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!
 

6th Class


6th 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
  • identify place value in whole numbers and decimals
  • round decimals
    • round decimals to one, two or three decimal places.
  
Strand Unit : Operations
 
  • 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
 
  • 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
    • common denominator 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
 
  • 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.
  
Strand Unit : Number Theory
 
  • 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
 
  • 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?
  
Strand Unit : Rules and properties
 
  • 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 ...
  
Strand Unit : Variables
 
  • 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
  • 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.
  

 

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
  • 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
  • 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.
  
Strand Unit : Lines and angles
  • 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.
  

 

Strand : Measures
Strand Unit : Length
  • 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.
  
Strand Unit : Area
  • 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.
  
Strand Unit : Weight
  • 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
  • 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
  • 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.
  
Strand Unit : Money - euro
  • 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.
  

 

 

Strand : Data
Strand Unit : Recognising and interpreting data
  • 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
  
Strand Unit : Chance
  • 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.
  
 

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