reasoning and problem solving addition and subtraction year 3

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Problem-Solving Investigations for Year 3 Addition and Subtraction

Last updated

9 August 2019

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Resources included (8)

Counting up subtraction with nos>100 - Problem-Solving Investigation - Year 3

Expanded addition: 3-digit numbers - 2 - Problem-Solving Investigation - Year 3

Add 3-digit numbers using expanded addition - Problem-Solving Investigation - Year 3

Use different strategies to subtract - Problem-Solving Investigation - Year 3

Problem-Solving Investigation: Mental calculation – complements to 100 (Y3 Addition & Subtraction)

Problem-Solving Investigation: Using place value to add/subtract (Year 3 Addition and Subtraction)

Problem-Solving Investigation: Add/subtract: efficient mental strategies (Yr 3 Addition/Subtraction)

Problem-Solving Investigation: Using number facts to add/subtract (Year 3 Addition and Subtraction)

These in-depth Year 3 Addition and Subtraction problem-solving investigations will develop maths meta-skills, and enable children to learn to think mathematically and articulate mathematical ideas.

These open-ended mathematical activities cover the following objectives:

• Using number facts to add/subtract
• Add/subtract: efficient mental strategies
• Using place value to add/subtract
• Mental calculation – complements to 100
• Use different strategies to subtract two numbers
• Add 3-digit numbers using expanded addition
• Subtract 2-digit numbers from numbers over 100 using counting up

In-depth Investigation: Puzzling Squares Children use reasoning skills to solve a number puzzle. They use numbers 0 to 7 to make a total of 10 on each side of a square.

In-depth Investigation: Twisted Subtractions Children subtract a number which is the reverse of another, e.g. 62 - 26.

In-depth Investigation: Magic 147 Children arrange the ‘nearly numbers’ in a square so that each row and column adds to Magic 147.

In-depth Investigation: Closest to 100 Following simple rules children find ways to make 100 based on four dice throws. They practise adding four numbers with a total around 100 and use this to find a solution.

In-depth Investigation: Magic Square Differences Children use the magic square to generate two-digit numbers and explore difference patterns.

In-depth Investigation: Expanded Elevens Children use base 10 equipment to create 3-digit numbers to add using expanded column addition.

In-depth Investigation: Pattern Subtractions Children subtract two-digit from three-digit numbers, by counting up, and look out for patterns in the numbers.

In-depth Investigation: Next Door Additions Children add pairs of three-digit numbers and look for patterns in the digital roots of the answers.

These problem-solving investigations are part of our Year 3 Addition and Subtraction block. Each Hamilton maths block contains a complete set of planning and resources to teach a terms worth of objectives for one of the National Curriculum for England’s maths areas.

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Reasoning/Problem Solving Maths Worksheets for Year 3 (age 7-8)

Money problems and challenges.

A variety of problem solving activities involving money.

50p to spend, but can you make sure you get the correct change?

Watch out when writing pence as pounds and remember to always have two digits after the decimal point.

The hardest part of these money problems is to read the question and work out what to do.

Put three items in your basket that you would like to buy and then use the money cards to work out the sum.

Solve money problems using the information provided.

Solve money problems at the skating rink.

Plenty of monkey business here!

It's a trip to the zoo to find the very best value.

Some tricky money problems to solve.

More tricky money problems to solve.

Finding different amounts from a given set of coins.

Number and calculating problems

Solve number problems and calculating using addition, subtraction, multiplication and division.

Find the 2-digit numbers that can be made using these digit cards.

Make 2-digit numbers and find the smallest and largest numbers.

More on finding 2-digit numbers from three digit cards.

Tricky little problems involving monsters' legs.

Use logic, addition and subtraction to find out how many strawberries are eaten.

Bar Model: addition and subtraction facts.

Use bar models to add and subtract.

Encourage children to make addition and subtraction come to life by writing short number stories.

What numbers can you make with digit cards?

What are the largest and smallest numbers that can be made with 3 cards?

More number stories to write: this time all about multiplication and division.

All the numbers are here, but the signs are missing! Can you work out what the signs should be?

Investigating odd and even numbers and what happens when you add them together.

Use knowledge of place value to find all possible answers.

Finding the numbers and missing digits to make number sentences correct.

Investigate statements involving odd and even numbers.

Investigate statements about multiplication and times tables.

I?m good at thinking of numbers, but can you work out what number I am thinking about ? I do give a clue!

Work out the missing value using division and addition.

Use reasoning to find the missing values.

More on finding the missing values - an early introduction to algebra.

Use division and addition to find the missing values.

Find the missing values from the information given.

More on finding the value using reasoning.

Real life and word problems

A selection of real life problems and word problems.

Tricky word problems.

More tricky word problems.

Tricky questions, but you only have to carry out one maths step to answer them.

Even trickier questions, and you have to carry out at least two steps to work them out!

More word problems, from the library to shopping and on to flying around the world.

Here we have four pages of questions all on time, including a trip to Alicante!

Solving tricky fraction problems.

More challenges and activities

A great selection of activities requiring logical thinking.

Investigation looking at possibilities when adding the digits from 1 to 5.

This time you can decide the total for the sides of the triangle.

Can you put the numbers 1 to 9 in the diagram so that the difference between each pair of joined numbers is odd?

This challenge is to find as many ways as possible of making 12 using three number cards and the add, subtract and multiply signs.

A development of the 'Caterpillar investigation' but using multiples of 10. Great for practising addition.

3 dinosaurs laid some eggs. They laid 19 altogether. How many did they each lay?

How many ways can three runners cover a distance of 19 miles? They all have to run an odd number of miles.

A book challenge here. How accurately can you guess the number of pages in books?

2D card shapes and a 3 x 3 pinboard are useful for these shape activities.

A calculator is needed to find how many different answers can be made from the numbers given. Good for working in an organised, logical way.

A brief summary of some of the most important maths concepts to be taught in Year 3 by way of challenges and investigations.

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Year 3 Maths Worksheets UK Hub Page

Welcome to our Year 3 Maths Worksheets area. Here you will find links to our Year 3 Math worksheets for your child will enjoy.

Come and take a look at our multiplication pages, or money flashcards. Perhaps you would prefer our telling the time worksheets, maths games or identifying 2d and 3d shapes in the geometry section?

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• This page contains links to other Math webpages where you will find a range of activities and resources.
• If you can't find what you are looking for, try searching the site using the Google search box at the top of each page.

Year 3 Maths Learning

Here are some of the key learning objectives for the end of Year 3:

• know and use Place value up to 1000
• Compare and order numbers up to 1000
• Counting on and back in 1s, 10s and 100s from different starting points
• Position numbers on a number line up to 1000
• know addition and subtraction facts to 20
• add or subtract 1s, 10s or 100s from a 3-digit number
• subtract 2- and 3-digit numbers in columns
• solve problems using addition and subtraction
• count from 0 in multiplies of 4, 8, 50 and 100
• recall and use multiplication and division facts from the 2, 3, 4, 5, 8 and 10 times tables
• multiply 2-digit numbers by a 1-digit number
• solve problems using multiplication and division
• count up and down in tenths
• understand tenths as decimals
• recognise and use fractions as numbers
• understand and use fractions of objects or shapes
• add and subtract amounts of money
• use £ and p notation correctly
• measure, compare, add and subtract lengths, mass and volume
• measure the perimeter of simple 2D shapes
• tell the time from an analogue clock
• convert between 12- and 24-hour clock
• measure and compare times
• Identify angles including right angles
• identify acute and obtuse angles
• identify horizontal, vertical, parallel and perpendicular lines
• recognise and draw 2D and 3D shapes
• interpret and present data in bar graphs, pictograms and tables
• solve 1-step and 2-step problems using data in tables, pictograms and graphs

Please note:

Our site is mainly based around the US Elementary school math standards.

Though the links on this page are all designed primarily for students in the US, but they are also at the correct level and standard for UK students.

The main issue is that some of the spelling is different and this site uses US spelling.

Year 3 is generally equivalent to 2nd Grade in the US.

On this page you will find link to our range of math worksheets for Year 3.

Quicklinks to Year 3 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions zone.

• Measurement Zone

Geometry Zone

Data analysis zone.

• Fun Zone: games and puzzles

Coronavirus Stay At Home Support

For those parents who have found themselves unexpectedly at home with the kids and need some emergency activities for them to do, we have started to develop some Maths Grab Packs for kids in the UK.

Each pack consists of at least 10 mixed math worksheets on a variety of topics to help you keep you child occupied and learning.

The idea behind them is that they can be used out-of-the-box for some quick maths activities for your child.

They are completely FREE - take a look!

• Free Maths Grabs Packs

Place Value & Number Sense Zone

Year 3 place value charts.

Here you will find a range of Free Printable Number Charts for Years 2 & 3.

These printable charts will help your child learn to read and write numbers.

Some of the charts are partially filled to help your child learn their place value.

Using these sheets will help your child to:

• learn to count in tens and ones;
• learn to read and write numbers.
• Printable Number Charts 0-99
• Hundred Number Charts (100 Squares)
• Number Grid up to 200
• Number Grid up to 300

Place Value & Counting Worksheets

Below are our selection of Place Value, Ordering and Rounding Worksheets

Using these Year 3 Maths worksheets will help your child to:

• learn to count by hundreds, tens, fives, twos and ones;
• learn their place value to Hundreds;
• order numbers to 999.
• Place Value Models and Representations
• Place Value Worksheets 3 Digits
• Math Practice - Counting by 1s 2s 5s 10s 100s

Ordering and Rounding Worksheets (3-digits)

Once your child is confident with their place value to hundreds, they can start learning about ordering and rounding numbers.

The Year 3 Maths worksheets here will help your child learn to compare numbers to 999, and round numbers to the nearest 10.

• Ordering Numbers Worksheets up to 3-Digits

Year 3 Number Line Worksheets

The following webpages involve correctly placing numbers on a number line.

Using these Year 3 maths worksheets will help your child to:

• count by 1s 2s 5s 10s 50s and 100s;
• position numbers on a number line;
• understand place value up to 3 digits.
• Number lines up to 100 (easier)
• Number Line Worksheets 3 Digits

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Year 3 Mental Maths Zone

Here you will find a range of printable mental math sheets for Year 3 to enjoy.

Each quiz tests the children on a range of math topics from number facts and mental arithmetic to geometry, fraction and measures questions.

A great way to revise topics, or use as a weekly math test or math quiz!

• Year 3 Mental Maths Worksheets Series A
• Year 3 Mental Maths Worksheets Series B

Year 3 Addition Worksheets

• learn their addition facts to 20+20
• learn how to solve addition sums where one of the addends is missing, but the total is given;
• learn to add numbers to 999 in columns.
• Number Bonds to 20
• Math Addition Facts to 20
• 2 Digit Column Addition Without Regrouping
• 2 Digit Column Addition Worksheets With Regrouping
• 3 Digit Column Addition Worksheets

Year 3 Subtraction Worksheets

The following worksheets involve using the skills of subtracting numbers, and solving subtraction problems.

• know their subtraction facts to 20;
• know how addition and subtraction are related to each other;
• learn to do 3 digit column subtraction.
• Subtraction Facts to 20 Worksheets
• Two Digit Subtraction Worksheets Without Regrouping
• 2 Digit Subtraction Worksheets With Regrouping
• 3 Digit Subtraction Worksheets

Addition & Subtraction Worksheets

You can create your own addition and subtraction worksheets with our random generator.

All you need to do is to set your number size and let the generator do the rest!

• Addition Subtraction Fact Worksheets
• Column Addition and Subtraction Worksheets

Year 3 Multiplication Worksheets

The following worksheets involve using the Year 3 Maths skills of multiplying, and solving multiplication problems.

• learn their multiplication tables up to 5 x 5;
• understand multiplication as repeated addition;
• learn how multiplication and division are related to each other.

Online Times Table Practice

• Times Tables Online Practice Zone
• Understanding Multiplication Worksheets
• Printable Times Tables - 2 Times Table sheets
• Printable Times Tables - 3 Times Table sheets
• Times Tables for kids - 4 Times Table sheets
• Times Table Math - 5 Times Table sheets
• Learning Times Tables - 8 Times Table

Multiplication Word Problems

• Year 3 Multiplication Word Problems (2nd Grade)

Randomly Generated Multiplication Worksheets

• Times Tables Worksheets (randomly generated)

2 Digit by 1 Digit Written Multiplication

• Multiplication Worksheets for 3rd Grade 2-digits by 1-digit
• Year 3 Division Worksheets

The following worksheets involve using the skills of dividing, and solving division problems.

Using these Year 3 maths worksheets will help your child learn to:

• understand division as repeated subtraction or sharing;
• understand different models of division;
• Division Facts Worksheets (randomly generated)

Here are a range of problems solving sheets for Year 3 children. Most of the sheets contain 'real-life' problems related to animal facts.

Using the sheets will help your child to:

• apply their addition, subtraction, and multiplication skills;
• 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. This link opens in a new tab.

• Year 3 Maths Challenges

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

• Year 3 Math Word Problems

These sheets involve solving a range of addition word problems within 100.

• Addition Word Problems 2nd grade

These sheets involve solving a range of subtraction word problems up to 100.

• Subtraction Word Problems 2nd grade
• 2nd Grade Addition and Subtraction Word Problems

These sheets involve solving a range of multiplication problems.

• Multiplication Word Problems Year 3

Year 3 Fraction Worksheets

• understand what a half is;
• shade in half of a shape;
• find different numbers involving 'halves' on a number line;
• find half of different numbers up to 20.
• Fraction Math Worksheets - Understanding a half
• Fraction Riddles for kids (easier)

Year 3 Geometry Worksheets

At a Year 3 level, children are introduced to a wider range of 2d and 3d shapes, and start to learn to reflect, flip and rotate shapes.

They are able to classify and sort two-dimensional shapes using different criteria, and they learn the properties of three-dimensional shapes.

The following worksheets will help your child to:

• Identify and name a range of 2d and 3d shapes;
• Draw 2d shapes;
• Know some of the properties of 2d shapes.
• Year 3 Geometry Worksheets (2nd Grade)

Symmetry Worksheets

• learn how to reflect simple shapes in a horizontal or vertical mirror line;
• learn how to reflect simple shapes in 2 mirror lines.
• Symmetry Worksheets - Block Symmetry

Measurement Zone, including Time & Money

Year 3 measurement worksheets.

These sheets involve reading scales going up in ones, fives, tens and hundreds to find the length, weight or liquid capacity.

Using these sheets will help children to consolidate their counting as well as learning to read a simple scale.

• Year 3 Measurement Worksheets (2nd Grade)

Counting Money Worksheets UK - £2, £1, 50p and 20p coins

Here you will find a selection of Counting Money sheets designed to help your child count different amounts of money using UK coins up to £2.

• count a range of coins up to £5
• compare money amounts
• apply their existing skills to puzzle out clues;
• understand money terminology;
• develop their thinking skills.

The free Year 3 Money worksheets in this section are suitable for children in Years 2 and 3.

• Free Money Worksheets UK Coins up to £1
• Year 3 Money Worksheets to £5
• Money Riddles for Kids (UK coins)
• Year 3 Money Challenges

Time Worksheets

Here are our collection of clock worksheets for Year 3. These sheets cover telling the time for quarter past and quarter to times.

• read times to the nearest 5 minutes;
• convert analogue to digital times;
• adding and subtracting hours from different times.
• Clock Worksheets - Quarter Past and Quarter To
• Telling Time to 5 Minutes Worksheets
• Add and Subtract Time Worksheets

Year 3 Bar Graph Worksheets

These sheets involve reading and interpreting a range of bar graphs and picture graphs with a scale going up in ones or twos.

Draw missing bars on a bar graph to the correct height.

Use the information in a bar graph to add data into a table.

Using the link below will open the 2nd grade Math Salamanders website in a new browser window.

• Year 3 Bar Graphs (2nd Grade)

Fun Zone: Puzzles, Games and Riddles

Year 3 math games.

All children like to play Math games, and you will find a good range of 2nd Grade Math Games here for your child to play and enjoy.

The following games involve different Second Grade Math activities which you and your child can enjoy together.

• Year 3 Math Games (2nd Grade)
• Year 3 Maths Puzzles

The puzzles will help your child practice and apply their addition, subtraction and multiplication facts as well as developing their thinking and reasoning skills in a fun and engaging way.

The Number Square Puzzles page will open a new browser window which will take you to the 2nd grade math salamanders website.

Using these puzzles will help your child to:

• learn their addition facts to 20+20;
• learn and practice subtraction facts to 20;
• pratice multiplying up to 5x5;
• develop thinking and reasoning skills;
• develop perseverance.
• Number Square Puzzles
• Math Puzzles at 2nd Grade Math Salamanders

Math Salamanders Year 3 Maths Games Ebook

Our Year 3 Maths Games Ebook contains all of our fun maths games, complete with instructions and resources.

This ebooklet is available in our store, use the link below to find out more!

• Year 3 Maths Games Ebook

Help & Support

Looking for a resource which is not here.

Take a look at our 2nd Grade Math Salamanders website.

On this site you will find a wider selection of Year 3 maths worksheets and free math resources.

• 2nd Grade Math Salamanders

Other UK Maths Worksheet pages

See below for our other maths worksheets hub pages designed for children in the UK.

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50 year 3 maths questions

Practise your maths skills with these 50 math questions for year 3 , covering addition, subtraction, place value, measurement, time, money, and geometry! Answers included.

Author Michelle Griczika

Published February 2024

• Key takeaways
• Mastering addition and subtraction skills helps us solve mathematical puzzles and apply them to real-life situations.
• Understanding place value enables us to correctly read, write, and compare numbers, developing our number sense and mathematical reasoning.
• Solving measurement word problems helps us apply mathematical concepts to practical scenarios, improving our problem-solving and critical thinking abilities.
• Exploring time and money concepts allows us to understand the world around us, manage our daily routines effectively, and develop essential life skills.
• Recognising shapes and their properties opens our eyes to the diverse world of geometry, helping us understand how objects are structured and enhancing our spatial awareness.

Table of contents

• Addition & subtraction
• Place value
• Measurement
• Time & money

Hello, year 3 mathematicians! Are you ready for some mind-boggling maths challenges?

We will be going over important maths skills needed to strengthen understanding of important mathematical concepts. Let’s dive in!

Section 1: Addition and subtraction

Section 2: place value.

Use the greater than symbol >, less than symbol <, or equal to symbol = to answer.

Answer: <

Answer: >

Section 3: Measurement

Answer: 53 centimetres

Answer: 38 centimetres

Answer: 32 centimetres

Answer: 35 centimetres

Answer: 55 centimetres

Answer: 68 centimetres

Answer: 84 centimetres

Answer: 40 centimetres

Answer: 50 centimetres

Section 4: Time & Money

Look at the analog clock and write the time to the nearest five minutes:

What time is shown on the digital clock?

Answer: £4.34

Answer: £5.08

Answer: 25 pence

Answer: £3.50

Answer: £4.37

Section 5: Geometry

Answer: Triangle

Answer: Square

Answer: Pentagon

Answer: Hexagon

Answer: Equilateral Triangle

Answer: Trapezoid

Answer: Cube

Maths practice for year 3 is super important because we use it every single day! For extra maths practice that comes in the form of fun maths games and interactive practice problems, try Doodle Learning’s maths help app .

Lesson credits

Michelle Griczika

Michelle Griczika is a seasoned educator and experienced freelance writer. Her years teaching coupled with her double certification in early childhood education lend depth to her understanding of diverse learning stages. Michelle enjoys running in her free time and undertaking home projects.

Parents, sign up for a DoodleMaths subscription and see your child become a maths wizard!

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