nrich problem solving addition and subtraction

National Curriculum Resource Tool

Materials to support teachers and schools in embedding the National Curriculum

• National Curriculum Tool

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

• Making connections
• Exemplification

Connections within Mathematics

Making connections to this topic in adjacent year groups.

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

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.

• Mental Calculation Strategies for Addition and Subtraction (pdf).

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.

• Why does Subtraction Seem Difficult to Teach or Learn.

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.

• Calculation Strategies used by Year 5 Children (pdf).

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.

Activity A – Two and Two

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

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

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

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

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.

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

• Basic column addition explained.
• Examples of column subtraction of numbers with up to 4 digits.
• Problem solving language – a lesson exploring how the language used in problems is related to the operations needed to solve them.

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Mathematical problem solving with NRICH

If this issue's Puzzle page whets your appetite for solving mathematical puzzles online then you might like to look at a new internet journal, Interact, published by the NRICH Maths project.

The journal, updated monthly, features a collection of problems designed to get you thinking. The problems are aimed at gifted 11-13 year olds and represents the first part of an experiment in extending the Royal Institution's series of Mathematics Masterclasses into the WWW. However, the NRICH team hope to extend the site to include material to appeal to budding mathematicians of all ages over the coming months.

For more information about the Interact journal see the NRICH Home Page . Information about the Mathematics Masterclasses for Year 9 students is available direct from the Royal Institution .

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Years 3 & 4: Addition and Subtraction

This list consists of visual resources, activities and games designed to support the new curriculum programme of study in Years 3 and 4. Containing tips on using the resources  and suggestions for further use it covers:

Year 3 : adding and subtracting numbers up to 3 digits mentally and using formal methods, estimating answers, using inverse operations to check answers and solving problems.

Year 4 : adding and subtracting numbers up to 4 digits using formal methods, estimating answers, using inverse operations to check answers and solving two step addition and subtraction problems.

Visit the primary mathematics webpage to access all lists.

'Wave 3 materials': supporting children with gaps in their mathematical understanding

Quality Assured Category: Mathematics Publisher: Department for Education

These booklets highlight common errors and misconceptions in addition and subtraction children may hold in KS2. E.g. page 23 highlights a possible reason for calculation errors; that a child may not yet be secure in number bonds to 20. An activity is detailed to help develop the child's understanding and help to fill in any gaps in their learning. A great resource for supporting small groups or individuals.

Quality Assured Category: Mathematics Publisher: SMILE

Three resource packs contains work cards including games, activities and calculations based around simple counting, number bonds to ten, addition using money and adding two and three digit numbers. Some activities use base ten to support column addition, others practise addition through games and investigation. They start with simple addition and extend to more difficult tasks.

Subtraction

Six work cards for running activities on subtracting two digit numbers using physical apparatus and using the column method. One card demonstrates how base ten apparatus may be used to aid subtraction of two digit numbers from two digit numbers. This could be extended to subtract two digit numbers from three digit numbers. It also includes games to practise subtraction.

Calculation Activities for Students Aged 7-9

Quality Assured Category: Mathematics Publisher: Nelson Thornes

A collection of worksheets which can be used to reinforce calculation skills. They are useful for homework or as a reinforcement of key ideas.

This selection of games may be laminated and used by children to practise calculation with many games on addition and subtraction. Use as a starter, activity with small groups, to extend or support or even for homework. The games practise addition subtraction with 1 or 3 digits.

NRICH: A Daring Dozen

Twelve resources to help children get you thinking mathematically.

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Year 5 Column Subtraction Worksheets (differentiated) and Other Resources

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

30 May 2022

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Resources on Column Subtraction for Year 5:

• Year 5 column subtraction worksheets (differentiated to 4 levels and with the answers)
• a link to an nrich problem-solving activity involving missing numbers in a column addition calculation (this is different to the higher level worksheet questions)
• a PowerPoint presentation
• a page with the steps for column subtraction
• success criteria

There is a PDF version and an editable version of each file.

Click here to see how people have rated other resources that we have on TES.

Other Year 5 Maths resources: https://www.tes.com/teaching-resource/-12160846 - Numbers in Words https://www.tes.com/teaching-resource/-12160851 - Place Value (Whole Numbers) https://www.tes.com/teaching-resource/-12160854 - Ordering Whole Numbers https://www.tes.com/teaching-resource/-12160859 - Rounding Whole Numbers https://www.tes.com/teaching-resource/-12160861 – Place Value (Decimals) https://www.tes.com/teaching-resource/-12161134 – Complements to 1 https://www.tes.com/teaching-resource/-12163410 – Comparing Decimals and Fractions https://www.tes.com/teaching-resource/-12163418 – Decimal Sequences https://www.tes.com/teaching-resource/-12163429 – Rounding Decimals https://www.tes.com/teaching-resource/-12163439 – Comparing and Ordering Decimals https://www.tes.com/teaching-resource/-12163443 – Multiply and Divide by 10, 100 & 1,000 https://www.tes.com/teaching-resource/-12163455 – Column Addition https://www.tes.com/teaching-resource/-12163587 – Column Subtraction https://www.tes.com/teaching-resource/-12163589 – Column Addition and Subtraction https://www.tes.com/teaching-resource/-12163592 – Add and Subtract By Partitioning https://www.tes.com/teaching-resource/-12163597 – Negative Numbers https://www.tes.com/teaching-resource/-12163601 – Addition and Subtraction Word Problems https://www.tes.com/teaching-resource/-12163606 – Short Multiplication https://www.tes.com/teaching-resource/-12163614 – Square and Cubed Numbers https://www.tes.com/teaching-resource/-12163616 – Short Division

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Addition & subtraction word problems

Add & subtract numbers < 50.

These grade 1 word problems worksheets involve the addition and subtraction of 1 and 2 digit numbers. Some problems have 3 or more terms.

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Resources tagged with: Addition and subtraction

There are 225 results.

The Add and Take-away Path

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Pairs of Numbers

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Follow the Numbers

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

How Do You Do It?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Even and Odd

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Sort Them Out (1)

Can you each work out the number on your card? What do you notice? How could you sort the cards?

It Was 2010!

If the answer's 2010, what could the question be?

Which Symbol?

Choose a symbol to put into the number sentence.

Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

Here is a chance to play a version of the classic Countdown Game.

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Shut the Box

An old game but lots of arithmetic!

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

How Much Did it Cost?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

The picture shows a lighthouse and some underwater creatures. Can you work out the distances between some of the different creatures?

Tug Harder!

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Caterpillars

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Making Longer, Making Shorter

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Domino Pick

Are these domino games fair? Can you explain why or why not?

The Twelve Pointed Star Game

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Diagonal Sums

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Number Differences

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Ring a Ring of Numbers

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Carrying Cards

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Robot Monsters

Use these head, body and leg pieces to make Robot Monsters which are different heights.

A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

The Deca Tree

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

1, 2, 3 Magic Square

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

This is an adding game for two players. Can you be the first to reach the target?

Cubes Within Cubes

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Two Primes Make One Square

Can you make square numbers by adding two prime numbers together?

One Wasn't Square

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

The Tomato and the Bean

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Abundant Numbers

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Zios and Zepts

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

What's in a Name?

What do you notice about these squares of numbers? What is the same? What is different?

Prison Cells

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

The Puzzling Sweet Shop

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

The Amazing Splitting Plant

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Ben has five coins in his pocket. How much money might he have?

Can you go through this maze so that the numbers you pass add to exactly 100?

Doplication

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Find a great variety of ways of asking questions which make 8.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.