Y6 good things to know for website(1)

International School, LuxembourgA.S.B.L.

Year 6Good Things to Know

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We hope you find this handbook useful, it contains information which is an extension of the Parent

Handbook you will have already received. You will receive further information in the form of termly

Year Group letters with in depth information on each of the subjects your child(ren) will be studying.

Learning is growing in doing, knowing and

understanding.

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TABLE OF CONTENTS

HOMEWORK .................................................................................................................................. 4

CORE LEARNING IN LITERACY ......................................................................................................... 5

CURSIVE ALPHABET ..................................................................................................................... 10

LETTER OUTLINES ....................................................................................................................... 11

SPELLING OBJECTIVES ................................................................................................................. 12

DIFFICULTIES WITH SPELLING ...................................................................................................... 13

FRENCH ..................................................................................................................................... 14

CORE LEARNING IN MATHEMATICS ................................................................................................ 16

PROGRESSION IN CALCULATIONS .................................................................................................. 21

FUN MATHS ACTIVITIES TO DO AT HOME ........................................................................................ 34

MATHS VOCABULARY ................................................................................................................... 38

INTERNATIONAL PRIMARY CURRICULUM TOPICS (IPC) .................................................................. 43

INTERNET SAFETY INFORMATION ................................................................................................... 44

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HOMEWORK

We are often asked questions by parents about homework – its purpose and the amount. This letter

will give you an introduction as to how we view homework here at St. George’s. A more detailed

programme for each class will be drawn up by the individual class teachers.

There is no doubt that parents who are involved in their child’s learning help them to make faster

progress, to gain confidence and to achieve better results. We appreciate the support that you

already give your children at home.

At St. George’s we believe that the main purposes of homework are:

1) To develop our links with you, the parents

2) To help you to understand what your children are learning at school

3) To give your child the opportunity to practise what they are learning, particularly in literacy

and numeracy

4) To develop self discipline and perseverance and become independent learners

5) To help your child to learn to plan the wise use of time and to develop confidence

6) To develop ‘The Homework Habit’

7) To increase self esteem through knowing that their achievements are regarded as important

by both home and school

8) To extend school learning

The purpose and the amount of homework change as your child gets older. For children in Reception

and Years 1 and 2 the homework could include reading, phonic practice, word games, spelling,

learning number facts and reading together. The time spent on homework will be about 1 hour each

week for Years 1 and 2 and 30 minutes for Reception.

We would also encourage you to share other books by reading with your child for between 10 and 20

minutes a day.

In Years 3 – 6 the main purpose of homework is to provide opportunities for your child to develop the

skills of independent learning. By the time your child reaches Year 6 their homework will cover a

range of tasks and curriculum content.

In years 3 – 6 homework could include:

1) Regular opportunities to practise word and sentence work

2) Finding out information

3) Reading in preparation for lessons

4) Regular opportunities to practise number skills

5) French or EAL

6) Speaking and recital skills

5

CORE LEARNING IN LITERACY – YEAR 6

Most children will learn to:

A. SPEAKING AND LISTENING

SPEAKING

Use a range of oral techniques to present persuasive arguments and engaging narratives.

Participate in whole-class debate using the conventions and language of debate, including standard

English.

Use the techniques of dialogic talk to explore ideas, topics or issues.

LISTENING AND RESPONDING

Make notes when listening for a sustained period and discuss how note-taking varies depending on

context and purpose.

Analyse and evaluate how speakers present points effectively through use of language and gesture.

Listen for language variation in formal and informal contexts.

Identify the ways spoken language varies according to differences in the context and purpose of its

use.

GROUP DISCUSSION AND INTERACTION

Consider examples of conflict and resolution, exploring the language used.

Understand and use a variety of ways to criticise constructively and respond to criticism.

DRAMA

Improvise using a range of drama strategies and conventions to explore themes such as hopes, fears

and desires.

Consider the overall impact of a live or recorded performance, identifying dramatic ways of conveying

characters’ ideas and building tension.

Devise a performance considering how to adapt the performance for a specific audience.

B. READING

UNDERSTANDING AND INTERPRETING TEXTS

Appraise a text quickly, deciding on its value, quality or usefulness.

Understand underlying themes, causes and points of view.

Understand how writers use different structures to create coherence and impact.

Explore how word meanings change when used in different contexts.

Recognise rhetorical devices used to argue, persuade, mislead and sway the reader.

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ENGAGING WITH AND RESPONDING TO TEXTS

Read extensively and discuss personal reading with others, including in reading groups.

Sustain engagement with longer texts, using different techniques to make the text come alive.

Compare how writers from different times and places present experiences and use language.

C. WRITING

WORD STRUCTURE AND SPELLING

Spell familiar words correctly and employ a range of strategies to spell difficult and unfamiliar words.

Use a range of appropriate strategies to edit, proofread and correct spelling in their own work, on

paper and on screen.

CREATING AND SHAPING TEXTS

Set their own challenges to extend achievement and experience in writing.

Use different narrative techniques to engage and entertain the reader.

In non-narrative, establish, balance and maintain viewpoints.

Select words and language drawing on their knowledge of literary features and formal and informal

writing.

Integrate words, images and sounds imaginatively for different purposes.

TEXT STRUCTURE AND ORGANISATION

Use varied structures to shape and organise text coherently.

Use paragraphs to achieve pace and emphasis.

SENTENCE STRUCTURE AND PUNCTUATION

Express subtle distinctions of meaning, including hypothesis, speculation and supposition, by

constructing sentences in varied ways.

Use punctuation to clarify meaning in complex sentences.

PRESENTATION

Use different styles of handwriting for different purposes with a range of media, developing a

consistent and personal legible style.

Select from a wide range of ICT programs to present text effectively and communicate information

and ideas.

7

CORE LEARNING IN LITERACY – YEAR 6 PROGRESSION TO YEAR 7

Most children learnt to:

A. SPEAKING AND LISTENING

SPEAKING

Use exploratory, hypothetical and speculative talk as a tool for clarifying ideas.

Tailor the structure, vocabulary and delivery of a talk or presentation so that it is helpfully sequenced

and supported by gesture or other visual aid as appropriate.

Use standard English consistently in formal situations and promote, justify or defend a point of view

using supporting evidence, example and illustration which are linked back to the main argument.

LISTENING AND RESPONDING

Listen for and recall the main points of a talk, reading or TV programme, reflecting on what has been

heard to ask searching questions, make comments or challenge the views expressed.

Identify the main methods used by presenters to explain, persuade, amuse or argue a case, e.g.

emotive language.

Investigate differences between spoken and written language structures.

GROUP DISCUSSION AND INTERACTION

Adopt a range of roles in discussion, including acting as a spokesperson, and contribute in different

ways such as promoting, opposing, exploring and questioning.

Identify and report the main points emerging from discussion.

Acknowledge other people’s views, justifying or modifying their own views in the light of what others

say.

Work together logically and methodically to solve problems, make deductions, share, test and

evaluate ideas.

DRAMA

Develop drama techniques to explore in role a variety of situations and texts or respond to stimuli.

Develop drama techniques and strategies for anticipating, visualising and problem solving in different

learning contexts.

Work collaboratively to devise and present scripted and unscripted pieces that maintain the attention

of an audience, and reflect on and evaluate their own presentations and those of others.

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B. READING

UNDERSTANDING AND INTERPRETING TEXTS

Locate resources for a specific task, appraising the value and relevance of information and

acknowledging sources.

Read between the lines and find evidence for their interpretation.

Identify how print, images and sounds combine to create meaning.

Infer the meanings of unknown words using syntax, context, word structures and origins.

Identify the ways writers of non-fiction match language and organisation to their intentions.

ENGAGING WITH AND RESPONDING TO TEXTS

Read a range of recent fiction texts independently as the basis for developing critical reflection and

personal response.

Explore the notion of literary heritages and understand why some texts have been particularly

influential or significant.

Write reflectively about a text, distinguishing between the attitudes and assumptions of characters

and those of the author and taking account of the needs of others who might read it.

C. WRITING

WORD STRUCTURE AND SPELLING

Revise, consolidate and secure knowledge of correct vowel choices, pluralisation, prefixes, word

endings and high frequency words.

Record and learn from personal errors, corrections, investigations, conventions, exceptions and new

vocabulary.

Draw on analogies to known words, roots, derivations, word families, morphology and familiar

spelling patterns.

CREATING AND SHAPING TEXTS

Independently write and present a text with the reader and purpose in mind.

Use a range of narrative devices to involve the reader.

Identify criteria for evaluating a situation, object or event, presenting findings fairly and adding

persuasive emphasis to key points.

Experiment with the visual and sound effects of language, including the use of imagery, alliteration,

rhythm and rhyme.

9

TEXT STRUCTURE AND ORGANISATION

Organise ideas into a coherent sequence of paragraphs.

In non-chronological writing, introduce, develop and conclude paragraphs appropriately.

SENTENCE STRUCTURE AND PUNCTUATION

Extend their use and control of complex sentences by deploying subordinate clauses effectively.

Use punctuation to convey and clarify meaning and to integrate speech into longer sentences.

Use standard English confidently and consistently in formal writing, with awareness of the differences

between spoken and written language structures.

PRESENTATION

Review the legibility and neatness of their handwriting.

Set personal targets to improve presentation, using a range of presentational devices, on paper and

on screen.

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Aªa B¶ø Cªc Dªd Eâ F¶<

Gªü H¶h I¶i J¶ý K¶„ L¶l

M¶m N¶n Oª‹ P¶ú Qªq R¶r

S¡ T¶t U¶u V¶v W¶w X¶ˆ

Y¶þ Z¶z

A¶l[l ªc]a[p[i[t]a[l ¶¯e[t[·e[rã ¶¥e]Ìi[n ¶>›om ¶t[«e

¶t]oú ¶l[i[±e. Cªa[p[i[t]a[l ¶¯e[t[·e[rã ªa[µÖ ¶n]Št

¶Ðoi[±e]d.

A¶l[l ¡[m]a[l[l ¶¯e[t[·e[rã ¶¥e]Ìi[n ¶>›om ¶t[«e

¶b]Št[t]om ¶l[i[±e. T¶«e ªon[l[þ â[ˆ]¦e[p[t[i]on¡

¶¥e]Ìi[n ªa[>·e[r ¶t[«e ¶¯e[t[·e[rã ª‹, ¶v, ¶w ªa[n]d

¶r.

If your child has already been taught to write in a different style, providing their work is

legible, then they will not be re-taught or required to change their style.

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SPELLING OBJECTIVES – YEAR 6

To use word roots, prefixes and suffixes as a support for spelling, e.g. aero, aqua, audi, bi, cede, clued, con, cred, duo, log(o)(y), hyd(ro)(ra), in, micro, oct, photo, port, prim, scribe, scope, sub, tele, tri, ex.

To investigate meanings and spellings of connectives: therefore, notwithstanding,

furthermore, etc.; link to Sentence Level work on connectives.

To examine the properties of words ending in vowels other than the letter e.

To investigate, collect and classify spelling patterns in pluralisation, construct rules of regular

spellings e.g. add s to most words; add es to most words ending in s, sh, ch; when y is

preceded by a consonant, change to ies; when y is preceded by a vowel, add s.

To investigate, collect and classify spelling in pluralisation, e.g. change f to ves.

To collect and investigate the meanings and spellings of words using the following prefixes:

auto, bi, trans, tele, circum.

To explore spelling patterns of consonants and formulate rules: ll in full becomes l when

used as a suffix.

To identify word roots, derivations, and spelling patterns, e.g. sign, signature, signal; bomb, bombastic, bombard; remit, permit, permission, in order to extend vocabulary and provide

support for spelling.

To explore spelling patterns and consonants and formulate rules: words ending with a single

consonant preceded by a short vowel double the consonant before adding ing.

To explore spelling patterns of consonants and formulate rules: e is usually soft when

followed by i, e.g. circus, accident.

To investigate words that have common letter strings but different pronunciations e.g. rough, cough, bough, boot, foot.

To distinguish between homophones, i.e. words with common pronunciations but different

spellings, e.g. eight, ate; grate, great; rain, rein, reign.

To recognise and spell the suffix: cian, etc.

The correct use and spelling of possessive pronouns, linked to work on grammar, e.g. their, theirs; your, yours; my, mine.

To spell unstressed vowels in polysyllabic words, e.g. company, portable, poisonous, interest, description, carpet, sector, freedom, extra, etc.

To investigate and learn spelling rules: words ending in modifying e drop e when adding ing,

e.g. taking; words ending in modifying e keep e when adding a suffix beginning with a

consonant, e.g. hopeful, lovely.

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Find the roots and

build them up

dis + appear

Say is as it is

written

Fascinating

Say each

syllable even if

it sounds funny

Wed – nes – day

Ways to help

with difficult

spellings

Say the word

clearly. Sound it

out syllable by

syllable

Yes – ter – day

Find out where the

word comes from.

Knif was the Viking

word for knife. Many

Viking words began

with kn.

Use the Computer

Remember the way it

feels to type the word.

Practice writing with

graphic programmes

Get the feel of the

word.

Write with your finger

in the air or chalk in big

letter on the board.

Rub out chalk writing

with your index

Look for words with

words

Together = To get her

Friend = I will be your

friend to the end

Hang

spelling

lists

on

bedroom

&

loo

doors

Make up

Funnies

Necessary has one collar

and two socks.

Because = Big

Elephants Can Always

Use Some Energy.

Spell the word out

loud, letter by letter,

as you write it down.

S – a – i – d

Take a mental

photograph of the word

Remember

14

FRENCH

By the end of Year 6, we would expect some of our pupils to attain level C1 if they have been

attending French at St George’s from Early Years.

Below is an explanation of the levels used to assess language levels:

The Common European Framework (CEFR) divides learners into three broad divisions that can be divided into six levels. It describes what a learner is supposed to be able to do in reading, listening,

speaking and writing at each level.

Level group A B C

Level group

name Basic User Independent User Proficient User

Level A1 A2 B1 B2 C1 C2

Description Can

understand and use

familiar everyday

expressions

and very basic

phrases aimed at the

satisfaction of needs of

a concrete type.

Can introduce

him / herself and others

and can ask and answer

questions

about personal

details such as where

he/she lives, people

he/she knows and

things

he/she has.

Can

understand sentences and

frequently used

expressions

related to areas of most

immediate relevance

(e.g. very basic personal

and family information,

shopping,

local geography,

employment).

Can communicate

in simple and

routine tasks requiring a

simple and direct

exchange of information

on familiar and routine

matters.

Can

understand the main

points of clear standard

input on

familiar matters

regularly encountered

in work, school,

leisure, etc.

Can deal with

most situations

likely to arise while

travelling in an area

where the

language is spoken.

Can produce

simple connected

text on topics

that are familiar or of

personal interest.

Can

understand the main

ideas of complex text

on both

concrete and abstract

topics, including

technical discussions in

his / her field of

specialisation.

Can interact

with a degree of fluency and

spontaneity that makes

regular

interaction with native

speakers quite possible

without strain for either

party.

Can

understand a wide range of

demanding, longer texts,

and recognise

implicit meaning.

Can express

ideas fluently and

spontaneously

without much obvious

searching for expressions.

Can use

language

flexibly and effectively for

social, academic and

professional purposes.

Can

understand with ease

virtually everything

heard or read.

Can summarise

information from different

spoken and written

sources,

reconstructing arguments and

accounts in a coherent

presentation.

15

Level A1 A2 B1 B2 C1 C2

Description Can interact in a simple

way

provided the other person

talks slowly and clearly

and is prepared to

help.

Can describe in simple

terms aspects

of his/her background,

immediate environment

and matters in areas of

immediate need.

Can describe experiences

and events,

dreams, hopes and

ambitions and briefly give

reasons and explanations

for opinions and plans.

Can produce clear, detailed

text on a wide

range of subjects and

explain a viewpoint on

a topical issue giving the

advantages and

disadvantages

of various options.

Can produce clear, well-

structured,

detailed text on complex

subjects, showing

controlled use of

organisational patterns,

connectors

and cohesive devices.

Can express him/herself

spontaneously,

very fluently and precisely,

differentiating finer shades of

meaning even in the most

complex situations.

SUPPORTING THE FRENCH LEARNER OUTSIDE OF SCHOOL

Language Camps: www.languages.lu/language-camps/

Tutoring: www.languages.lu/school-tutoring/

Tutoring: www.mastercraft.lu/en/soutien_scolaire.html

Sports and Languages: www.inlingua.lu/?q=en/node/136

After-school: www.inlingua.lu/?q=en/node/135

Little Gym: www.thelittlegym.eu/lu-fr

SUPPORTING THE EAL LEARNER OUTSIDE OF SCHOOL

Little Gym: www.thelittlegym.eu/lu-en

Ceramics School: www.ceramics.lu/index.htm

British Guides in Luxembourg: www.bglux.eu

Telstar Scout Group: www.telstar.lu

Newsround: www.bbc.co.uk/newsround

Online Talking Stories: http://resources.woodlands-junior.kent.sch.uk/interactive/onlinestory.htm

British Council: http://learnenglishkids.britishcouncil.org/en/

http://www.languages.lu/language-camps/

http://www.languages.lu/school-tutoring/

http://www.mastercraft.lu/en/soutien_scolaire.html

http://www.inlingua.lu/?q=en/node/136

http://www.inlingua.lu/?q=en/node/135

http://www.thelittlegym.eu/lu-fr

http://www.thelittlegym.eu/lu-en

http://www.ceramics.lu/index.htm

http://www.bglux.eu/

http://www.telstar.lu/

http://www.bbc.co.uk/newsround

http://resources.woodlands-junior.kent.sch.uk/interactive/onlinestory.htm

http://learnenglishkids.britishcouncil.org/en/

16

CORE LEARNING IN MATHEMATICS – YEAR 6

* Key objectives are in bold.


USING AND APPLYING MATHEMATICS

Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and

use appropriate calculation strategies at each stage, including calculator use.

Tabulate systematically the information in a problem or puzzle; identify and record the steps or

calculations needed to solve it, using symbols where appropriate; interpret solutions in the original

context and check their accuracy.

Suggest, plan and develop lines of enquiry; collect, organise and represent information, interpret

results and review methods; identify and answer related questions.

Represent and interpret sequences, patterns and relationships involving numbers and shapes;

suggest and test hypotheses; construct and use simple expressions and formulae in words then

symbols (e.g. the cost of c pens at 15 pence each is 15c pence).

Explain reasoning and conclusions, using words, symbols or diagrams as appropriate.

COUNTING AND UNDERSTANDING NUMBER

Find the difference between a positive and a negative integer, or two negative integers, in context.

Use decimal notation for tenths, hundredths and thousandths; partition, round and order decimals

with up to three places, and position them on the number line.

Express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice

pizza represents 8/5 or 13/5 pizzas); simplify fractions by cancelling common factors; order a set of

fractions by converting them to fractions with a common denominator.

Express one quantity as a percentage of another (e.g. express £400 as a percentage of

£1000); find equivalent percentages, decimals and fractions.

Solve simple problems involving direct proportion by scaling quantities up or down.

KNOWING AND USING NUMBER FACTS

Use knowledge of place value and multiplication facts to 10 × 10 to derive related

multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6).

Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the

corresponding squares of multiples of 10.

Recognise that prime numbers have only two factors and identify prime numbers less than 100; find

the prime factors of two-digit numbers.

Use approximations, inverse operations and tests of divisibility to estimate and check results.

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CALCULATING

Calculate mentally with integers and decimals: U.t ± U.t, TU × U, TU ÷ U, U.t × U, U.t ÷ U.

Use efficient written methods to add and subtract integers and decimals, to multiply and

divide integers and decimals by a one-digit integer, and to multiply two-digit and three-

digit integers by a two-digit integer.

Relate fractions to multiplication and division (e.g. 6 ÷ 2 = ½ of 6 = 6 × 1/2); express a quotient as a

fraction or decimal (e.g. 67 ÷ 5 = 13.4 or 13 2/5); find fractions and percentages of whole-number

quantities (e.g. 5/8 of 96, 65% of £260).

Use a calculator to solve problems involving multi-step calculations.

UNDERSTANDING SHAPE

Describe, identify and visualise parallel and perpendicular edges or faces; use these properties to

classify 2-D shapes and 3-D solids.

Make and draw shapes with increasing accuracy and apply knowledge of their properties.

Visualise and draw on grids of different types where a shape will be after reflection, after

translations, or after rotation through 90° or 180° about its centre or one of its vertices.

Use coordinates in the first quadrant to draw, locate and complete shapes that meet given properties.

Estimate angles, and use a protractor to measure and draw them, on their own and in shapes;

calculate angles in a triangle or around a point.

MEASURING

Select and use standard metric units of measure and convert between units using

decimals to two places (e.g. change 2.75 litres to 2750 ml, or vice versa).

Read and interpret scales on a range of measuring instruments, recognising that the measurement

made is approximate and recording results to a required degree of accuracy; compare readings on

different scales, for example when using different instruments.

Calculate the perimeter and area of rectilinear shapes; estimate the area of an irregular shape by

counting squares.

HANDLING DATA

Describe and predict outcomes from data using the language of chance or likelihood.

Solve problems by collecting, selecting, processing, presenting and interpreting data,

using ICT where appropriate; draw conclusions and identify further questions to ask.

Construct and interpret frequency tables, bar charts with grouped discrete data, and line graphs;

interpret pie charts.

Describe and interpret results and solutions to problems using the mode, range, median and mean.

18

CORE LEARNING IN MATHEMATICS – YEAR 6 PROGRESSION TO YEAR 7

* Key objectives are in bold.


USING AND APPLYING MATHEMATICS

Solve problems by breaking down complex calculations into simpler steps; choose and use operations

and calculation strategies appropriate to the numbers and context; try alternative approaches to

overcome difficulties; present, interpret and compare solutions.

Represent information or unknown numbers in a problem, for example in a table, formula or

equation; explain solutions in the context of the problem.

Develop and evaluate lines of enquiry; identify, collect, organise and analyse relevant information;

decide how best to represent conclusions and what further questions to ask.

Generate sequences and describe the general term; use letters and symbols to represent unknown

numbers or variables; represent simple relationships as graphs.

Explain and justify reasoning and conclusions, using notation, symbols and diagrams; find a counter-

example to disprove a conjecture; use step-by-step deductions to solve problems involving shapes.

COUNTING AND UNDERSTANDING NUMBER

Compare and order integers and decimals in different contexts.

Order a set of fractions by converting them to decimals.

Recognise approximate proportions of a whole and use fractions and percentages to describe and

compare them, for example when interpreting pie charts.

Use ratio notation, reduce a ratio to its simplest form and divide a quantity into two parts

in a given ratio; solve simple problems involving ratio and direct proportion (e.g. identify

the quantities needed to make a fruit drink by mixing water and juice in a given ratio).

KNOWING AND USING NUMBER FACTS

Consolidate rapid recall of number facts, including multiplication facts to 10 × 10 and the associated

division facts.

Recognise the square roots of perfect squares to 12 × 12.

Recognise and use multiples, factors, divisors, common factors, highest common factors and lowest

common multiples in simple cases.

Make and justify estimates and approximations to calculations.

19

CALCULATING

Understand how the commutative, associative and distributive laws, and the relationships between

operations, including inverse operations, can be used to calculate more efficiently; use the order of

operations, including brackets.

Consolidate and extend mental methods of calculation to include decimals, fractions and percentages.

Use standard column procedures to add and subtract integers and decimals, and to multiply two-digit

and three-digit integers by a one-digit or two-digit integer; extend division to dividing three-digit

integers by a two-digit integer.

Calculate percentage increases or decreases and fractions of quantities and measurements (integer

answers).

Use bracket keys and the memory of a calculator to carry out calculations with more than

one step; use the square root key.

UNDERSTANDING SHAPE

Use correctly the vocabulary, notation and labelling conventions for lines, angles and shapes.

Extend knowledge of properties of triangles and quadrilaterals and use these to visualise and solve

problems, explaining reasoning with diagrams.

Know the sum of angles on a straight line, in a triangle and at a point, and recognise

vertically opposite angles.

Use all four quadrants to find coordinates of points determined by geometric information.

Identify all the symmetries of 2-D shapes; transform images using ICT.

Construct a triangle given two sides and the included angle.

MEASURING

Convert between related metric units using decimals to three places (e.g. convert 1375 mm to 1.375

m, or vice versa).

Solve problems by measuring, estimating and calculating; measure and calculate using

imperial units still in everyday use; know their approximate metric values.

Calculate the area of right-angled triangles given the lengths of the two perpendicular sides, and the

volume and surface area of cubes and cuboids.

HANDLING DATA

Understand and use the probability scale from 0 to 1; find and justify probabilities based

on equally likely outcomes in simple contexts.

Explore hypotheses by planning surveys or experiments to collect small sets of discrete or continuous

data; select, process, present and interpret the data, using ICT where appropriate; identify ways to

extend the survey or experiment.

20

Construct, interpret and compare graphs and diagrams that represent data, for example compare

proportions in two pie charts that represent different totals.

Write a short report of a statistical enquiry and illustrate with appropriate diagrams, graphs and

charts, using ICT as appropriate; justify the choice of what is presented.

21

PROGRESSION IN CALCULATIONS

WRITTEN METHODS FOR ADDITION OF WHOLE NUMBERS

The aim is that children use mental methods when appropriate, but for calculations that they cannot

do in their heads they use an efficient written method accurately and with confidence. Children are

entitled to be taught and to acquire secure mental methods of calculation and one efficient written

method of calculation for addition which they know they can rely on when mental methods are not

appropriate. These notes show the stages in building up to using an efficient written method for

addition of whole numbers by the end of Year 4.

To add successfully, children need to be able to:

recall all addition pairs to 9 + 9 and complements in 10;

add mentally a series of one-digit numbers, such as 5 + 8 + 4;

add multiples of 10 (such as 60 + 70) or of 100 (such as 600 + 700) using the related

addition fact, 6 + 7, and their knowledge of place value;

partition two-digit and three-digit numbers into multiples of 100, 10 and 1 in different ways.

Note: It is important that children's mental methods of calculation are practised and secured

alongside their learning and use of an efficient written method for addition.

Method Example

STAGE 1: THE EMPTY NUMBER LINE

Steps in addition can be recorded on a number

line. The steps often bridge through a multiple of 10.

The mental methods that lead to column

addition generally involve partitioning, e.g. adding the tens and ones separately, often

starting with the tens. Children need to be able to partition numbers in ways other than

into tens and ones to help them make

multiples of ten by adding in steps. The empty number line helps to record the

steps on the way to calculating the total.

8 + 7 = 15

48 + 36 = 84

or:

STAGE 2: PARTITIONING

The next stage is to record mental methods

using partitioning. Add the tens and then the ones to form partial sums and then add these

partial sums. Partitioning both numbers into tens and ones

mirrors the column method where ones are

placed under ones and tens under tens. This

also links to mental methods.

Record steps in addition using partitioning: 47 + 76 = 47 + 70 + 6 = 117 + 6 = 123

47 + 76 = 40 + 70 + 7 + 6 = 110 + 13 = 123 Partitioned numbers are then written under one

another:

22

Method Example

STAGE 3: EXPANDED METHOD IN COLUMNS

Move on to a layout showing the addition of

the tens to the tens and the ones to the ones separately. To find the partial sums either the

tens or the ones can be added first, and the total of the partial sums can be found by

adding them in any order. As children gain

confidence, ask them to start by adding the ones digits first always.

The addition of the tens in the calculation 47

+ 76 is described in the words 'forty plus seventy equals one hundred and ten',

stressing the link to the related fact 'four plus seven equals eleven'.

The expanded method leads children to the

more compact method so that they

understand its structure and efficiency. The amount of time that should be spent teaching

and practising the expanded method will depend on how secure the children are in

their recall of number facts and in their

understanding of place value.

Write the numbers in columns Adding the tens first:

Adding the ones first:

Discuss how adding the ones first gives the same

answer as adding the tens first. Refine over time to adding the ones digits first consistently.

STAGE 4: COLUMN METHOD

In this method, recording is reduced further.

Carry digits are recorded below the line, using the words 'carry ten' or 'carry one hundred',

not 'carry one'. Later, extend to adding three two-digit

numbers, two three-digit numbers and

numbers with different numbers of digits.

Column addition remains efficient when used

with larger whole numbers and decimals. Once learned, the method is quick and reliable.

WRITTEN METHODS FOR SUBTRACTION OF WHOLE NUMBERS




method of calculation for subtraction which they know they can rely on when mental methods are not

appropriate.

These notes show the stages in building up to using an efficient method for subtraction of two-digit

and three-digit whole numbers by the end of Year 4.

To subtract successfully, children need to be able to:

recall all addition and subtraction facts to 20

subtract multiples of 10 (such as 160 - 70) using the related subtraction fact, 16 - 7, and

their knowledge of place value

partition two-digit and three-digit numbers into multiples of one hundred, ten and one in

different ways (e.g. partition 74 into 70 + 4 or 60 + 14).

23

Method Example


alongside their learning and use of an efficient written method for subtraction.

STAGE 1: USING THE EMPTY NUMBER LINE

The empty number line helps to record or

explain the steps in mental subtraction. A

calculation like 74 - 27 can be recorded by counting back 27 from 74 to reach 47. The

empty number line is also a useful way of

modelling processes such as bridging through a multiple of ten.

The steps can also be recorded by counting

up from the smaller to the larger number to

find the difference, for example by counting

up from 27 to 74 in steps totalling 47.

With practice, children will need to record less

information and decide whether to count back or forward. It is useful to ask children whether

counting up or back is the more efficient for calculations such as 57 - 12, 86 - 77 or 43 -

28.

Steps in subtraction can be recorded on a

number line. The steps often bridge through a multiple of 10.

15 – 7 = 8

74 – 27 =47 worked by counting back:

The steps may be recorded in a different order:

or combined:

The notes below give more detail on the counting-up method using an empty number line.

THE COUNTING-UP METHOD

The mental method of

counting up from the smaller

to the larger number can be recorded using either

number lines or vertically in columns. The number of

rows (or steps) can be

reduced by combining steps. With two-digit numbers, this

requires children to be able to work out the answer to a

calculation such as 30 + ? = 74 mentally.

or

With three-digit numbers the

number of steps can again

be reduced, provided that children are able to work out

answers to calculations such as 178 + ? = 200 and 200 +

? = 326 mentally.

or

24

Method Example

The most compact form of

recording remains

reasonably efficient.

The method can be used

with decimals where no

more than three columns are required. However, it

becomes less efficient when

more than three columns are needed.

This counting-up method

can be a useful alternative for children whose progress

is slow, whose mental and

written calculation skills are weak and whose projected

attainment at the end of Key Stage 2 is towards the lower

end of level 4.

or

STAGE 2: PARTITIONING

Subtraction can be recorded using partitioning

to write equivalent calculations that can be

carried out mentally. For 74 - 27 this involves partitioning the 27 into 20 and 7, and then

subtracting from 74 the 20 and the 4 in turn. Some children may need to partition the 74

into 70 + 4 or 60 + 14 to help them carry out

the subtraction.

Subtraction can be recorded using partitioning:

74 - 27 = 74 - 20 - 7 = 54 - 7 = 47

74 - 27 = 70 + 4 - 20 - 7 = 60 + 14 - 20 - 7 = 40 + 7

This requires children to subtract a single-digit

number or a multiple of 10 from a two-digit number mentally. The method of recording links

to counting back on the number line.

STAGE 3: EXPANDED LAYOUT, LEADING TO COLUMN METHOD

Partitioning the numbers into tens and ones

and writing one under the other mirrors the column method, where ones are placed under

ones and tens under tens. This does not link directly to mental methods of counting back

or up but parallels the partitioning method for

addition. It also relies on secure mental skills. The expanded method leads children to the

more compact method so that they

understand its structure and efficiency. The amount of time that should be spent teaching

and practising the expanded method will depend on how secure the children are in

their recall of number facts and with

partitioning.

Partitioned numbers are then written under one another:

Example: 74 - 27

Example: 741 - 367

25

Method Example

THE EXPANDED METHOD FOR THREE-DIGIT NUMBERS

Example: 563 − 241, no adjustment or decomposition needed

Expanded method

leading to

Start by subtracting the ones, then the tens, then

the hundreds. Refer to subtracting the tens, for example, by saying 'sixty take away forty', not

'six take away four'.

Example: 563 − 271, adjustment from the

hundreds to the tens, or partitioning the

hundreds

Begin by reading aloud the number from which we are subtracting: 'five hundred and sixty-

three'. Then discuss the hundreds, tens and ones components of the number, and how 500 + 60

can be partitioned into 400 + 160. The

subtraction of the tens becomes '160 minus 70', an application of subtraction of multiples of ten.

Example: 563 − 278, adjustment from the hundreds to the tens and the tens to the ones

26

Method Example

Here both the tens and the ones digits to be subtracted are bigger than both the tens and the

ones digits you are subtracting from. Discuss how 60 + 3 is partitioned into 50 + 13, and then how

500 + 50 can be partitioned into 400 + 150, and

how this helps when subtracting.

Example: 503 − 278, dealing with zeros when

adjusting

Here 0 acts as a place holder for the tens. The

adjustment has to be done in two stages. First the 500 + 0 is partitioned into 400 + 100 and

then the 100 + 3 is partitioned into 90 + 13.

WRITTEN METHODS FOR MULTIPLICATION OF WHOLE NUMBERS




method of calculation for multiplication which they know they can rely on when mental methods are

not appropriate.

These notes show the stages in building up to using an efficient method for two-digit by one-digit

multiplication by the end of Year4, two-digit by two-digit multiplication by the end of Year 5, and

three-digit by two-digit multiplication by the end of Year 6.

To multiply successfully, children need to be able to:

recall all multiplication facts to 10 × 10

partition number into multiples of one hundred, ten and one

work out products such as 70 × 5, 70 × 50, 700 × 5 or700 × 50 using the related fact 7 × 5

and their knowledge of place value

add two or more single-digit numbers mentally

add multiples of 10 (such as 60 + 70) or of 100 (such as 600 + 700) using the related

addition fact, 6 + 7, and their knowledge of place value

add combinations of whole numbers using the column method (see above).


alongside their learning and use of an efficient written method for multiplication.

27

Method Example

STAGE 1: MENTAL MULTIPLICATION USING PARTITIONING

Mental methods for multiplying TU × U can be based on the distributive law of multiplication

over addition. This allows the tens and ones to be multiplied separately to form partial products.

These are then added to find the total product.

Either the tens or the ones can be multiplied first but it is more common to start with the tens.

Informal recording might be:

Also record mental multiplication using partitioning:

Note: These methods are based on the

distributive law. Children should be introduced to the principle of this law (not its name) in Years 2

and 3, for example when they use their

knowledge of the 2, 5 and 10 times-tables to work out multiples of 7:

STAGE 2: THE GRID METHOD

As a staging post, an expanded method which

uses a grid can be used. This is based on the

distributive law and links directly to the mental method. It is an alternative way of

recording the same steps.

It is better to place the number with the most

digits in the left-hand column of the grid so that it is easier to add the partial products.

38 × 7 = (30 × 7) + (8 × 7) = 210 + 56 = 266

The next step is to move the number being

multiplied (38 in the example shown) to an extra row at the top. Presenting the grid this

way helps children to set out the addition of the partial products 210 and 56.

The grid method may be the main method

used by children whose progress is slow, whose mental and written calculation skills are

weak and whose projected attainment at the

end of Key Stage 2 is towards the lower end of level 4

28

Method Example

STAGE 3: EXPANDED SHORT MULTIPLICATION

The next step is to represent the method of

recording in a column format, but showing the

working. Draw attention to the links with the grid method above.

Children should describe what they do by

referring to the actual values of the digits in the columns. For example, the first step in 38

× 7 is 'thirty multiplied by seven', not 'three times seven', although the relationship 3 × 7

should be stressed.

Most children should be able to use this

expanded method for TU × U by the end of Year 4.

STAGE 4: SHORT MULTIPLICATION

The recording is reduced further, with carry

digits recorded below the line.

If, after practice, children cannot use the

compact method without making errors, they should return to the expanded format of stage

3.

The step here involves adding 210 and 50

mentally with only the 5 in the 50 recorded. This highlights the need for children to be able to add

a multiple of 10 to a two-digit or three-digit number mentally before they reach this stage.

STAGE 5: TWO-DIGIT BY TWO-DIGIT PRODUCTS

Extend to TU × TU, asking children to

estimate first. Start with the grid method. The partial

products in each row are added, and then the

two sums at the end of each row are added to find the total product.

As in the grid method for TU × U in stage 4,

the first column can become an extra top row as a stepping stone to the method below.

56 × 27 is approximately 60 × 30 = 1800.

Reduce the recording, showing the links to the

grid method above.


Reduce the recording further.

The carry digits in the partial products of 56 ×

20 = 120 and 56 × 7 = 392 are usually

carried mentally. The aim is for most children to use this long

multiplication method for TU × TU by the end

of Year 5.


29

Method Example

STAGE 6: THREE-DIGIT BY TWO-DIGIT PRODUCTS

Extend to HTU × TU asking children to

estimate first. Start with the grid method. It is better to place the number with the most

digits in the left-hand column of the grid so

that it is easier to add the partial products.


Reduce the recording, showing the links to the

grid method above.

This expanded method is cumbersome, with

six multiplications and a lengthy addition of numbers with different numbers of digits to

be carried out. There is plenty of incentive to move on to a more efficient method.

Children who are already secure with

multiplication for TU × U and TU × TU should

have little difficulty in using the same method

for HTU × TU. Again, the carry digits in the partial products

are usually carried mentally.


WRITTEN METHODS FOR DIVISION OF WHOLE NUMBERS




method of calculation for division which they know they can rely on when mental methods are not

appropriate.

These notes show the stages in building up to long division through Years 4 to 6 - first long division

TU ÷ U, extending to HTU ÷ U, then HTU ÷ TU, and then short division HTU ÷ U.

To divide successfully in their heads, children need to be able to:

understand and use the vocabulary of division - for example in 18 ÷ 3 = 6,the 18 is the

dividend, the 3 is the divisor and the 6 is the quotient

partition two-digit and three-digit numbers into multiples of 100, 10 and 1 in different ways

recall multiplication and division facts to 10 × 10, recognise multiples of one-digit numbers

and divide multiples of 10 or 100 by a single-digit number using their knowledge of division

facts and place value

30

Method Example

know how to find a remainder working mentally - for example, find the remainder when 48 is

divided by 5

understand and use multiplication and division as inverse operations.


alongside their learning and use of an efficient written method for division.

To carry out written methods of division successful, children also need to be able to:

understand division as repeated subtraction

estimate how many times one number divides into another - for example, how many sixes

there are in 47, or how many 23s there are in 92

multiply a two-digit number by a single-digit number mentally

subtract numbers using the column method.

STAGE 1: MENTAL DIVISION USING PARTITIONING

Mental methods for dividing TU ÷ U can be

based on partitioning and on the distributive law of division over addition. This allows a

multiple of the divisor and the remaining

number to be divided separately. The results are then added to find the total quotient.

Many children can partition and multiply with

confidence. But this is not the case for division. One reason for this may be that

mental methods of division, stressing the correspondence to mental methods of

multiplication, have not in the past been given

enough attention. Children should also be able to find a

remainder mentally, for example the

remainder when 34 is divided by 6.

One way to work out TU ÷ U mentally is to partition TU into a multiple of the divisor plus the

remaining ones, then divide each part separately.

Informal recording in Year 4 for 84 ÷ 7 might be:

In this example, using knowledge of multiples, the 84 is partitioned into 70 (the highest multiple

of 7 that is also a multiple of 10 and less than 84) plus 14 and then each part is divided

separately using the distributive law.

Another way to record is in a grid, with links to the grid method of multiplication.

As the mental method is recorded, ask: 'How many sevens in seventy?' and: 'How many

sevens in fourteen?'

Also record mental division using partitioning:

31

Method Example

Remainders after division can be recorded

similarly.

STAGE 2: SHORT DIVISION OF TU ÷ U

'Short' division of TU ÷ U can be introduced

as a more compact recording of the mental method of partitioning.

Short division of two-digit number can be

introduced to children who are confident with

multiplication and division facts and with subtracting multiples of 10 mentally, and

whose understanding of partitioning and place value is sound.

For most children this will be at the end of

Year 4 or the beginning of Year 5.

The accompanying patter is 'How many threes

divide into 80 so that the answer is a multiple of 10?' This gives 20 threes or 60, with 20

remaining. We now ask: 'What is 21 divided by three?' which gives the answer 7.

For 81 ÷ 3, the dividend of 81 is split into 60, the highest multiple of 3 that is also a multiple 10

and less than 81, to give 60 + 21. Each number

is then divided by 3.

The short division method is recorded like this:

This is then shortened to:

The carry digit '2' represents the 2 tens that have

been exchanged for 20 ones. In the first

recording above it is written in front of the 1 to show that 21 is to be divided by 3. In second it is

written as a superscript.

The 27 written above the line represents the

answer: 20 + 7, or 2 tens and 7 ones.

STAGE 3: 'EXPANDED' METHOD FOR HTU ÷ U

This method is based on subtracting multiples

of the divisor from the number to be divided,

the dividend. For TU ÷ U there is a link to the mental

method.

As you record the division, ask: 'How many

nines in 90?' or 'What is 90 divided by 9?' Once they understand and can apply the

method, children should be able to move on

from TU ÷ U to HTU ÷ U quite quickly as the

principles are the same. This method, often referred to as 'chunking',

32

Method Example

is based on subtracting multiples of the

divisor, or 'chunks'. Initially children subtract several chunks, but with practice they should

look for the biggest multiples of the divisor

that they can find to subtract. Chunking is useful for reminding children of

the link between division and repeated

subtraction.

However, children need to recognise that

chunking is inefficient if too many subtractions

have to be carried out. Encourage them to

reduce the number of steps and move them

on quickly to finding the largest possible

multiples.

The key to the efficiency of chunking lies in

the estimate that is made before the chunking starts. Estimating for HTU ÷ U involves

multiplying the divisor by multiples of 10 to

find the two multiples that 'trap' the HTU dividend.

Estimating has two purposes when doing a

division: o to help to choose a starting point for the

division; o to check the answer after the calculation.

Children who have a secure knowledge of

multiplication facts and place value should be

able to move on quickly to the more efficient recording on the right.

To find 196 ÷ 6, we start by multiplying 6 by 10, 20, 30, … to find that 6 × 30 = 180 and 6 × 40

= 240. The multiples of 180 and 240 trap the

number 196. This tells us that the answer to 196 ÷ 6 is between 30 and 40.

Start the division by first subtracting 180, leaving

16, and then subtracting the largest possible multiple of 6, which is 12, leaving 4.

The quotient 32 (with a remainder of 4) lies between 30 and 40, as predicted.

STAGE 4: SHORT DIVISION OF HTU ÷ U

'Short' division of HTU ÷ U can be introduced

as an alternative, more compact recording. No chunking is involved since the links are to

partitioning, not repeated subtraction. The accompanying pattern is 'How many

threes in 290?' (the answer must be a multiple

of 10). This gives 90threes or 270, with 20

remaining. We now ask: 'How many threes in 21?' which has the answer 7.

Short division of a three-digit number can be

introduced to children who are confident with multiplication and division facts and with

subtracting multiples of 10 mentally, and

whose understanding of partitioning and place value is sound.

For most children this will be at the end of

Year 5 or the beginning of Year 6.

For 291 ÷ 3, because 3 × 90 = 270 and 3 × 100 = 300, we use 270 and split the dividend of 291

into 270 + 21. Each part is then divided by 3.

The short division method is recorded like this:

This is then shortened to:

33

Method Example

The carry digit '2' represents the 2 tens that have been exchanged for 20 ones. In the first

recording above it is written in front of the 1 to show that a total of 21 ones are to be divided by

3.

The 97 written above the line represents the answer: 90 + 7,or 9 tens and 7 ones.

STAGE 5: LONG DIVISION

The next step is to tackle HTU ÷ TU, which for most children will be in Year 6.

The layout on the right, which links to chunking,

is in essence the 'long division' method. Recording the build-up to the quotient on the left

of the calculation keeps the links with 'chunking'

and reduces the errors that tend to occur with the positioning of the first digit of the quotient.

Conventionally the 20, or 2 tens, and the 3 ones

forming the answer are recorded above the line, as in the second recording.

How many packs of 24 can we make from 560 biscuits? Start by multiplying 24 by multiples of

10 to get an estimate. As 24 × 20 = 480 and 24 × 30 = 720, we know the answer lies

between 20 and 30 packs. We start by

subtracting 480 from 560.

In effect, the recording above is the long division method, though conventionally the digits of the

answer are recorded above the line as shown below.

34

FUN MATHS ACTIVITIES TO DO AT HOME

FAVOURITE FOOD

Ask your child the cost of a favourite item of food.

Ask them to work out what 7 of them would cost, or 8 or 9.

How much change would there be from €50?

Repeat with his/her least favourite food.

What is the difference in cost between the two?

SALE OF THE CENTURY

When you go shopping, or see a shop with a sale on, ask your child to work out what some

items would cost with:

50% off

25% off

10% off

5% off

Ask your child to explain how she/he worked it out.

TV ADDICTS

Ask your child to keep a record of how long she/he watches TV each day of the week. Then ask

her/him to do this.

Work out the total watching time for the week.

Workout the average watching time for a day (that is, the total time divided by 7).

Instead of watching TV, you could ask them to keep a record of time spent eating meals, or playing

outdoors, or anything else they do each day. Then work out the daily average.

FOUR IN A LINE

Draw a 6 x 7 grid and fill it with numbers under 100.

Take turns.

Roll three dice, or roll one dice three times.

Use all three numbers to make a number on the grid.

You can add, subtract, multiply or divide the numbers, e.g. if you

roll 3, 4 and 5, you could make 3 x 4 – 5 = 7, 54 ÷ 3 = 18,

(4 + 5) x 3 = 27, and so on.

Cover the number you make with a coin or counter.

The first to get four of their counters in a straight line wins.

35

RHYMES

Make up rhymes together to help your child to remember the harder times-tables facts, e.g.

6 x 7 = 42 phew! 7 x 7 = 49 fine! 6 x 8 = 48 great!

RECIPES

Find a recipe for 4 people and rewrite it for 8 people, e.g.

4 people 8 people

125g flour 250 g flour

50g butter 100g butter

75g sugar 150 g sugar

30ml treacle 60 ml treacle

1 teaspoon ginger 2 teaspoons ginger

Can you rewrite it for 3 people? Or 5 people?

FOURS

Use exactly four 4s each time.

You can add, subtract, multiply or divide them.

Can you make each number from 1 to 100?

Here are some ways of making the first two numbers

1 = (4 + 4) ÷ (4 + 4)

2 = 4 ÷ 4 + 4 ÷ 4

THREE IN A ROW

For this game you need a calculator. Draw a line like this:

Take it in turns to choose a fraction, say 2/5. Use the calculator to convert it to a decimal (i.e.

2 ÷ 5 = 0.4) and mark your initials at this point on the line.

The aim of the game is to get 3 crosses in a row without any of the other player’s marks in

between.

Some of the fractions are harder to place than others, e.g. ninths.

36

FLOWERS

Take turns to think of a flower.

Use an alphabet code, A = 1, B = 2, C = 3... up to Z = 26.

Find the numbers for the first and last letters of your flower, e.g. for a ROSE, R = 18, E = 5.

Multiply the two numbers together, e.g. 18 x 5 = 90.

The person with the biggest answer scores a point.

The winner is the first to get 5 points.

When you play again you could think of animals, or countries.

JOURNEYS

Use the chart in the front of a road atlas that tells you the distance between places.

Find the nearest place to you.

Ask your child to work out how long it would take to travel to some place in Luxembourg or

neighbouring countries if you travelled at an average of 60 km per hour, i.e. 1 kilometre per

minute, e.g.

Luxembourg City to Trier: 47km 47 minutes

Luxembourg City to Brussels: 212km 3 hours and 32 minutes

Encourage your child to count in 60s to work out the answers mentally.

ONE MILLION EUROS

Assume you have €1 000 000 to spend or give away.

Plan with your child what to do with it, down to the last penny.

CARD GAME

Use a pack of playing cards. Take out the jacks, queens and kings.

Take turns.

Take a card and roll a dice.

Multiply the two numbers.

Write down the answer. Keep a running total.

The first to go over 301 wins!

37

REMAINDERS

Draw a 6 x 6 grid like this.

Choose the 7, 8, or 9 times table.

Take turns.

Roll a dice.

Choose a number on the board, e.g. 59. Divide it by the

tables number e.g. 7. If the remainder for 59 ÷ 7 is the same

as the dice number, you can cover the board number with a

counter or coin.

The first to get four of their counters in a straight line wins!

DOUBLES AND TREBLES

Roll two dice.

Multiply the two numbers to get your score.

Roll one of the dice again. If it is an even number, double your score. If it is an odd number,

treble your score.

Keep a running total of your score.

The first to get over 301 wins.

38

This is the Maths vocabulary that your child will be exposed to this year. We don’t expect you to

teach it to them, but would like you to be aware of the words that will be used in case your child

would like help or reassurance in their understanding. If English is not their first language, it will

enable you to be aware of the vocabulary they are learning.

* Words new to Year 5 are in red.

NUMBERS AND THE NUMBERING

SYSTEM

PLACE VALUE AND ORDERING

units, ones

tens, hundreds, thousands

ten thousand, hundred thousand, million

digit, one-, two- or three-, or four-digit

number

numeral

‘teens’ number

place, place value

stands for, represents

exchange

the same number as, as many as

equal to

Of two objects/amounts:

>, greater, more, larger, bigger

<, less, fewer, smaller

≥, greater than or equal to

≤, less than or equal to

Of three objects/amounts:

greatest, most, biggest, largest

least, fewest, smallest

one... ten... one hundred... one thousand

more/less

compare, order, size

ascending/descending order

first... tenth... twentieth

last, last but one

before, after

next

between, half way between

guess how many, estimate

nearly, roughly, close to, about the same as

approximate, approximately

≈, is approximately equal to

just over, just under

exact, exactly

too many, too few, enough, not enough

round (up or down), nearest

round to the nearest ten/hundred/ thousand

integer, positive, negative

above/below zero, minus

PROPERTIES OF NUMBERS AND NUMBER

SEQUENCES

number, count, how many?

odd, even

every other

how many times?

multiple of

digit

next, consecutive

sequence

continue

predict

pattern, pair, rule

relationship

sort, classify, property

formula

divisible (by), divisibility, factor, factorise

square number

one squared, two squared... (12, 22...)

prime, prime factor

FRACTIONS, DECIMALS, PERCENTAGES, RATIO

AND PROPORTION

part, equal parts

fraction, proper/improper fraction

mixed number

numerator, denominator

equivalent, reduced to, cancel

one whole

half, quarter, eighth

third, sixth, ninth, twelfth

fifth, tenth, twentieth, hundredth, thousandth

proportion, ratio

in every, for every

39

to every, as many as

decimal, decimal fraction

decimal point, decimal place

percentage, per cent, %

CALCULATIONS

ADDITION AND SUBTRACTION

add, addition, more, plus, increase

sum, total, altogether

score

double, near double

how many more to make...?

subtract, subtraction, take (away), minus,

decrease

leave, how many are left/left over?

difference between

half, halve

how many more/fewer is... than...?

how much more/less is...?

equals, sign, is the same as

tens boundary, hundreds boundary

units boundary, tenths boundary

inverse

MULTIPLICATION AND DIVISION

lots of, groups of

times, multiply, multiplication, multiplied by

multiple of, product

once, twice, three times... ten times...

times as (big, long, wide... and so on)

repeated addition

array, row, column

double, halve

share, share equally

one each, two each, three each...

group in pairs, threes... tens

equal groups of

divide, division, divided by, divided into

remainder

factor, quotient, divisible by

inverse

USING A CALCULATOR

calculator, display, key

enter, clear, sign change

constant, recurring memory, operation key

MAKING DECISIONS AND REASONING

pattern, puzzle

calculate, calculation

mental calculation

method, strategy

jotting

answer

right, correct, wrong

what could we try next’?

how did you work it out?

number sentence

sign, operation, symbol, equation

MONEY

money

coin, note

penny, pence, pound (£), cent, euro (€)

price, cost

buy, bought, sell, sold

spend, spent

pay

change

dear, costs more, more/most expensive

cheap, costs less, cheaper, less/least

expensive

how much...? how many...?

total, amount, value, worth

discount, profit, loss

currency

HANDLING DATA count, tally, sort, vote

survey, questionnaire

data, database

graph, block graph, line graph

pictogram,

represent

group, set

list, chart, bar chart, bar line chart

tally chart

table, frequency table

Carroll diagram, Venn diagram

label, title, axis, axes

diagram

most popular, most common

least popular, least common

40

mode, range, mean, average, median

statistics, distribution

maximum/minimum value

classify, outcome

PROBABILITY

fair, unfair

likely, unlikely, likelihood, equally likely

certain, uncertain

probable, possible, impossible

chance, good chance

poor chance, no chance

equal chance, even chance, fifty-fifty chance

risk, doubt

biased, random

MEASURES, SHAPE AND SPACE

MEASURES (GENERAL)

measure, measurement

size

compare

unit, standard unit

metric unit, imperial unit

measuring scale, division

guess, estimate

enough, not enough

too much, too little

too many, too few

nearly, roughly, about, close to

about the same as, approximately

just over, just under

LENGTH

length, width, height, depth, breadth

long, short, tall, high, low

wide, narrow, deep, shallow, thick, thin

longer, shorter, taller, higher... and so on

longest, shortest, tallest, highest... and so on

far, further, furthest, near, close

distance apart/between, distance to... from...

edge, perimeter, circumference

kilometre (km), metre (m)

centimetre (cm), millimetre (mm)

mile, yard, feet, foot, inches, inch

ruler, metre stick, tape measure, compasses

MASS

mass: big, bigger, small, smaller, balances

weight: heavy/light, heavier/lighter,

heaviest/lightest

weigh, weighs

tonne, kilogram (kg), half-kilogram, gram (g)

pound (lb), ounce (oz)

balance, scales

CAPACITY

capacity

full, half full

empty

holds, contains

litre (l), half-litre, centilitre (cl) millilitre (ml)

pint, gallon

container, measuring cylinder

AREA

area, covers, surface

square centimetre (cm2), square metre (m2)

square millimetre (mm2)

TIME

time

days of the week: Monday, Tuesday...

months of the year: January, February...

seasons: spring, summer, autumn, winter

day, week, fortnight, month

year, leap year, century, millennium

weekend, birthday, holiday

calendar, date, date of birth

morning, afternoon, evening, night

am, pm, noon, midnight

today, yesterday, tomorrow

before, after, next, last

now, soon, early, late, earliest, latest

quick, quicker, quickest, quickly

fast, faster, fastest, slow, slower, slowest,

slowly

old, older, oldest, new, newer, newest

takes longer, takes less time

how long ago? how long will it be to...?

how long will it take to...?

timetable, arrive, depart

hour, minute, second

41

o'clock, half past, quarter to, quarter past

clock, watch, hands

digital/analogue clock/watch, timer

24-hour clock, 12-hour clock

Greenwich Mean Time, British Summer Time

International Date Line

how often?

always, never, often, sometimes, usually

SHAPE AND SPACE

shape, pattern

flat, line

curved, straight

round

hollow, solid

corner

point, pointed

face, side, edge, end

sort

make, build, construct, draw, sketch

centre, radius, diameter

circumference, concentric, arc

net

surface

angle, right-angled

congruent

intersecting, intersection

plane

base, square-based

vertex, vertices

layer, diagram

regular, irregular

concave, convex

open, closed

tangram

3D SHAPES

3D, three-dimensional

cube, cuboid

pyramid

sphere, hemi-sphere, spherical

cone

cylinder, cylindrical

prism

tetrahedron, polyhedron, octahedron,

dodecahedron

2D SHAPES

2D, two-dimensional

circle, circular, semi-circle

triangle, triangular

equilateral triangle, isosceles triangle, scalene

triangle

square, rhombus

rectangle, rectangular, oblong

pentagon, pentagonal

hexagon, hexagonal

heptagon

octagon, octagonal

polygon

quadrilateral

kite

parallelogram, trapezium

PATTERNS AND SYMMETRY

size, bigger, larger, smaller

symmetrical

line of symmetry, axis of symmetry

line symmetry, reflective symmetry

fold

match

mirror line, reflection, reflect

pattern, repeating pattern, translation

POSITION DIRECTION AND MOVEMENT

position

over, under, underneath

above, below, top, bottom, side

on, in, outside, inside, around

in front, behind, front, back

before, after, beside, next to

opposite, apart

between, middle, edge, centre

corner

direction

journey, route, map, plan

left, right

up, down, higher, lower

forwards, backwards, sideways, across

close, far, near

along, through, to, from, towards, away from

ascend, descend

grid, row, column

42

origin, coordinates

clockwise, anti-clockwise

compass point, north, south, east, west (N, S,

E, W)

north-east, north-west, south-east, south-west

(NE, NW, SE, SW)

horizontal, vertical, diagonal

parallel, perpendicular

x-axis, y-axis

quadrant

movement

slide, roll

whole turn, half turn, quarter turn

rotate, rotation

angle, ...is a greater/smaller angle than

right angle, acute, obtuse, reflex

degree

straight line

stretch, bend

ruler, set square

angle measurer, compasses, protractor

INSTRUCTIONS listen, join in, say, recite

think, imagine, remember

start from, start with, start at

look at, point to, show me

put, place

arrange, rearrange

change, change over

adjusting, adjust

split, separate

carry on, continue, repeat

what comes next? predict

describe the pattern, describe the rule

find, find all, find different

investigate

choose, decide

collect

use, make, build, construct, bisect

tell me, define, describe, name, pick out,

identify

discuss, talk about

explain

explain your method/answer/reasoning

give an example of...

show how you...

show your working

justify

make a statement

read, write, record

write in figures

present, represent

interpret

trace, copy

complete, finish, end

fill in, shade, colour

label, plot

tick, cross

draw, sketch

draw a line between, join (up), ring, arrow

cost, count, tally

calculate, work out, solve, convert

investigate, interrogate (data), question, prove

answer

check

GENERAL same, identical, different

missing number(s)

number facts, number pairs, number bonds

greatest value, least value

number line, number track

number square, hundred square

number cards, number grid

abacus

counters, cubes, blocks, rods

die, dice, spinner

dominoes

pegs, peg board, pin board

geo-strips

same way, different way

best way, another way

in order, in a different order

not, all, every, each

43

INTERNATIONAL PRIMARY CURRICULUM TOPICS

(IPC TOPICS)

TERM 1

IPC Topic Corresponding Science Topic

What a Wonderful World More about Dissolving; Reversible and Irreversible Changes

What a Wonderful World Forces in Action

TERM 2


What Price is Progress How we see Things

What Price is Progress Microorganisms

TERM 3


Black Gold Changing Circuits

The Holiday Show Interdependence and Adaptation

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PR

IVA

CY

AN

D S

ECU

RIT

Y R

ISK

S?Yo

ur c

ompu

ter

is a

t ris

k fr

om s

pyw

are,

vir

uses

and

oth

er in

vasi

ve

prog

ram

mes

if y

ou a

re s

hari

ng fi

les

on n

on-r

egul

ated

site

s. P

rote

ct

your

com

pute

r an

d pe

rson

al fi

les

by v

isiti

ng r

eput

able

site

s an

d by

in

stal

ling

a fi r

ewal

l and

ant

i-vi

rus

soft

war

e.

For

furt

her

info

rmat

ion

visi

t: w

ww

.chi

ldne

t.co

m/d

ownl

oadi

ng

MO

BIL

E P

HO

NE

S W

hils

t mob

ile d

evic

es o

ffer

op

port

uniti

es in

term

s of

co

mm

unic

atio

n, in

tera

ctio

n an

d en

tert

ainm

ent,

child

ren

can

be a

t ri

sk o

f acc

essi

ng a

nd d

istr

ibut

ing

inap

prop

riat

e co

nten

t and

imag

es

and

talk

ing

to s

tran

gers

aw

ay fr

om

pare

ntal

sup

ervi

sion

. Chi

ldre

n ca

n re

ceiv

e ab

usiv

e te

xt m

essa

ges,

be

vuln

erab

le to

com

mer

cial

mob

ile p

hone

pre

ssur

es a

nd r

un u

p la

rge

phon

e bi

lls.

It is

ver

y im

port

ant t

o en

cour

age

your

chi

ldre

n no

t to

give

out

thei

r m

obile

num

bers

to s

tran

gers

eith

er o

nlin

e or

in r

eal l

ife a

nd h

elp

them

to u

se th

eir

mob

ile s

afel

y an

d re

spon

sibl

y.

For

mor

e ad

vice

vis

it: w

ww

.cha

tdan

ger.

com

/mob

iles

GA

ME

S C

ON

SOLE

S A

ND

HA

ND

HEL

D G

AM

ING

DE

VIC

ES

Hom

e en

tert

ainm

ent c

onso

les

such

as

the

Play

stat

ion,

Wii

and

Xbox

ar

e ca

pabl

e of

con

nect

ing

to th

e in

tern

et a

s ar

e ha

ndhe

ld g

ames

co

nsol

es li

ke th

e D

Si a

nd P

lays

tatio

n Po

rtab

le.

For

mor

e ad

vice

on

onlin

e ga

min

g an

d ho

w to

sta

y sa

fe v

isit

ww

w.c

hild

net.

com

/dow

nloa

ds/O

nlin

e-ga

min

g.pd

f

THE

INTE

RN

ET –

ALW

AYS

CHA

NG

ING

K

eepi

ng u

p to

dat

e w

ith c

hild

ren’

s us

e of

tech

nolo

gy is

cha

lleng

ing

for

man

y ad

ults

. It c

an b

e ha

rd to

sup

ervi

se w

hat y

oung

peo

ple

are

view

ing

and

crea

ting

onlin

e, w

ho th

ey a

re c

hatt

ing

to a

nd te

xtin

g,

and

wha

t the

y ar

e do

wnl

oadi

ng.

WH

AT A

RE

THE

RIS

KS?

Th

e ri

sks

for

child

ren

whe

n us

ing

the

inte

rnet

and

mob

ile p

hone

s in

clud

e in

appr

opri

ate:

CO

NTA

CT

Pote

ntia

l con

tact

from

som

eone

onl

ine

who

may

wis

h to

bul

ly o

r ab

use

them

. It i

s im

port

ant f

or c

hild

ren

to r

emem

ber

that

onl

ine

cont

acts

may

not

be

who

they

say

they

are

. Chi

ldre

n m

ust k

eep

pers

onal

det

ails

pri

vate

and

agr

ee n

ot to

mee

t uns

uper

vise

d w

ith

anyo

ne th

ey h

ave

only

con

tact

ed v

ia th

e in

tern

et. I

t’s im

port

ant

that

you

dis

cuss

with

you

r ch

ild w

ho th

ey c

an r

epor

t ina

ppro

pria

te

conv

ersa

tions

, mes

sage

s an

d be

havi

ours

to a

nd h

ow.

CO

ND

UC

TCh

ildre

n m

ay b

e at

ris

k be

caus

e of

thei

r ow

n an

d ot

hers

’ onl

ine

beha

viou

r, s

uch

as th

e pe

rson

al in

form

atio

n th

ey m

ake

publ

ic. T

hey

may

als

o be

com

e ei

ther

per

petr

ator

s or

targ

ets

of c

yber

bully

ing

(the

use

of i

nfor

mat

ion

and

com

mun

icat

ion

tech

nolo

gies

to

delib

erat

ely

upse

t som

eone

els

e).

CO

NTE

NT

Inap

prop

riat

e m

ater

ial i

s av

aila

ble

to c

hild

ren

onlin

e.Co

nsid

er u

sing

fi lt

erin

g so

ftw

are

and

agre

e gr

ound

rul

es a

bout

w

hat s

ervi

ces

you

are

happ

y fo

r yo

ur c

hild

ren

to u

se. G

ive

them

st

rate

gies

for

deal

ing

with

any

con

tent

they

are

not

com

fort

able

w

ith –

suc

h as

turn

ing

off t

he c

ompu

ter

scre

en a

nd te

lling

an

adul

t th

ey tr

ust.

Ther

e ca

n be

lega

l con

sequ

ence

s fo

r co

pyin

g co

pyri

ghte

d co

nten

t. Yo

ung

peop

le n

eed

to b

e aw

are

that

pla

giar

isin

g co

nten

t and

do

wnl

oadi

ng c

opyr

ight

ed m

ater

ial w

ithou

t the

aut

hor’

s pe

rmis

sion

is

ille

gal.

CO

MM

ERCI

ALI

SMYo

ung

peop

le’s

pri

vacy

can

be

inva

ded

by a

ggre

ssiv

e ad

vert

isin

g an

d m

arke

ting

sche

mes

.

Enco

urag

e yo

ur c

hild

ren

to k

eep

thei

r pe

rson

al in

form

atio

n pr

ivat

e,

lear

n ho

w to

blo

ck p

op-u

ps a

nd s

pam

em

ails

, and

use

a fa

mily

em

ail

addr

ess

whe

n fi l

ling

in o

nlin

e fo

rms.

CYB

ERB

ULL

YIN

GN

ew te

chno

logi

es p

rovi

de a

n ap

pare

ntly

ano

nym

ous

met

hod

by

whi

ch b

ullie

s ca

n to

rmen

t the

ir v

ictim

s at

any

tim

e of

the

day

or

nigh

t. W

hile

the

bully

ing

may

not

be

phys

ical

, the

vic

tim m

ay r

ecei

ve

an e

mai

l, ch

at o

r te

xt m

essa

ges

or b

e th

e ta

rget

of u

nfav

oura

ble

web

site

s or

soc

ial n

etw

orki

ng p

rofi l

es th

at m

ake

them

feel

em

barr

asse

d, u

pset

, dep

ress

ed o

r af

raid

. Thi

s ca

n da

mag

e th

eir

self-

este

em a

nd p

ose

a th

reat

to th

eir

psyc

holo

gica

l wel

l-be

ing.

For

mor

e ad

vice

on

prev

entin

g an

d re

spon

ding

to c

yber

bully

ing

see:

w

ww

.dig

izen

.org

DO

WN

LOA

DIN

G, P

2P A

ND

FIL

E-SH

AR

ING

AC

CESS

ING

TH

E IN

TER

NET

ON

O

THER

DE

VICE

S Th

e in

tern

et c

an b

e ac

cess

ed th

roug

h m

obile

pho

nes,

han

dhel

d ga

min

g de

vice

s an

d ga

min

g co

nsol

es a

s w

ell a

s ot

her

devi

ces

like

the

iPod

Tou

ch a

nd iP

ad. I

nter

net s

afet

y is

sues

app

ly to

thes

e in

tera

ctiv

e te

chno

logi

es.

44

NOTES

45

NOTES

46

NOTES

St George’s International School, Luxembourg A.S.B.L

11, rue des PeupliersL-2328 Luxembourgtel: +352 42 32 24fax: +352 42 32 34www.st-georges.lu

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