will shine for two hours tomorrow
The teacher will fall asleep at 11 o'clock today - identify and record outcomes of simple random processes
toss a coin ten or twenty times and record results
draw a cube from a bag containing, for example, 4 blue cubes and 8 red cubes a number of times, replacing the drawn cube each time; discuss results.
Content for fourth class
The child should be enabled to
- use vocabulary of uncertainty and chance: chance, likely, unlikely, never, definitely
- order events in terms of likelihood of occurrence
- identify and record outcomes of simple random processes
toss a coin, roll a die ten or twenty times and record results
draw a cube from a bag of two red, one blue and one yellow cube a number of times, replacing drawn cube each time; discuss results and record outcomes.
Integration
Music:Composing-Improvising and creating
The treatment of content as suggested in the exemplars is common to both classes.