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National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

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Year 5 - Addition and Subtraction

New Curriculum

  • add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
  • add and subtract numbers mentally with increasingly large numbers
  • use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
  • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Non-Statutory Guidance

Pupils practice using the formal written methods of columnar addition and subtraction with increasingly large numbers to aid fluency (see Appendix 1).

They practice mental calculations with increasingly large numbers to aid fluency

(e.g. 12 462 – 2 300 = 10 162).

Links and Resources

Connections within Mathematics

Making connections to this topic in adjacent year groups

Year 4

  • Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
  • Estimate and use inverse operations to check answers to a calculation
  • Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why

Year 6

  • add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
  • add and subtract numbers mentally with increasingly large numbers
  • use rounding to check answers to calculations and determine, in the context of a 
problem, levels of accuracy
  • solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Cross-curricular and real life connections

Learners will encounter addition and subtraction when focusing on:

Money – when required to add prices, calculate change, add surcharges or interest, or subtract discounts;

Measurement – when required to add lengths, calculate remaining distance in a journey, find how much more/less liquid is needed, add quantities when cooking, calculate perimeters of regular and irregular shapes, work out time differences e.g. how many days until Christmas, how many minutes until break time etc.;

Statistics – comparing and combining sets of data, interpreting data.

Learners will encounter addition and subtraction in:

Science – when adding and subtracting test measurements;

History – when comparing historical data from different periods, calculating the duration of monarchs' reign;

Geography – when comparing populations, temperatures and other data for contrasting regions around the world.

Ian Thompson explores the strategies used by children when calculating mentally and concludes that some are particularly important for later work.

Thompson, I. (1999). Mental Calculation Strategies for Addition and Subtraction. Mathematics in School. 28 (5), 1-4. Last accessed 2nd September 2013.

A brief exploration of some of the reasons for difficulties with subtraction and the connections which need to be made for a fuller understanding.

Devon Primary Maths Team. Why does Subtraction seem Difficult to Teach or Learn.Last accessed 20th August 2013.

A study of the calculation strategies used by Year 5 children in practice, which argues that children need mental strategies as well as written algorithms.

Borthwick, A. and Harcourt-Heath, M.. (2007). Calculation Strategies Used by Year 5 Children. Proceedings of the British Society for Learning Mathematics. 27 (1), 12-17. Last accessed 2nd September 2013.

Programme of Study statements Activities
A B C D E
Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)        
Add and subtract numbers mentally with increasingly large numbers        
Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy      
Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why        

Activity A – Two and Two

Challenging activity which requires finding the numbers which each letter stands for in an alphanumeric question

Addition

Activity B- Reach 100

A challenging activity from Nrich requiring the children to place digits in a 2x2 grid so that the four 2-digit numbers made, total 100. Can they extend it to a 3x3 grid? What might their total be? What about a 4x4 grid? Can their reach a total that is a multiple of 1000?

Activity C- Rounding Spreadsheets

‘Rounding’ and ‘Rounding Decimals’ are two spreadsheets from this wider set, produced by the National Strategies, and now hosted in the STEM Centre E-library. They allow a number of a given size to be generated and a level or accuract for the number to be rounded to. The rounded number can then be revealed. Teachers’ notes are also included.

Activity D- Ordering the Problems

Children could be provided with a variety of one and two-step problems. They can be asked to estimate the answers to each, then order the problems according to their estimates.

Activity E-CIMT Problems (pdf)

Pages 70 – 75 of this workbook contain a variety of multi-step problems

Write the Problems

Children could be given written calculations such as 23 456 + 46 019. They could be asked to write an imaginative problem that would require this calculation. Can they extend their problem to make it a multi-step problem?

As a variation of this, give children a selection of cards. Some should contain word problems and others should contain the corresponding calculations. Children should match the problems to the appropriate calculation.

Other problem solving opportunities

Wherever possible, try to link problems to cross-curricular topics, so that children get used to solving problems with a real-life context.

Display a ‘problem of the week’ in the classroom, with an opportunity for pupils to respond, perhaps by posting their answer into a box or container.

Examples of what children should be able to do, in relation to each (boxed) Programme of Study statement

add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)

Children should be able to use standard written methods for addition and subtraction,

e.g. calculate 14 136 + 3258 + 487 or 23 185 – 2078

Use written methods to find missing numbers in addition and subtraction calculations,

e.g. 6432 + □ = 8025

Use written methods to add and subtract numbers with different numbers of digits,

e.g. Find all the different totals that can be made using any three of these five numbers:
14 721, 76, 9534, 788, 6

add and subtract numbers mentally with increasingly large numbers

Children should be able to respond rapidly to oral or written questions, explaining the strategy used,

e.g. 750 take away 255, take 400 from 1360, 4500 minus 1050, subtract 3250 from 7600, 1800 less than 3300, 4000 less than 11 580

Derive quickly related facts,

e.g. 80 + 50 = 130, 130 – 50 = 80, 800 + 500 = 1300, 1300 – 800 = 500

Derive quickly number pairs that total 100 or pairs of multiples of 50 that total 1000,

e.g. 32 + 68 = 100 or 150 + 850 = 1000

Identify and use near doubles,

e.g. work out 28 + 26 = 54 by doubling 30 and subtracting first 2, then 4, or by doubling 26 and adding 2

Add or subtract the nearest multiple of 10, 100 or 1000 and adjust,

e.g. adding or subtracting 9, 19, 29 ... to/from any two-digit number

Work out mentally by counting up from a smaller to a larger number e.g. 8000 – 2785 is 5 + 10 + 200 + 5000 = 5215

Understand and use language associated with addition and subtraction, e.g. difference, sum, total

use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

Children should be able to use rounding to approximate and check e.g. 2593 + 6278 must be more than 2500 + 6200, 2403 – 1998 is about 2400 – 2000

Write approximate answers to calculations, e.g. write an approximate answer for 516 ÷ (15 + 36)

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

Children should be able to choose the appropriate operations to solve multi-step problems, decide whether the calculations can be done mentally or using a written method and explain and record how the problem was solved using numbers, signs and symbols.

e.g. 13 502 people were at the match last week and there are 2483 more this week, how many more people need to attend to bring the total to the club’s target of 20 000 people?

Identify and obtain the necessary information to solve the problem and determine if there is any important information missing,

e.g. calculating total cost of a holiday for a family, given prices for adults and children and surcharges for particular resorts.

NCETM

A suite of videos looking at elements of progression in subtraction in KS2, with a particular focus on the vertical written method.

STEM

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