Calculation Progression

Ysgol Llangatwg

Purpose of the Meeting1.To make parents aware of the

requirements of the Foundation Phase and the National Curriculum.

2.To demonstrate some strategies used in school, so parents can support their children at home.

3.To suggest ways parents can help their children at home.

4.To make parents aware of the Literacy and Numeracy Framework.

5.To share examples of National Numeracy tests.

Number & Calculations Foundation Phase Outcomes 1-

6Outcome 4Children use mathematics as an integral part of classroom activities. They count, order, add and subtract numbers when solving problems involving up to 10 objects. They count on and back in steps of different sizes and from different numbers. They can read and write numbers up to 10.Outcome 5Children choose the appropriate operation when solving addition or subtraction problems. They use mental calculation strategies to solve number, money and measures problems. They count sets of objects reliably, and use mental recall of number facts to 10 to add or subtract larger numbers. They order numbers to 100. Outcome 6Children organise their work and try different approaches. They use place value in numbers up to 1000 to make approximations. They develop further mental strategies for adding and subtracting numbers with at least two digits. They use mental recall of the 2, 3, 4,5 and 10 multiplication tables in solving whole-number problems involving multiplication and division, including those giving rise to remainders.

Outcome 1Children participate, follow, respond to and join in with familiar number rhymes, stories, songs, activities and games. They show an awareness of number activities, recite, sign or indicate one or more numbers to five and count or indicate two objects.Outcome 2Children use mathematics in day-to-day activities and in their play, responding appropriately to key vocabulary and questions. They join in rote counting of numbers from 1-10. They recognise and name numbers 1 to 3, and count up to three objects reliably. They record numbers initially by making marks or drawing pictures. They begin to develop an understanding of one-to-one correspondence by matching pairs of different objects or pictures. They understand the concept of ‘one more’.Outcome 3Children use familiar words in practical situations. They rote count to beyond 10, and onwards from a given small number. They carry out simple addition using 1-5 and understand that zero means none. They recognise and try to record numerals from one to nine. They understand the concept of ‘one less’.

Number & Calculations Progression Level 1-3 are the same as Foundation Phase

Outcomes 4, 5 and 6.

LEVEL 3Pupils organise their work, check results, and try different approaches. They talk about and explain their work. They use and interpret mathematical symbols and diagrams. They find particular examples that satisfy a general statement. They develop further mental strategies for adding and subtracting numbers with at least two digits. They use mental recall of the 2, 3, 4,5 and 10 multiplication tables in solving whole-number problems involving multiplication and division, including those giving rise to remainders. LEVEL 4Pupils develop their own strategies for solving problems, and present information and results systematically. They search for a solution by trying out ideas of their own. They use their understanding of place value to multiply and divide whole numbers by 10 and 100. They use a variety of mental and written methods for computation, including recall of multiplication facts up to 10x10. They add and subtract decimal to two places. They check their results are reasonable by considering the context or the size of the numbers. They use simple fractions and percentages to describe approximate parts of a whole. They recognise and describe number patterns and relationships and use simple formulae expressed in words.

LEVEL 5Pupils identify and obtain information to solve problems, and check whether their results are sensible in the context of the problem. They describe situations mathematically using symbols, words and diagrams and draw their own conclusions, explaining their reasoning. They make general statements of their own, based on available evidence. They use their understanding of place value to multiply and divide whole numbers and decimals. They order, add and subtract negative numbers. They check their solutions by applying inverse operations or estimating using approximations. They calculate fractional or percentage parts or quantities and measurements. They construct and use formulae involving one or two operations. LEVEL 6Pupils solve complex problems by breaking them down into smaller tasks, and give some mathematical justifications to support their methods, arguments or conclusions. They interpret, discuss and synthesise information presented in a variety of mathematical forms. They use trial-and improvement methods involving approximating and ordering decimals. They calculate one number as a fraction or percentage of another. They use the equivalences between fractions, decimals and percentages and calculate using ratios in appropriate situations. They find and describe in words the rule for the next term or nth term of a sequence where the rule is linear, and they formulate and solve a variety of simple linear equations. They represent mappings expressed algebraically.

• Singing songs and counting games• Finding numbers around the classroom• Chanting numbers-to 5 then 10.• Count two objects.• Identify 1 more than a number to 5.• Use mathematics in their daily play, both

inside and out and in roleplay. • Recognise and name numbers 1-3 and

reliably count three objects.• Begin to record numbers by making marks

or drawing.• Begin to make one to one correspondence

and match pairs of different objects together.

• Use ‘one more then’ and ‘one less than’ in their play.

• Develop mathematical language and use it in practical situations eg add, together.

• Rote count to beyond 10 from various numbers.

• Understand zero means none.• Use simple addition using numbers to 5.

Progression in Number/Calculation

Foundation Phase• Use mathematics across all classroom activities. (Role play)

• Count, order, add and subtract numbers when solving problems.

• They count on/back in steps of different sizes and from different numbers.

• Read/write numbers up to 10.• Choose the appropriate ‘sum’ when solving

addition/subtraction problems.• Use mental calculation strategies to solve

problems.• Count sets of objects reliably.• Use mental recall of number facts to 10 to

add/subtract.• Order numbers up to 100.• Use halves and quarters in practical situations.• Organise their work and try different approaches.• Use place value to 1000 to make approximations.• Develop more strategies for adding/subtracting

numbers with at least 2 digits.• Use mental recall of 2,3,5 and 10 times tables in

solving whole number.• Use multiplication and division• Use decimal notation problems and those giving

rise to remainders.

RANGE• Develop an interest in number.• Recognise importance of certain numbers and numerals to

them selves eg. Birthdays, house numbers.• Use number names accurately, matching the symbol to the

sound.• Count, read, write, compare and order numbers, and

appreciate the conservation of number.• Use numbers naturally in their play and daily activities,

including number rhymes, songs, stories and counting activities from Wales and around the World.

• Experiment with numbers, observe numbers and patterns in the environment and everyday life.

• Begin to develop their mental calculation strategies, during counting and grouping activities, games and through day-to-day classroom activities.

• Progress from counting on or back in steps, to mental mathematics involving all four operations with small numbers, using their own methods to record their calculations.

• Explore patterns in numbers, tables and sequences.• Begin to understand the relationships between addition and

subtraction, between multiplication and division, between halving and doubling.

• Match pairs of objects in practical contexts, leading to an understanding of one-to-one correspondence.

Number and Calculation in the Foundation Phase

SKILLS• Select and use appropriate mathematical ideas,

equipment and materials to solve practical problems.• Develop a variety of mental approaches and

strategies.• Estimate solutions to calculations, check their answers

in various ways.• Develop their mathematical language.• Present their work orally, pictorially and in written

form, moving on to using more formal methods of recording when they developmentally ready.

• Devise and refine informal, personal methods of recording mental calculations, gradually moving to using words and symbols in number sentences.

• Develop a variety of mental and written strategies of computation.

• Interpret solutions to calculations within the context of the given problem.

• Recognise patterns, sequences and relationships through practical activities and discussion.

• Investigate repeating patterns and relationships and make simple predictions.

Progression in Calculations

Y3• TU ± U• TU ± near multiple of 10• HTU – HTU (small difference)• U / TU x 10 / 100• TU x U (partition)• TU ÷ U (linked to recall facts)• Fractions of amounts (eg ¼ of

£24)• Rounding for estimation

Y4• TU ± TU• +/– multiples of 10 / 100• ThHTU – ThHTU (small

difference)• x / ÷ by 10 / 100 (whole

no. answer)• M of 10 x U (including

near multiples)• Divide using factors (eg

2400 ÷ 20)• Solve problems involving

money, measures & time• Fractions of quantities

(eg 2/3 of 24 cm)

Progression in Calculations

Y5• +/– decimals: apply known

facts & bridge through landmarks

• ThHTU – ThHTU (eg 7012 – 3984)

• x / ÷ whole nos. & decimals by 10 / 100 / 1000

• Rounding for estimation (integers & decimals)

• Integers x / ÷ U• Fractions of amounts

(eg ¾ of £220)

Y6

• Mental multiplication and division with decimals (U.t x / U)

• Efficient written methods: - add and subtract whole numbers and decimals;

- multiply and divide whole numbers and decimals by a one-digit number, TU x TU and HTU x TU

Support for Calculations• Number lines• Numicon

• 100 squares• Jottings

• Partitioning• Tables and division facts ( trios)

• Adjusting• Estimating• Rounding

• Inverse operations• Mutilink

• EASE Numberline

• Key Resources : Piece of string, bead strings, Ruler Number Lines

Important Things For Children To Know

1. Make one to one correspondence2. Recognise numbers3. Number bonds to 10 and 204. Symbols and equations5. Tables6. Counting in various ways eg2s, 5s and 10s7. Tens and units8. Understand place value-including using zero eg 1029. Important mathematical language eg different ways

of saying add/subtract10.More than/less than11.Estimating

Addition/Subtraction in the Foundation Phase

• Counting , grouping, combining and subtracting objects

• Lots of practical experiences through play• Introducing the language of maths through

practical every day activities• The use of the outdoors and role play• Demonstrating how to organise/write

calculations• Use of OWN numberlines

Addition

Number line

Partitioning 15 + 42 = • 10 + 40 = 50• 5 + 2 = 7• 50 + 7 =57

Written Methods-Compact vertical 233 +416 649

297+165

462 11

Subtraction-1Number Line20 – 5 = 1520 - 6 = 14

Partitioning98 – 62 = 3698 - 60 - 2 = 36

Find the difference by counting on/back depending on the numbers. (Estimating)20 - 8 = Count back from 20

20 - 18 = Count on from 18

6

Subtraction-2 Written Method– Decomposition

Without having to regroup tens/units

378 -254 124

With regrouping

3 5 8 -1 7 9 1 7 9

1

2 14

MultiplicationRepeated Addition

5 x 3 or 3 x 5

Partition and Combine Method17 x 410 x 4 = 40 7 X 4 = 2840 + 28 = 68

Expanded vertical 43 x 6 18 ( 3 x 6) 240 (40 x 6) 258

o 3 6 9 12 15

1 2 3 4 5

DivisionSharing-practically -10 sweets shared between 2.Counting in 2s, 5s,10s etc.Chanting tables eg 1 x 2 =2

Learning Times Tables2 x 5 = 10How many 5’s in 10?10 5 = 2

Division Signs / Language 10 2= 10 2 With bigger numbers, multiply up eg. 540 divided by 24.

2

102

Resources We Use

• Fingers!

• Mutilink

• Numberlines• 100 squares• Numicon• Multiplication grids• Counters/cubes• Base 10

Lessons – What Do They Look Like ?

Rec -Y6 – children have a daily numeracy lesson ( mental/oral, main input, differentiated group work or independent task, plenary)

Foundation Phase – maths happens throughout the day, children explore maths through a range of child initiated and adult led activitiesThe Numeracy Framework places a firm emphasis on maths being used across the curriculum

• http://www.bbc.co.uk/schools/bitesize/• http://www.woodlands-junior.kent.sch.uk/maths/• http://ictgames.com/resources.html• www.iboard.co.uk• Wide variety of apps for tablets etc.

Useful Websites

How You Can Help Your Child At Home1. Talk to you child about his/her maths homework. Encourage

them to talk through what they are doing and explain why they have chosen to do it that way.

2. Counting and making one-to-one correspondence.3. Importance of adding on and taking away 1, 2 etc.4. Help your child to learn number bonds to 10/20.5. Help your child to learn tables-in the car, out for a walk.

Anywhere!6. Use money with your child.

Read the question carefully

Check you understand what it means. Work out the problem

What if I..?CalculateDo the sum.Have you done all the steps?What is the answer?Is it close to your estimate? 

Highlight all the important information

Underline all the important words.What are you trying to find out?Is there more than one step?What information don’t you need? 

How did you do it? Think about, or tell someone else, how you did it.Why did you do it like that? 

What do I need to do to solve the problem?

How are you going to work it out?Have a sensible guess/estimate.What sort of sum is it?Where shall we start?Is there a pattern?Is there anything that might help?

Check Is your answer reasonable?Have you answered the question?Does it make sense?

PROBLEM SOLVINGThese steps may help your child to solve the problem.

 

USEFUL MATHEMATICAL LANGUAGE

+ -plus

altogethertotal

makesand

sum of

morecombine

addincreasecount on

take awayminus

count backleaves

decreaseless

differencehow many left?

X

repeated additiongroups of

lots of times

multiplyproduct

pairdouble

sharedividegroupsplit

share equallydivisible

divided byWhat fraction of?

What percentage of?

=

is the same astotalsequalsmakes

balances