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 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.