subtraction year 3 problem solving

Addition & subtraction in Year 3 (age 7–8)

In Year 3, your child will use a range of strategies for calculating addition and subtraction problems. They will need to be able to explain how they have solved problems, especially when using mental maths.

The key words for this section are  commutative , difference , and place value .

What your child will learn

Take a look at the National Curriculum expectations for addition and subtraction in Year 3 (ages 7–8):

Add and subtract numbers mentally

Your child will need to mentally calculate sums involving:

  • a three-digit number and 1s (for example, 234 +/– 7)
  • a three-digit number and 10s (for example, 534 +/– 20)
  • a three-digit number and 100s (for example, 635 +/– 300)

They will be taught lots of strategies to do this. It is good to use several strategies to check answers.

Add and subtract numbers with up to three digits

Estimate answers to calculations and use inverse operations to check answers.

Estimate £5.73 + £13.12 + £2.14 = ? Rounding to the nearest £1, the sum is £6 + £13 + £2 = £21. So, when we work out the answer accurately, we can except the answer to be about £21. If it is not, we know that something has probably gone wrong with our calculation.

Solve complex problems using number facts and place value

Your child should now know several different ways to work out addition and subtraction problems. These include using place value, number facts, partitioning, and diagrams. They will need to be able to choose a method to solve a problem, and to check their answer using a different method.

Your child should be able to explain how they have solved a problem and why they have chosen a particular method. Using pictures and symbols can be a good way to explain your thought process.

How to help at home

There are lots of quick and easy ways that you can help your child to understand addition and subtraction. Here are just a few everyday ideas to support your child’s learning:

1. Use the language of addition and subtraction

Using the correct mathematical vocabulary will get your child used to deconstructing word problems, and will make them familiar with the kinds of words they will hear in school.

Try to use mathematical language like  add , altogether , more , plus , total ,   and sum when adding. When your child finds the answer to an addition calculation, encourage them to use the word total or sum . If they talk about the fact that you can add numbers in any order and get the same answer, encourage them to use the word commutative .

There is also a lot of mathematical vocabulary related to subtraction. When your child tells you the answer to a subtraction calculation, encourage them to refer to this as the difference . For example, ‘7 – 3 = 4’ could be read as ‘the difference between 7 and 3 is 4’. They should also try to use the language take away , subtract , minus , less , fewer , and so on.

Try writing out the addition and subtraction symbols (‘+’ and ‘–’) along with the related words on cards (for example,  add , altogether , more , plus , total , sum , take away , subtract , minus , less , and  fewer) . Help your child to link the words to the correct symbol. If necessary, help them to read some of the words.

2. Try calculating mentally

It’s important for your child to develop their mental calculation skills. It is useful in everyday life, especially when technology (and paper) may not be available or appropriate, such as when you are shopping. Confidence in mental maths will help your child when making quick estimates and checking their calculations, too.

Encourage your child to use different methods when calculating mentally, such as counting on, counting back, and partitioning numbers. Your child should use their knowledge of place value, rounding, and inverse operations to make estimates and check their answers.

If your child is working on a problem and they announce the answer, ask them to explain how they solved the problem. They could draw pictures or diagrams to help them explain their method.

Ask your child to tackle the activities below using mental maths to keep their skills sharp!

Activity: Missing numbers

subtraction year 3 problem solving

Fill in the missing numbers.

Activity: Addition and subtraction

subtraction year 3 problem solving

3. Play Place Value Pandemonium

Activity: place value pandemonium.

subtraction year 3 problem solving

4. Try lots of different methods

Encourage your child to use different methods for solving addition and subtraction problems. These could include:

  • Partitioning numbers into parts to add or subtract. For example, to solve the problem 243 + 65, we could partition each number. Encourage your child to explain this to you, and perhaps model it to them first:
‘I partitioned 243 into 200, 40, and 3. Then, I partitioned 65 into 60 and 5. Then, I added the ones: 5 + 3 which equal 8. Then, I added the tens: 40 + 60 = 100. Then, I have the 200. So, I added the 200 to the 100, and then added the 8, to get a total of 308.’
  • Drawing pictures.
  • Using number lines or hundred squares.
  • Using written methods of column addition and subtraction.

Your child will understand subtraction as ‘taking away’ as well as ‘difference’. Methods could include:

  • Placing groups of objects into two rows to compare and find the difference.
  • Finding the difference between two numbers by counting back or counting up. For example, 27 – 18 could be interpreted as ‘what is the difference between 27 and 18?’ Your child may count back from 27 to 18 to find the difference of 9, or count up from 18 to 27 to find the difference of 9.
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20 Word Problems For Year 3: Develop Their Problem Solving Skills Across Single and Mixed KS2 Topics

Emma Johnson

Word problems for Year 3 are an important tool for improving number fluency. The key focus in maths in Year 3 of primary school is on ensuring pupils are becoming more fluent with number facts and the concept of place value. Children are starting to develop more efficient written methods by this stage and are beginning to carry out calculations with increasingly larger whole numbers.

As children progress through school, they are exposed to a wider variety of problem solving questions covering a range of concepts. In Year 3 maths these include the four operations, fractions, measures and statistics.  

It is important that children are regularly exposed to reasoning and problem solving questions, alongside the fluency work each lesson. It is also important to remember that all children need exposure to reasoning and problem solving questions, not just the higher attaining pupils who finish quickest.

We have put together a collection of 20 word problems, aimed at Year 3 pupils.

Years 3 to 6 Rapid Reasoning (Weeks 1-6)

Years 3 to 6 Rapid Reasoning (Weeks 1-6)

Download this free pack of word problems to improve your class' problem solving skills. Includes questions for Years 3 - 6.

Place value

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In Year 3, pupils focus on one-step problems, covering a range of topics across the National Curriculum. At this stage the majority of word problems pupils are tackling will have one-step, but they may also start to be introduced to simple two-step word problems. Here is a breakdown of topics that will be covered and expectations in Year 3. 

Solve number problems and practical problems involving recognising the place value of each digit of a 3-digit number; comparing and ordering numbers up to 1000 and identifying, representing and estimating numbers using different representations.

Solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction word problems .

Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems

 Solve problems involving counting in tenths; recognising unit and non-unit fractions; recognising equivalent fractions and adding/ subtracting fractions with the same denominator.

Solve problems involving length, volume and mass; adding and subtracting within money word problems ; perimeter and problems involving time.

Solve-step and two-step questions (For example, ‘How many more?’ and ‘How many fewer’?) using information presented in scaled bar charts, pictograms and tables.

By Year 3, children are starting to learn how to use some of the formal written methods of addition and subtraction. It is important that the link between maths in school and maths in real-life continues to be made. Word problems are a key element in helping pupils to make this link. 

When teaching maths problems to Year 3, it’s important to think of ways to make them fun, engaging and something the children are able to relate to. This might include acting out the problem, using concrete resources and providing visual images, to bring the problems to life. 

Benefits of pairs, groups and class discussion 

Children should have plenty of opportunity to talk in pairs, groups and as a whole class, to share their understanding of what is being asked and their strategies for solving the problem. As with Key Stage One, the use of manipulatives is important and all children should have access to a range of maths resources when solving problems like this.

Pupils need to be encouraged to read word problems carefully and to make sure they understand what is being asked, before attempting to tackle the problem. This is where the use of a partner and group discussion can really help children’s understanding. Students then need to think about what they already know and how they can use this to help them answer the question. Where appropriate, pupils should also be encouraged to draw diagrams and pictures to help them solve the question.

Here is an example:

Mason needs 4 apples to make an apple pie.

If he has 28 apples. How many apple pies can he make?

How to solve:

What do you already know?

  • We know 4 apples are needed to make an apple pie.
  • We are told how many apples Mason has in total, so we must have to divide the total number by 4.
  • In year 3, children should be building confidence with multiplication and division facts for the 4 times table, so some will be able to quickly recall these facts to solve the problem.
  • Children who aren’t apple to recall quickly could use counters to represent the apples, or draw a bar model to help solve it.

How can this be drawn/represented pictorially?

We can draw a bar model or counters to represent this problem:

7 groups of 4 as bar model and with counters

  • To calculate how pies the 28 apples will make, we can either use or draw 28 counters and put them into groups of 4. We can see that 28 counters will make 7 groups of 4.
  • Using the bar model, we can keep adding 4 to the bar until we reach 28. From the bar we can see that 7 x 4 = 28.
  • 7 apple pies can be made from the 28 apple pies that Mason has.

In Year 3, pupils are exposed to a range of addition word problems , including problems involving mental addition and addition of up to 3-digits using formal written methods.

See also: Mental maths Year 3

Addition question 1

A family driving on holiday, travel 146 miles from home to the first service station.

They then drive a further 175 miles to reach their destination.

How far have they travelled altogether?

Answer (1 mark): 321 miles

146 + 175 = 321

Addition question 2

Evie is buying a bottle of drink from a vending machine. She has put in 40p. The vending machine shows she still needs to put in £1.25. 

How much is the bottle of drink?

Answer (1 mark): £1.65

125p + 40p = 165p

Addition question 3

Jamie scored 643 on his new online game.

Jared scored 468.

How many points did they score between them?

Answer (1 mark): 1111 points

643 + 468 = 1111

At Third Space Learning we often tie word problems into our one-to-one online tuition. With each programme personalised to the needs of each individual student, children are able to develop their problem solving skills, maths fluency and grow confidence in maths.

year 3 addition word problem slide

Subtraction word problems in Year 3 also need to comprise of a combination of mental calculation questions and those involving formal written subtraction up to 3-digits. Children should also be starting to estimate answers and check their calculations by using the inverse.

Subtraction question 1

Ahmed collects 374 stickers.

He needs 526 stickers to fill his sticker album.

How many more stickers does he need to collect?

Answer (1 mark): 152 stickers

526 – 374 = 152

Subtraction question 2

 A bag of carrots weigh 360g

A bag of tomatoes weighs 235g.

How much heavier is the bag of carrots?

Answer (1 mark): 125g

360 – 235 = 125

Subtraction question 3

 Ahmed buys a bag of sweets for £1.45.

He has a £2 coin. How much change will he get?

Answer (1 mark): 55p

200 – 145 or count up from £1.45 to £2

By the end of Year 3, pupils should be able to recall and use multiplication facts for the 3, 4 and 8 times table. They should also be starting to progress to using the formal written method for solving multiplication word problems involving 2 digits multiplied by a 1-digit number. 

Multiplication question 1

It costs £7 for a cinema ticket

Amber’s mum pays for Amber and her 3 friends. 

How much does she pay for all the tickets?

Answer (1 mark): £28

7 x 4 = 28 

Multiplication question 2

5 mini buses are used to take Year 3 pupils on a school trip.

Each minibus transports 15 children.

How many children go on the school trip?

Answer (1 mark): 75 children

15 x 5 = 75

Multiplication question 3

There are 24 questions on a word problems worksheet. 

A group of 8 children each complete the worksheet.

How many questions will the teacher be marking?

Answer (1 mark): 112 questions

24 x 8 = 112

In Year 3, pupils will need to learn the division facts for the 3, 4 and 8 multiplication tables. At this stage, pupils are required to learn the formal method for division, division word problems will involve mainly mental calculations.

Division question 1

6 children share 18 cookies between them. 

How many cookies does each child get?

 Answer (1 mark): 3 cookies

Division question 2

The school choir needs to travel to the concert hall.

There are 32 children in the choir and parents have been asked to help transport the children.

Each parent is able to take 4 children in their car. How many cars will be needed to get all the children to the concert?

Answer (1 mark): 8 cars

 32 ÷ 4 = 8

Division question 3

 Cakes come in packs of 4.

If Jessica needs 36 cakes for her party, how many packs does she need to buy?

Answer (1 mark): 9 packs

In Year 3 pupils are exposed to a range of fraction word problems , including questions involving counting up and down in tenths; equivalent fractions and adding/subtracting fractions with the same denominator.

Fraction question 1

Jude had 28 sweets.

He gave \frac{1}{4} of his sweets to his little sister.

How many did he have left?

Answer (1 mark): 21 sweets

\frac{1}{4} of 28 = 7

\frac{3}{4} of 28 = 21 or 28 – 7 = 21

Fraction question 2

Khalifa ate \frac{2}{8} of the chocolate bar and Abdulrahman ate \frac{3}{8} of it.

How much chocolate did they have left?

Answer (1 mark): \frac{3}{8}

\frac{2}{8} + \frac{3}{8} = \frac{5}{8} eaten

\frac{8}{8} – \frac{5}{8} = \frac{3}{8}

Fraction question 3

 Molly ate half of a pizza and Rosie ate \frac{3}{6} .

Who ate the most?

Answer (1 mark): They both ate the same amount

\frac{3}{6} is equivalent to \frac{1}{2} .

In Year 3 time word problems may be incorporated into maths problem solving. Students are expected to know time vocabulary, be able to compare time in terms of seconds, minutes and hours and know how many seconds are in a minute and minutes are in an hour. 

Time question 1

The Smith family are driving to the beach.

They leave at 9:05am and arrive at 9:50am.

How long does the journey take them?

Answer (1 mark): 45 minutes

50 – 5 = 45    or     count up from 9:05 to 9:50 = 45 

Time question 2

Holly puts her cake in the oven at 4:22pm and takes it out again at 4:47. 

How long is the cake baking for?

Answer (1 mark): 25 minutes

47 – 22 = 25    or   count up from 4:22 to 4:47

When children first move into lower Key Stage 2, word problems are predominantly one-step. As they become more confident they can be exposed to more word problems, requiring a second step or multi-step word problems .

Multi-step question 1

Oliver had 3 bags of sweets.

Each bag contained 15 sweets.

If he shared the sweets between him and 4 friends, how many sweets would they all 5 of them get?

Answer (2 marks): 9 sweets

3 x 15 = 45 

45  ÷ 5 = 9

Multi-step question 2

A teacher photocopies 95 maths worksheets and 80 English worksheets in one week.

Teachers can print a maximum of 300 worksheets per week. 

How many can the teacher print for other subjects.

Answer (2 marks): 125 worksheets

 95 + 80 = 175

300 – 175 = 125

Multi-step question 3

Three friends go trick or treating. They add all their sweets together and share them out, so they all have an equal number of sweets.

If Ben gets 34 sweets, Sophie gets 28 and Maisie gets 22 sweets. How many will they each get, once they have put them together and shared them out?

Answer (2 marks): 28 sweets each

34 + 28 + 22 = 84 sweets

84  ÷ 3 = 28

We hope that this collection of word problems for Year 3 becomes a useful resource in your Year 3 maths classroom. For more Year 3 maths resources, take a look at our library of Year 3 maths worksheets .

Third Space Learning also offers a wide array of maths and word problems resources for other year groups such as word problems for year 6 , word problems for Year 5 and word problems for year 4 . Our practice word problems cover all four operations and include more specific topics such as percentage word problems and ratio word problems .

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3rd Grade Addition and Subtraction

Word problems.

Welcome to our 3rd Grade Addition and Subtraction Word Problems page. Here is our selection of free addition and subtraction word problem worksheets, which will help your child practice solving a range of addition and subtraction problems using 3-digit and 4-digit numbers.

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  • Addition & Subtraction Word Problems up to 1000 Online Quiz

3-digit and 4-digit Word Problems

Each sheet consists of a range of 5 addition and subtraction word problems with numbers up to thousands.

There is a space on each sheet for working out, so that your child can write out the problem and solve it.

We have split the worksheets up into 3-digit word problems and 4-digit word problems.

Using these sheets will help your child to:

  • add and subtract numbers with 3-digit and 4-digit numbers;
  • solve addition and subtraction word problems with and without regrouping.
  • recognise the language used in addition and subtraction - sum, total, difference, how many more, etc.
  • solve problems involving more than 1 step.

3rd Grade Addition and Subtraction Word Problems

3-digit addition and subtraction word problems.

There are two versions of each sheet.

The first version (version A) contains problems where no regrouping is needed.

The second version (version B) contains similar problems but regrouping is needed to solve them.

Answers have been provided with each sheet, along with the calculation needed to solve the problem.

The following sheets are all 1-step addition or subtraction word problems.

  • 3-Digit Addition and Subtraction Word Problems Sheet 1A (no regrouping)
  • PDF version
  • 3-Digit Addition and Subtraction Word Problems Sheet 1B
  • 3-Digit Addition and Subtraction Word Problems Sheet 2A (no regrouping)
  • 3-Digit Addition and Subtraction Word Problems Sheet 2B

4-digit Addition and Subtraction Word Problems

The word problems all involve either addition or subtraction (both with and without regrouping).

  • 4-Digit Addition and Subtraction Word Problems Sheet 1
  • 4-Digit Addition and Subtraction Word Problems Sheet 2

Harder 2-Step Addition and Subtraction Word Problems

These problems are trickier than those above.

Each problem involved two steps to solve, and may involve just addition, just subtraction or both operators.

There are 4 problems on each sheet, and more space to work out the solutions.

  • 2-Step Addition Subtraction Problems up to 3-digits Sheet 1
  • 2-Step Addition Subtraction Problems up to 4-digits Sheet 1

Looking for some easier worksheets?

Take a look at our Subtraction word problems for first graders.

On this page, your child will learn to work out basic subtraction word problems with numbers to 20.

  • 2nd Grade Addition and Subtraction Word Problems (up to 100)

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More 3rd Grade Addition and Subtraction Worksheets

Here you will find some more of our Addition and Subtraction Worksheet generators for creating your own bespoke addition and subtraction worksheets.

  • Addition Subtraction Fact Worksheets (randomly generated)
  • Column Addition and Subtraction Worksheets (randomly generated)

More 3rd Grade Math Word Problems

Using the 3rd Grade Math worksheets will help your child to:

  • apply their addition, subtraction, and multiplication skills;
  • develop their knowledge of fractions;
  • apply their knowledge of rounding and place value;
  • solve a range of 'real life' problems.

These sheets involve solving one or two more challenging longer problems.

  • 3rd Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

  • Math Word Problems for kids 3rd Grade

These sheets involve solving 3-digit and 4-digit addition word problems.

  • Addition Word Problems 3rd Grade (3- and 4-digits)

These sheets involve solving 3-digit and 4-digit subtraction problems.

  • Subtraction Word Problems 3rd Grade

These sheets involve solving a range of multiplciation problems.

  • Multiplication Word Problem Worksheets 3rd Grade

These sheets involve solving a range of division problems.

  • Division Worksheets Grade 3 Word Problems

Addition and Subtraction Word Problems to 1000 Online Quiz

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Addition & Subtraction Workbook for Grades 2-3

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Subtraction word problems for 3rd grade

Simple subtraction.

These grade 3 word problems use simple (horizontal) subtraction. The student should read the problem, write a subtraction equation from it and then answer the problem. Students should understand the meaning of subtraction and have studied their subtraction math facts prior to attempting these worksheets.

subtraction year 3 problem solving

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Year 3 Addition & Subtraction

Click on an objective for related worksheets and resources.

Pupils should be taught to:
add and subtract numbers mentally including a three-digit number and ones, a three-digit number and tens, a three-digit number and hundreds
add and subtract numbers with up to three-digits, using formal written methods of columnar addition and subtraction
estimate the answer to a calcuation and use inverse operations to check answers
solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction
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Maths word problems differentiated worksheets (y3)

Maths word problems differentiated worksheets (y3)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

L_E1984

Last updated

16 November 2014

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It's really great. I became very happy . Because I found all the math for my kids on this page. Many thanks

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a very well crafted differentiated to get students of all abilities thinking and moving through the RAG LMH boundaries Thanks a lot Martin Primary tutor

Just what I needed. Thank you.

audrey dean

The differentiation is great, thank you.

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Subtraction Word Problem Worksheets

The extensive set of subtraction word problems featured here will require the learner to find the difference between minuends and subtrahends, which includes problems with regrouping and without regrouping. This large collection of printable word problem worksheets, ideal for children in kindergarten through grade 4 features scenarios that involve single-digit subtraction, two-digit subtraction, three-digit subtraction, and subtraction of large numbers up to six digits. Give yourself a head-start with our free subtraction worksheets!

Word Problems for Beginners: 0 to 10

Word Problems for Beginners: 0 to 10

Find the difference between the numbers that ranges from 0 to 10 in the set of kindergarten worksheets featured here. Use the answer key to verify your responses.

  • Download the set

Subtraction within 20

Subtraction within 20

Ascend from a beginner to a proficient in performing subtraction up to 20 as you explore this bunch of well-researched word problems and work out the difference within 20.

Two-digit Subtraction: No Regrouping (No Borrowing)

Two-digit Subtraction: No Regrouping (No Borrowing)

The series of worksheets for grade 1 and grade 2 presented here involve two-digit subtraction word problems that do not require regrouping. Find the differences between the two-digit subtrahends and minuends featured here.

Two-digit Subtraction: Regrouping (Borrowing)

Two-digit Subtraction: Regrouping (Borrowing)

The two-digit subtraction word problems presented in the 2nd grade worksheets here require regrouping (borrowing). Determine the difference between the two-digit numbers by following the place value columns correctly.

Theme based Subtraction Problems

Theme based Subtraction Problems

The colorful theme-based worksheet pdfs for kids in 1st grade through 3rd grade are based on three engaging real-life themes - Beach, Italian Ice and Birthday Party.

Three-digit and Two-digit Subtraction

Three-digit and Two-digit Subtraction

The set of subtraction word problem pdfs featured here will require grade 3 student to find the difference between three-digit minuends and two-digit subtrahends. Use the answer keys to verify your responses.

Three-digit Subtraction Word Problems

Three-digit Subtraction Word Problems

Each printable worksheet contains five word problems finding difference between three-digit numbers. Some problems may require regrouping.

Four-digit Subtraction Word Problems

Four-digit Subtraction Word Problems

This section contains subtraction word problems on finding the difference between four-digit numbers. Both borrowing and no borrowing problems are included. Some problems may involve subtraction across zero.

Advanced: Large Number Subtraction

Advanced: Large Number Subtraction

The word problems featured in the 4th grade pdf worksheets here include large numbers with minuends and subtrahends up to six digits. Determine the difference between the large numbers by following the place value columns correctly.

Related Worksheets

» Addition Word Problems

» Subtraction within 10

» 2-Digit Subtraction

» Word Problems

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Daily Maths Word Problems – Year 3

Updated:  04 Oct 2023

A set of 20 problem solving questions suited to year 3 students.

Non-Editable:  PDF

Pages:  6 Pages

  • Curriculum Curriculum:  AUS V8, NSW, VIC, AUS V9
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Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies

AdditionandSubtraction - uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers

Multiplication and Division - uses mental and informal written strategies for multiplication and division

Fractions and Decimals - represents, models and compares commonly used fractions and decimals

Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies

Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of t

Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator

Daily Maths Word Problems – Year 3 teaching resource

Advance Your Students’ Problem-Solving Skills

This set of problem-solving questions has been designed to support teachers when teaching students about problem-solving in mathematics. It provides students with the opportunity to work through 20 maths word problems, identifying the important information and how they can work it out using a variety of methods.

An answer sheet has been included. Use this resource in conjunction with the Daily Maths Problems PowerPoint.

NAPLAN Year 3 Maths Preparation

These simple problem-solving questions are also a great way to help students understand some of the word problems they may encounter when sitting NAPLAN. It’s important to give your students strategies that they can draw on when presented with a word problem in maths. Using these problem-solving questions here are some suggested strategies you can empower your students with:

  • Daily practice. After spending time explicitly explaining how to work through a word problem – use the word problems from these worksheets as daily problem-solving practice.
  • Teach them the strategies. There are many ways students can solve maths word problems such as; breaking the word problem into smaller parts and drawing a picture to visualise what the problem is asking.
  • Underline. Teach your students to underline the important parts of a maths word problem – remind them that there is often trick information in word problems that they don’t need to solve the problem.

How to Use This Resource

Once you download the PDF, there are many ways you can use the resource. Here are some suggestions:

  • Print and create booklets for your students to use.
  • Cut and laminate each word problem and have students use mini whiteboard markers to solve one problem a day.

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Addition and Subtraction of Integers

Adding two positive integers results in positive integers, whereas adding two negative integers will result in the sum with a negative sign. But the addition of two different signed integers will result in subtraction only and the sign of the result will be the same as the larger number.

Table of Content

What are Integers?

Addition of integers, subtraction of integers, rules for adding and subtracting integers, addition and subtraction of integers on number line.

  • Solved Examples

Integers are whole numbers that can be either positive, negative, or zero. They are represented by the symbol Z and are written as:

Z = \{ \dots, -3, -2, -1, 0, 1, 2, 3, \dots \}
  • Positive integers: 1, 2, 3
  • Negative integers: -1, -2, -3
  • Zero: 0 (neither positive nor negative)

The addition of integers is based on the sign of the integers to be added.

Same Signs: If both integers have the same sign, add their absolute values, and the result takes the common sign.

  • (+a) + (+b) = + (a + b)
  • (-a) + (-b) = – (a + b)

For Example:

(+3) + (+5) = +8 (-4) + (-7) = -11

Different Signs: If the integers have different signs, subtract the smaller absolute value from the larger absolute value, and take the sign of the larger absolute value.

  • (+a) + (-b) = (+ \text{or} -)(a – b)
(+8) + (-5) = +3 (-9) + (+4) = -5

Properties of Addition of Integers

Some properties of addition of integers are:

  • Closure Property: The sum of any two integers is always an integer. Example: 3 + (-5) = -2
  • Commutative Property: Changing the order of the addends does not change the sum. Example: 4 + (-7) = -7 + 4 = -3.
  • Associative Property: The way in which integers are grouped does not affect their sum. Example: (2 + 3) + (-4) = 2 + (3 + (-4))
  • Additive Identity: Adding zero to any integer does not change its value. Example: 6 + 0 = 6

Subtracting an integer is the same as adding its opposite.

  • a – b = a + (-b)
7 – 4 = 7 + (-4) = 3 -3 – 5 = -3 + (-5) = -8

Properties of Subtraction of Integers

Some properties of subtraction of integers are:

  • Non-Commutative Property: Changing the order of the numbers changes the result. Example: 5 – 3 \neq 3 – 5 .
  • Subtraction as the Addition of the Opposite: Subtracting an integer is the same as adding its opposite. Example: 7 – 4 = 7 + (-4) = 3
  • Subtraction of Zero: Subtracting zero from an integer does not change its value. Example: 9 – 0 = 9

The table below represents the rules for adding and subtracting integers.

Lightbox

The addition and subtraction of integers on number line are given below.

Addition of Integers on a Number Line

Steps to add integers on number line.

  • To add a positive integer, move right.
  • To add a negative integer, move left.

Example: 2 + 3 = 5 (move 3 units right from 2).

Subtraction of Integers on a Number Line

Steps to subtract integers on number line.

  • To subtract a positive integer, move left.
  • To subtract a negative integer, move right.

Example: 4 – 6 = -2 (move 6 units left from 4).

Solved Examples on Addition and Subtraction of Integers

Example 1: Add integers 12 and 8.

(+12) + (+8) = +20 Since both integers are positive, we simply add them.

Example 2: Add Integers (+6) + (-9)

(+6) + (-9) = -3 Here, subtract 6 from 9, and since 9 has the larger absolute value and is negative, the result is -3

Example 3: Subtract Integers 10 – (-5)

10 – (-5) = 10 + 5 = 15 We change subtraction to addition and change the sign of -5 to +5

Example 4: Subtract: -7 – (-2)

-7 – (-2) = -7 + 2 = -5 Here, subtract 2 is the same as adding +2, which results in -5

Example 5: Solve (+14) – (+5) + (-8)

(+14) – (+5) + (-8) = 14 – 5 – 8 = 1 First, subtract 5 from 14 to get 9, then subtract 8, resulting in +1

Practice Problems

Q1. (-7) + (+12) =?

Q2. (+20) + (-13) =?

Q3. (-11) – (+6) =?

Q4. 18 – (-9) =?

Q5. (-22) + (+14) =?

Q6. (-4) – (-6) + (+2) =?

Q7. (+5) + (-10) – (-3) =?

  • (-7) + (+12) = +5
  • (+20) + (-13) = +7
  • (-11) – (+6) = -17
  • 18 – (-9) = +27
  • (-22) + (+14) = -8
  • (-4) – (-6) + (+2) = +4
  • (+5) + (-10) – (-3) = -2

From the above discussion we can conclude that in addition of integers if both the integers have same sign, we add the integers, and the resultant sign is the sign of both the integers and if both the signs are different the subtract both integers and resultant sign is of the larger number sign. In subtraction of integers, we subtract both integers and the resultant sign is of larger integer.

  • Subtraction
  • Multiplication

FAQs on Addition and Subtraction of Integers

How to solve addition of integers.

To solve the addition of integers, use the rules: If the two int are positive, we add the absolute values of the two int and retain their like sign. Notice that the numbers differ in sign, subtract the sign to the number with the lesser absolute value from the number with the greatest absolute value while accepting the sign from the number bearing the greatest absolute value. Example: 5 + (-3) = 2

What is the rule for adding and subtracting integers?

There is no single formula, but the rules are as follows: For addition: a + b . For subtraction: a – b = a + (-b) .

What are 3 steps in subtraction of integers?

To make the subtraction equal to addition, replace the second integer with the + opposite. Add two integers, if they are both positive or if they are both negative, if one integer is positive and the other is negative subtract the second integer from the first integer. Simplify and write the final result of the equation below.

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IMAGES

  1. Math Scenarios

    subtraction year 3 problem solving

  2. Double Digit Addition And Subtraction Word Problems

    subtraction year 3 problem solving

  3. Subtraction Across Zero Worksheets

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  4. Reading Worksheets For 2Nd Grade for download free

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  5. 3 digit subtraction worksheets

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  6. Word Problems Addition And Subtraction

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VIDEO

  1. Subtract 3-digit numbers with mental math: use place value

  2. BISM

  3. Year 3

  4. Mathematics Year 3 Problem Solving Involving Multiplication & Division

  5. Practice Our Subtraction Facts for 3

  6. Subtraction Year 2

COMMENTS

  1. Subtraction Word Problems 3rd Grade

    3-digit Subtraction Word Problems. There are two versions of each of the 3-digit subtraction sheets. The first version (version A) contains problems where no regrouping is needed. The second version (version B) contains similar problems but regrouping is needed to solve most of them.

  2. Year 3 Subtraction Word Problems

    You might also find useful our collection of year 3 maths worksheets. Or try our Year 3 Maths Curriculum Checklist to help make sure children stay on track in line with the National Curriculum. 3 examples of Year 3 subtraction word problems: Jimmy buys a sausage roll that costs 65p. He pays with a £2 coin. How much change should he get?

  3. Year 3 Maths Worksheets

    The following worksheets involve using the skills of subtracting numbers, and solving subtraction problems. Using these sheets will help your child to: know their subtraction facts to 20; ... Here are a range of problems solving sheets for Year 3 children. Most of the sheets contain 'real-life' problems related to animal facts.

  4. * New * Addition and Subtraction Word Problems Year 3

    Word problems for Year 3 addition and subtraction. This handy worksheet includes a range of addition and subtraction word problems for Year 3 pupils. They are perfect for developing children's fluency, reasoning and problem-solving skills. To make marking and self-assessment easier, it comes complete with a helpful answer sheet. Show more. word ...

  5. Addition and Subtraction Word Problems Year 3

    This handy worksheet includes a range of addition and subtraction word problems for year 3 pupils. These are perfect for developing children's fluency, reasoning and problem-solving skills. The problems will help them practise essential skills by learning to complete the required calculations needed to solve addition and subtraction problems. Featuring ten questions in total as well as a ...

  6. Year 3 Problem Solving Addition and Subtraction Maths Mastery ...

    Challenge your Year 3 students with this PowerPoint with a range of maths mastery activities based around the Year 3 objective: Solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction. Support their learning with different pictorial representations including both base ten and bar modelling.

  7. * New * Addition and Subtraction Word Problems Year 3

    Examples of Addition and Subtraction Word Problems for Year 3. Maths word problems are an important skill for children to learn, as they help improve logic, reasoning and creative thinking. Here are some examples of practical problems, which children should be able to solve by the end of year 3: Emi buys a drink for 79p. She pays with a £1 coin.

  8. Grade 3 Subtraction Worksheets

    Subtract a 3-digit number from any whole thousand (missing number) 4,000 - ___ = 3,179: Subtraction in columns: Subtract 3-digit numbers: 872 - 542 : Subtract 4-digit numbers: 5,122 - 2,014 : Borrow over two zeros: 600 - 89 : Borrow over three zeros: 3,000 - 131: Subtraction word problems: Grade 3 subtraction word problems

  9. Year 3 Addition and Subtraction Problem Solving

    year 3 maths. Provide year 3 students with a range of problem-solving opportunities using our addition and subtraction maths worksheets, activities and investigations. Our resource range include missing number problems, multi-step problems, word problems, investigative-led activities and much more.

  10. Addition & subtraction in Year 3 (age 7-8)

    Addition & subtraction in Year 3 (age 7-8) In Year 3, your child will use a range of strategies for calculating addition and subtraction problems. ... Encourage your child to use different methods for solving addition and subtraction problems. These could include: Partitioning numbers into parts to add or subtract. For example, to solve the ...

  11. Word Problems For Year 3 To Improve Problem Solving Skills

    643 + 468 = 1111. At Third Space Learning we often tie word problems into our one-to-one online tuition. With each programme personalised to the needs of each individual student, children are able to develop their problem solving skills, maths fluency and grow confidence in maths. Example of addition word problems from a Third Space Learning ...

  12. Year 3 Subtraction Word Problems

    Or try our Year 3 Maths Curriculum Checklist to help make sure children stay on track in line with the National Curriculum. 3 examples of Year 3 subtraction word problems: Jimmy buys a sausage roll that costs 65p. He pays with a £2 coin. How much change should he get? Tom buys a packet of biscuits. There are 30 biscuits in the packet.

  13. 469 Top "Year 3 Subtraction" Teaching Resources curated for you.

    2-Digit Column Subtraction Activities 89 reviews. Year3Subtraction Word Problems Differentiated Worksheets 27 reviews. 3 -Digit Column Addition Worksheet 89 reviews. Subtracting 4 Digit Numbers with Exchanging Worksheet 31 reviews. Addition and Subtraction Worksheets - Year3 49 reviews.

  14. 3rd Grade Addition and Subtraction Word Problems

    Using these sheets will help your child to: add and subtract numbers with 3-digit and 4-digit numbers; solve addition and subtraction word problems with and without regrouping. recognise the language used in addition and subtraction - sum, total, difference, how many more, etc. solve problems involving more than 1 step.

  15. Subtraction Word Problems for 3rd Grade

    These grade 3 word problems use simple (horizontal) subtraction. The student should read the problem, write a subtraction equation from it and then answer the problem. Students should understand the meaning of subtraction and have studied their subtraction math facts prior to attempting these worksheets. Worksheet #1 Worksheet #2 Worksheet #3 ...

  16. Year 3 Addition & Subtraction

    Year 3 Addition & Subtraction. Click on an objective for related worksheets and resources. Pupils should be taught to: add and subtract numbers mentally including a three-digit number and ones, a three-digit number and tens, a three-digit number and hundreds ... solve problems, including missing number problems, using number facts, place value ...

  17. Maths word problems differentiated worksheets (y3)

    Maths word problems differentiated worksheets (y3) Addition and subtraction word problem questions. Some 2 step problems on higher ability sheet. Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

  18. Subtraction Word Problem Worksheets

    The word problems featured in the 4th grade pdf worksheets here include large numbers with minuends and subtrahends up to six digits. Determine the difference between the large numbers by following the place value columns correctly. Download the set. Explore these subtraction word problem worksheets that deal with real-life situations.

  19. Year 3 Addition and Subtraction Primary Resources

    Year 3 Problem Solving Addition and Subtraction Maths Mastery PowerPoint. 4.5 (8 reviews) Year 3 Diving into Mastery: Step 9 Subtract 10s Across a 100 Teaching Pack ... Step 13 Add Two Numbers (Across a 10) Teaching Pack. 4.7 (6 reviews) Year 3 Addition and Subtraction Crack the Case of the Missing Puzzle Cubes Activity Pack. Year 3 Diving into ...

  20. Daily Maths Word Problems

    A set of 20 problem solving questions suited to year 3 students. ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation

  21. PDF Year 3 Subtract 3-Digits from 3-Digits 2 Reasoning and Problem Solving

    National Curriculum Objectives: Mathematics Year 3: (3C1) Add and subtract numbers mentally, including: three-digit number and ones. three-digit number and tens. three-digit number and hundreds Mathematics Year 3: (3C2) Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction.

  22. Year 3 Problem Solving Addition and Subtraction Maths Mastery ...

    Challenge your Year 3 students with this PowerPoint with a range of maths mastery activities based around the Year 3 objective: Solve problems, including missing number problems, using number facts, place value and more complex addition and subtraction. Support their learning with different pictorial representations including both base ten and bar modeling.

  23. Addition and Subtraction of Integers

    In this article, we will solve addition and subtraction problems. Table of Content What are Addition and Subtra. 4 min read. Number Line for Addition and Subtraction. Number lines are essential visual tools in mathematics that help students understand and perform basic arithmetic operations. This article explores how to use number lines for ...

  24. Y3 Diving into Mastery: Subtract Two Numbers (Across a 10)

    The presentation and worksheets contain mastery-approach questions that provide opportunities to develop reasoning and problem-solving skills. The content is written to complement teaching and learning of the year 3 White Rose Maths autumn block 2 'Addition and subtraction' with a particular focus on the small step 15 'Subtract two numbers ...