Primary Schools

Content of Mathematics Curriculum: fifth and sixth classes

Skills development for fifth and sixth 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 particular 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 solve problems
  • reflect upon and evaluate solutions to problems
Communicating and expressing
  • discuss and explain the processes used and the results of mathematical activities, problems and projects in an organised way
  • 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 and carry out analyses
Integrating and connecting
  • connect informally acquired mathematical ideas and processes with formal mathematical ideas and processes
  • recognise mathematics in the environment
  • represent mathematical ideas and processes in different modes: verbal, pictorial, diagrammatic and symbolic
  • understand the connections between mathematical procedures and the concepts he/she uses
  • 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
  • search for 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 facts, definitions and formulae.

Strand: Number

Strand unit: Place value


Content for fifth class

The child should be enabled to

  • read, write and order whole numbers and decimals
    extend previous conceptual and practical work to include larger numbers and decimals
  • identify place value in whole numbers and decimals
    extend previous conceptual and practical work to include larger numbers and decimals
  • round whole numbers and round decimals
    round whole numbers to nearest ten, hundred, thousand
    round decimals to nearest whole number.

Content for sixth class

The child should be enabled to

  • read, write and order whole numbers and decimals
  • identify place value in whole numbers and decimals
  • round decimals
    round decimals to one, two or three decimal places.


Strand unit: Operations


Content for fifth class

The child should be enabled to

  • estimate sums, differences, products and quotients of whole numbers
    use strategies for estimation, e.g. front-end estimation, rounding, clustering, special numbers
    estimate calculations and compute answers with a
    calculator
    e.g. 450 x 9 = 4500 (estimation based on 450 x 10)
    estimate first, then use calculator to get actual result
  • add and subtract whole numbers and decimals (to three decimal places) without and with a calculator
    develop and extend the use of existing algorithms
  • multiply a decimal (up to three places) by a whole number, without and with a calculator
    develop and extend the use of existing algorithms 8.125 x 9
  • divide a three-digit number by a two-digit number, without and with a calculator
    explore the concept of division with concrete materials
    develop the long division algorithm from repeated
    subtraction and multiples of repeated subtraction
  • divide a decimal number by a whole number, without and with a calculator
    explore the concept of division of decimals with concrete materials, money and measurement
    extend the algorithm in conjunction with place value 75.6 divided by 4.

Content for sixth class

The child should be enabled to

  • estimate sums, differences, products and quotients of decimals
    use strategies for estimation
    estimate calculations and compute answers with a calculator
  • add and subtract whole numbers and decimals (to three decimal places) without and with a calculator
  • multiply a decimal by a decimal, without and with a calculator
    develop and extend the use of existing algorithms
    7.25 x 1.5; 13.2 x 0.75
    understand that multiplication does not always make larger
  • divide a four-digit number by a two-digit number, without and with a calculator
    develop and extend the use of existing algorithms 7852 divided by 26
  • divide a decimal number by a decimal, without and with a calculator
    explore the concept of division by decimals with
    concrete materials, money and measurement
    36.92 divided by 2.6; 27.6 divided by 0.2
    understand that division does not always make smaller.

Strand unit: Fractions


Content for fifth class

The child should be enabled to

  • compare and order fractions and identify equivalent forms of fractions with denominators 2 - 12
    explore, compare and record simple equivalence using concrete materials, paper folding, and fraction charts
  • express improper fractions as mixed numbers and vice versa and position them on the number line
    establish equivalence by using concrete materials explore, compare and record simple improper fractions and mixed numbers diagrammatically, numerically and on the number line
  • add and subtract simple fractions and simple mixed numbers
    use equivalent fractions to simplify calculations
  • multiply a fraction by a whole number
    develop concepts with concrete materials, paper folding and fraction charts
    four x three quarters of a pizza is how many pizzas?
  • express tenths, hundredths and thousandths in both fractional and decimal form
    explore and compare using concrete materials
    express as fractions and as decimals.

Content for sixth class

The child should be enabled to

  • compare and order fractions and identify equivalent forms of fractions
    order equivalent fractions on the number line and on fraction charts
  • express improper fractions as mixed numbers and vice versa and position them on the number line
  • add and subtract simple fractions and simple mixed numbers
    commondenominator should be found by listing multiples
  • multiply a fraction by a fraction
    explore and develop concept by using concrete materials and the number line and by drawing diagrams to illustrate examples, leading to the development of analgorithm
  • express tenths, hundredths and thousandths in both fractional and decimal form
  • divide a whole number by a unit fraction
    how many quarters in 2?
    2 divided by one quarter 4 ; 15 divided by one fifth 5
  • understand and use simple ratios
    explore and record the relationship between the natural numbers and their multiples.

Strand unit: Decimals and percentages


Content for fifth class

The child should be enabled to

  • develop an understanding of simple percentages and relate them to fractions and decimals
    express percentages as fractions and as decimals, and vice versa calculate simple percentages, e.g. 50%, 25% 10%
  • compare and order fractions and decimals
    explore, compare and record using concrete materials and money order diagrammatically or on the number line
  • solve problems involving operations with whole numbers, fractions, decimals and simple percentages
    use diagrams; estimate and compute answers with acalculator, include simple discount and increase examples 10% off all jeans, 20%extra free.

Content for sixth class

The child should be enabled to

  • use percentages and relate them to fractions and decimals
    express quantities as percentages
  • compare and order percentages of numbers
  • solve problems relating to profit and loss, discount, VAT, interest, increases, decreases.

Linkage
Measures: Money
Integration
Geography: Human environments

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


Strand unit: Number theory


Content for fifth class

The child should be enabled to

  • identify simple prime and composite numbers
    define a prime number, i.e. a number greater than 1 with exactly two divisors, itself and 1
    identify simple prime numbers by trial and error, e.g. 2, 5, 7, 11
    identify and record primes with Sieve of Eratosthenes
    define a composite number, i.e. a number that has more than two divisors, e.g. 4, 6, 9
    identify and record composite numbers using number facts and/or a calculator
    investigate relationship with odd and even numbers
  • identify square and rectangular numbers
    construct diagrams on geoboards, pegboards and squared paper to illustrate simple square and rectangular numbers explore, compare and record these numbers
  • identify factors and multiples
    identify factors and multiples from basic multiplication facts.

Content for sixth class

The child should be enabled to

  • identify simple prime and composite numbers
  • identify and explore square numbers
    16 = 4 x 4 = 4 to the power of 2
  • explore and identify simple square roots
    construct diagrams
    record and relate to square numbers
  • identify common factors and multiples
    explore and record factors and multiples to identify common factors and multiples
  • write whole numbers in exponential form
    1000 = 10 x 10 x 10 = 10 to the power of 3
    8 = 2 x 2 x 2 = 2 to the power of 3 .

Strand: Algebra

Strand unit: Directed Numbers


Content for fifth class

The child should be enabled to

  • identify positive and negative numbers in context
    examine and discuss money affairs, video counters and calculator displays, sports reports, golf scores, temperature, sea level and lifts, leading to the need to
    distinguish between amounts above and below zero
    refer to positive and negative numbers as 'positive seven' and 'negative three' record positive and negative numbers with + or -
    signs raised e.g. + 7, - 3
    rewind a video tape
    pupils draw and label a thermometer, mark in temperatures, consult weather forecasts in newspapers.

Integration
Geography: Natural environments: weather, climate and atmosphereContent for sixth class

Content for sixth class

The child should be enabled to

  • identify positive and negative numbers on the number line
    walk the number line to experience positive and negative numbers that arise in discussion and/or in context, identify and mark positive and negative numbers on
    personal and class number lines
  • add simple positive and negative numbers on the number line
    add simple positive and negative numbers by walking the number line and by counting on the class and personal number line
    +5 + -7 = ? 9 + -3 = ?
    -8 + +2 =
    add positive and negative numbers that arise contextually, e.g. a golfer's score over four rounds was 6 under par, 2 over par, 3 under par, and 1 under par; what was her final score relative to par?

Integration
Geography: Natural environments: weather, climate and atmosphere

Strand unit: Rules and properties


Content for fifth class

The child should be enabled to

  • explore and discuss simple properties and rules about brackets and priority of operation
    identify, discuss and compute expressions with brackets in a variety of positions
    10 + (4 + 7) = _
    (10 + 4) + 7 = _
    (8 - 1) + 4 = _
    8 - (1 + 4) = _
    (3 x 4) + 5 = _
    3 x (4 + 5) = _
    8 divided by (2 + 2) = _
    (8 divided by 2) + 2 = _
    what is the significance of the positions of the brackets?
    identify, discuss and compute expressions with brackets excluded
    4 + 3 x 5 = _
    12 x 6 + 3 = _
    2.45 divided by 5 - 0.75 = _
    96 divided by 8 - 12 = _
    what is the significance of starting operations at different points?
    e.g. 4 + 3 before 3 3 5 or vice versa in 4 + 3 3 5
    establish the value of brackets, leading to the priority of multiplication and division over addition and subtraction
    explore these properties and rules without and with a calculator
  • identify relationships and record verbal and simple symbolic rules for number patterns
    identify and discuss rules for simple number sequences 2.0, 3.5, 5.0, 6.5 ... i.e. sequence increases by adding 1.5
    81, 27, 9 ... decreases by dividing by 3
    1, 4, 9, 16, 25, 36 ...

Content for sixth class

The child should be enabled to

  • know simple properties and rules about brackets and priority of operation
    use the calculator in exercises to find missing numerals and missing operator
    e.g. 37 ? 21 ? 23 = 800
    27 ? (36 ? 11) = 675
  • identify relationships and record symbolic rules for number patterns
    deduce and record rules for given number patterns
    2, 6, 12, 20, 30 ...
    4:1, 8:2, 16:4 ...

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

Strand unit: Variables


Content for sixth class

The child should be enabled to

  • explore the concept of a variable in the context of simple patterns, tables and simple formulae and substitute values for variables
    identify and discuss simple formulae from other strands
    e.g. d = 2 x r; a = l x w
    substitute values into formulae and into symbolic rules developed from number patterns.

Strand unit: Equations


Content for fifth class

The child should be enabled to

  • translate number sentences with a frame into word problems and vice versa
    create number stories to describe a given number sentence
    how many teams of four can the teacher make for relays from a class of twenty-eight children?
    28 / 4 = _
    a man has twenty-eight windows to clean; it takes him an hour to clean four; how long will it take him altogether?
    construct number sentences to describe mathematically a given word problem
  • solve one-step number sentences and equations
    75 - 43 = _ 3.5 x _ - 14
    25% of _ = 15.

Content for sixth class

The child should be enabled to

  • translate word problems with a variable into number sentences
    Peter cut a length of ribbon into five equal parts; each part was 30 cm long. How long was the ribbon before it was cut?
    x / 5 - 30
  • solve one-step number sentences and equations
    -3 + +6 - _
    -4 + _ -+1
    10 x _ - 8 x 5.

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 fifth class

The child should be enabled to

  • make informal deductions about 2-D shapes and their properties
  • use angle and line properties to classify and describe triangles and quadrilaterals
    name, explore and compare a wide variety of three and four-sided figures in terms of size and number of angles, type and number of sides e.g. trapezium, scalene
    triangle, regular hexagon
  • identify the properties of the circle
    explore and compare circles of various unit diameters
    measure and identify the relationship of diameter to radius
    examine area by counting square units
  • construct a circle of given radius or diameter
    draw using a compass
  • tessellate combinations of 2-D shapes
  • classify 2-D shapes according to their lines of symmetry
    explore, compare and record lines of symmetry in 2-D shapes
  • use 2-D shapes and properties to solve problems
    make a specified shape with Tangram shapes.

Content for sixth class

The child should be enabled to

  • make informal deductions about 2-D shapes and their properties
  • use angle and line properties to classify and describe triangles and quadrilaterals
  • construct triangles from given sides or angles
    complete the construction of triangles, given two sides and the angle between them or given two angles and the line between them
  • identify the properties of the circle
    relate the diameter of a circle to its circumference by measurement
    measure the circumference of a circle or object such as a rolling-pin or wheel e.g. use a piece of string
  • construct a circle of given radius or diameter
  • tessellate combinations of 2-D shapes
  • construct a circle of given radius or diameter
  • classify 2-D shapes according to their lines of symmetry
  • plot simple co-ordinates and apply where appropriate
    use geoboards and squared paper
  • use 2-D shapes and properties to solve problems.

Strand unit: 3-D shapes


Content for fifth class

The child should be enabled to

  • identify and examine 3-D shapes and explore relationships, including tetrahedron (faces, edges and vertices)
    explore, compare and record the number of faces of 3-D shapes
    identify number of edges and vertices of 3-D shapes
    name the shape of the faces deconstruct 3-D shapes into nets; examine and discuss
  • draw the nets of simple 3-D shapes and construct the shapes
    discuss and draw simple net including flaps where necessary
    construct 3-D shapes from nets.

Integration
Visual arts: Construction

Content for sixth class

The child should be enabled to

  • identify and examine 3-D shapes and explore relationships, including octahedron (faces, edges and vertices)
  • draw the nets of simple 3-D shapes and construct the shapes.

Integration
Visual arts: Construction

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

Strand unit: Lines and angles


Content for fifth class

The child should be enabled to

  • recognise, classify and describe angles and relate angles to shape and the environment
    explore and compare a wide variety of angles and shapes measure and record angles as acute, obtuse, reflex or right angles, and determine the number of such angles in relation to common regular shapes
  • recognise angles in terms of a rotation
    examine, measure and record the angles (including the reflex angle) formed by the hands of a clock at a variety of different times
    extend by using manipulatives, e.g. straws, lollipop sticks, Meccano, string, 360¡ protractor, LOGO computer language if available
  • estimate, measure and construct angles in degrees
    measure and record a wide variety of angles using a protractor
    construct angles of various sizes using a protractor
    estimate angle sizes and check by measuring with a protractor
  • explore the sum of the angles in a triangle
    cut off the three corners of a paper triangle and put them together to make 180 degrees
    measure the angles in a variety of triangles using a protractor
    calculate and record their sum
    examine and discuss results.

Content for sixth class

The child should be enabled to

  • recognise, classify and describe angles and relate angles to shape
    identify types of angles in the environment
  • recognise angles in terms of a rotation
  • estimate, measure and construct angles in degrees
  • explore the sum of the angles in a quadrilateral
    cut off the four corners of a paper quadrilateral and put them together to make 360 degrees
    measure the angles in a variety of quadrilaterals and calculate their sums.

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

Strand: Measures

Strand unit: Length


Content for fifth class

The child should be enabled to

  • select and use appropriate instruments of measurement
    ruler for shorter objects
    metre stick for longer objects or distances
    trundle wheel for distances
  • estimate and measure length using appropriate metric units
    estimate and measure a large variety of objects and places, both outdoors and indoors: books, desks, corridors, driveways, playing-pitch sidelines
    how far can you throw a ball? jump?
    run in 20 seconds?
    use appropriate measuring units
    mm (shorter objects) cm (longer objects)
    m (short distances) km (long distances)
  • estimate and measure the perimeter of regular and irregular shapes.

Integration
Physical education: Athletics; Outdoor and adventure activities

Content for sixth class

The child should be enabled to

  • select and use appropriate instruments of measurement
  • rename measures of length
    rename measurements of appropriate metric units; express results as fractions and decimal fractions of appropriate metric units
    233 m = 0.233 km
    1 m 11 cm = 1.11 m
  • estimate and measure the perimeter of regular and irregular shapes
  • use and interpret scales on maps and plans
    identify given scale on a map or plan and draw items to a larger or smaller scale.

Integration
Geography: Natural environments
Physical education: Athletics; Outdoor and adventure activities

Strand unit: Area


Content for fifth class

The child should be enabled to

  • discover that the area of a rectangle is length by breadth
    determine by repeated experiments using rectangles withsides measured in whole centimetres and square units of one square centimetre
  • estimate and measure the area of regular and irregular 2-D shapes
    measure a wide variety of regular and irregular shapes using square units of onesquare centimetre and one square metre
  • calculate area using square centimetres and square metres
    choose appropriate measuring units:
    square centimetres (smaller objects)
    square metres (large objects or rooms)
  • compare visually square metres and square centimetres.

Content for sixth class

The child should be enabled to

  • recognise that the length of the perimeter of a rectangular shape does not determine the area of the shape
    construct rectangles of constant perimeter with varying areas
  • calculate the area of regular and irregular 2-D shapes
    estimate and calculate area of shapes, and check by measuring with square centimetre units circles: calculate by counting squares only
  • measure the surface area of specified 3-D shapes
    measure 3-D surfaces by measuring individual 2-D faces or by extending into nets
  • calculate area using ares and hectares
    fields, large playgrounds, car parks
  • identify the relationship between square metres and square centimetres
    explore and compare areas of one, four, twenty-five and one hundred square centimetres to establish relationships
  • find the area of a room from a scale plan
    measure and calculate area of rectangular shapes by partitioning into rectangles and combining individual areas
    extend to finding area of room plans (rectangular)
    extend to using scale to find area of rooms from plans.

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

Strand unit: Weight


Content for fifth class

The child should be enabled to

  • select and use appropriate instruments of measurement choose measurement instruments appropriate to given tasks, e.g. balance, kitchen scales, bathroom scales and spring balance
  • estimate and measure weight using appropriate metric units
    estimate and measure a large variety of objects use appropriate measuring units
    grams (pencils and copybooks) kilograms (school bags and people).

Content for sixth class

The child should be enabled to

  • select and use appropriate instruments of measurement
  • rename measures of weight
    rename measurements of appropriate metric units
    express results as fractions or decimals of appropriate metric units
    750 g = 0.75 kg
    4 kg 45 g = 4.045 kg.

Strand unit: Capacity


Content for fifth class

The child should be enabled to

  • select and use appropriate instruments of measurement
    choose measurement instruments appropriate to given tasks graduated jugs, litre containers or fractional litre containers
  • estimate and measure capacity using appropriate metric units
    estimate and measure a large variety of objects use appropriate measuring units
    millilitres (cups), litres (watering-can).

Content for sixth class

The child should be enabled to

  • select and use appropriate instruments of measurement
  • rename measures of capacity
    rename measurements of appropriate metric units
    express results as fractions or decimals of appropriate metric unit
    625 ml = 5 eighths of a litre = 0.625 l
    8 l 253 ml = 8.253 l
  • find the volume of a cuboid experimentally
    fill a cuboid container with water and measure capacity in litres
    fill a cuboid container with unit cubes and count.

Strand unit: Time


Content for fifth class

The child should be enabled to

  • read and interpret timetables and the 24-hour clock (digital and analogue)
    bus, train, air, ship, films, theatre, school, class
  • interpret and convert between times in 12-hour and 24-hour format
    10:30 p.m. = 22:30 hours
    07:50 hours = 7:50 a.m.

Content for sixth class

The child should be enabled to

  • explore international time zones
    identify and discuss the need for time zones calculate time differences between Ireland and other countries
  • explore the relationship between time, distance and average speed
    measure, using a stop-watch, the time taken for short journeys to be completed or short distances to be covered and compile database to examine averages.

Linkage
Data: Representing and interpreting
Integration
Physical education: Athletics

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

Strand unit: Money - euro


Content for fifth class

The child should be enabled to

  • compare 'value for money' using unitary method
    compare the cost of 6 apples costing 75 cents and 4 apples costing 50 cents
    calculate pay, based on hourly or daily rate
    calculate totals of shop bills.

Content for sixth class

The child should be enabled to

  • explore value for money
    calculate sale prices, e.g. 10% discount, 20% VAT added
  • convert other currencies to euro and vice versa
    identify and discuss exchange rates from newspaper
    calculate major currency equivalents for basic sums of euro
    convert sums of money in other currencies to euro equivalents.

Linkage
Number: Operations, Decimals and percentages

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

Strand: Data

Strand unit: Representing and interpreting data


Content for fifth class

The child should be enabled to

  • collect, organise and represent data using pictograms, single and multiple bar charts and simple pie charts
    collect data from the environment in tabular form and represent in appropriate format
    discuss and explore modes of representation
  • read and interpret pictograms, single and multiple bar charts, and pie charts
    examine and discuss class-based examples and interpret
    charts from newspapers, magazines and computergenerated
    charts

Linkage
Number: Fractions
Shape and space: Angles
Integration
Geography: Human environments

  • compile and use simple data sets
    compile lists of statistics from children's experiences
    e.g. personal data (height, age, hair colour) sports results (wins, losses, scores)
    use data as source for representation, interpretation and setting problems

  • explore and calculate averages of simple data sets
    identify the most frequently occurring item in a data set
    calculate average by adding all the values and dividingby the number of items (use a calculator)
  • use data sets to solve problems
    solve problems based on data sets and representations used in class
    what were the most popular buns at a cake sale?

Content for sixth class

The child should be enabled to

  • collect, organise and represent data using pie charts and trend graphs
    sales or rainfall per month
  • read and interpret trend graphs and pie charts
    e.g. height or weight in relation to age

Linkage
Number: Fractions
Shape and space: Angles
Integration
Geography: Human environments

  • compile and use simple data sets
    compile lists of statistics from children's experiences e.g. personal data (height, age, hair colour) sports results (wins, losses, scores)
    use data as source for representation, interpretation and setting problems
  • explore and calculate averages of simple data sets
    identify the most frequently occurring item in a data set
    compare calculated averages with the most frequently occurring items
  • use data sets to solve problems.

Strand unit: Chance


Content for fifth class

The child should be enabled to

  • identify and list all possible outcomes of simple random processes
    discuss and list all possible outcomes of:
    rolling a die (1, 2, 3, 4, 5, 6)
    tossing two coins (2 heads, 2 tails, head and tail)
    drawing a cube from a bag containing blue, red and green cubes (blue cube, red cube, green cube)
  • estimate the likelihood of occurrence of events
    if we toss a coin, say, 100 times, how many heads would we expect to get? a head has 50 chances in 100, or 1 chance in 2, of appearing; heads and tails are equally likely to occur if we roll a die: how often would we expect to get a 2? (1 chance in 6);
    each of the 6 outcomes is equally likely; this activity can be done in groups with
    each child or group throwing the die (or coin) 20 times and pooling the results; discuss the fairness of board games
  • construct and use frequency charts and tables
    perform the experiment (toss a coin, roll a die, draw a cube from a bag containing 3 blue and 6 green cubes ...) a large number of times (50-100 times) this activity can be done in groups with each child or group throwing the die (or coin) 20 times and pooling the results
    record the outcomes and use to construct a frequency table; for example, if drawing a cube from a bag as above, the table might be as follows:
    colour number of times drawn
    blue 36
    green 64
    we estimate the likelihood of a blue cube to be 36 in 100 and that of a green cube to be 64 in 100
    discuss: is that what we expected?
    data sets compiled from children's experiences (personal data, weather, sports) might be used; for example, a survey of favourite cereals might have produced the
    following table:
    cereal number of pupils who prefer it
    corn flakes 19
    porridge 4
    crispies 9
    muesli 3
    the likelihood that a pupil picked at random prefers corn flakes is estimated to be 19 in 35.

Integration
Music:Improvising and creating

Content for sixth class

The child should be enabled to

  • identify and list all possible outcomes of simple random processes
    discuss and list all possible outcomes of:
    rolling two dice and calculating the total
    (2, 3, 4 ... 12)
    selecting two numbers at random from the numbers
    1, 2, 3, 4, 5 (ten possibilities)
  • estimate the likelihood of occurrence of events; order on a scale from 0 to 100%, 0 to 1
    when tossing a coin, a head has 1 chance in 2 of occurring; thus the likelihood of a head is 1 in 2, or 1-2 or 50%, similarly for a tail when rolling a die, each outcome has a 1 in 6 chance of occurring -- therefore the likelihood is 1-6 when drawing a cube from a bag containing 3 red and 6 blue cubes, a blue cube has 6 chances in 9 of occurring and thus has a probability of 6-9 or 2-3 ; the probability of drawing a red cube is 3-9 or 1-3 what if the bag contains 5 red, 5 blue and 5 green cubes? or 3 red, 6 blue and 6 green?
  • construct and use frequency charts and tables
    perform the experiment (toss two coins, draw a cube from a bag containing a number of different-coloured cubes) a large number of times; larger numbers of throws can be achieved by using group work
    record the outcomes and use to construct a frequency table; for example, when tossing two coins, the table might look as follows:
    outcome frequency
    2 heads 20
    2 tails 28
    1 head, 1 tail 52
    we estimate the chance of 2 heads to be 20/100, that of 2 tails to be 28/100, that of one head and one tail to be 52/100:
    discuss, is this what we expected?
    using two coins of different colours may help examine a table of school attendance for the class what is the chance of full attendance on any one day?
    what is the chance of more than 20% of the class being absent on any one day?
    pupils are given a bag and told it contains 10 cubes in 3 different colours; by drawing a cube repeatedly, say 50 times, and constructing a frequency table, they must estimate how many cubes of each colour there are in the bag.

Integration
Music:Improvising and creating

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

 
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