4 to 12 Maths
My 3 kids were fighting to get on the computer last night to do Maths. I think its brilliant - they even missed X-factor to do Maths!
 

5th Class


5th Class Overview

Skills

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.


Strands & Strand Units


Strand: Number
Strand Unit : PlaceValue
 
  • 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.
  
Strand Unit : Operations
 
  • 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.
 
  
Strand Unit : Fractions
 
  • 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.
  
Strand Unit : Decimals and Percentages
 
  • 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 a calculator, include simple discount and increase examples 10% off all jeans, 20%extra free.
  
Strand Unit : Number Theory
 
  • 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.
  

 

Strand : Algebra
Strand Unit : Directed Numbers
 
  • 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.
  
Strand Unit : Rules and properties
 
  • 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 ...
  
Strand Unit : Equations
 
  • 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.
  

 

Strand : Shape & Space
Strand Unit :2-D shapes
 
  • 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.
  
Strand Unit : 3-D shapes
 
  • 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.
  
Strand Unit : Lines and angles
 
  • 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, 360ยก 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.
  

 

Strand : Measures
Strand Unit : Length
 
  • 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.
  
Strand Unit : Area
 
  • discover that the area of a rectangle is length by breadth
    • determine by repeated experiments using rectangles with sides 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 one square 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.
  
Strand Unit : Weight
 
  • 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).
  
Strand Unit : Capacity
 
  • 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).
  
Strand Unit : Time
  • 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.
  
Strand Unit : Money - euro
 
  • 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.
  

 

 

Strand : Data
Strand Unit : Recognising and interpreting data
 
  • 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 computer generated charts
  
Strand Unit : Chance
 
  • 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.
  
 

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