reasoning and problem solving decimals year 4

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Free Year 4 Maths Worksheets And Homework – Download, Print, Or View Online

Anantha Anilkumar

Here you’ll find all our free Year 4 maths worksheets and Year 4 maths tests, many of which are suitable for homework as well as classroom teaching.

You can use these resources and workbooks as you like; most of the KS2 maths worksheets come in pdf format and all of them are printable if you want to give children something physical to work with. But they can also be downloaded and kept, or viewed online, if you prefer to keep things electronic. 

To supplement these we also have a range of maths activities , lesson plans and powerpoints for classroom teaching which are available from our White Rose maths  page.

Many of these worksheets and maths tests are aimed at helping children improve their number work – we have mental maths practice work, place value worksheets , addition and subtraction worksheets , multiplication & division worksheets etc.

All our maths worksheets and tests come with answer sheets too, including advice from the National Curriculum (about the range of answers that are acceptable, for example), where needed.

If you’re a  parent  looking for more advice, try our  home learning  hub full of  home learning packs , tips and teaching ideas for  Year 4 Maths  at home and  maths homework .

If you’re a  teacher or school leader  who is interested in improving maths attainment in your school or classroom, then this whole website is for you. Third Space Learning is dedicated to improving outcomes in maths with our  online tutoring  programme of  maths interventions , together with  maths resources  and CPD. You’re welcome to link to these free resources from your own website like thousands of other schools do.

Free Year 4 Maths Worksheets and Tests

A collection of free Year 4 maths activities from the Third Space Maths Hub. You need to register to download (but it's free). Use Google Chrome.

Year 4 Maths Worksheets for fluency, reasoning, and problem solving

Year 4 times tables worksheets, year 4 place value worksheets, year 4 addition and subtraction worksheets , year 4 multiplication and division worksheets , year 4 decimals worksheets , year 4 measurement worksheets, year 4 fractions worksheets, year 4 statistics worksheets, year 4 maths tests: all topics, year 4 maths worksheets to improve fluency, mental maths and arithmetic skills: fluent in five.

Fluent in Five worksheets provide a series of questions designed to take no more than 5-10 minutes and to help children develop their written and mental maths skills. Developing maths fluency in a key skill for children, especially in Year 4 with the newly-introduced times tables check to work towards. 

Download  Fluent in Five Arithmetic Pack (Year 4) Weeks 1-6

Year 4 Maths Worksheets for improving reasoning and problem solving skills: Rapid Reasoning

The Rapid Reasoning resource was created to fulfil the greater emphasis that a maths mastery approach gives to children’s ability to reason well. ‘Explaining your reasoning’ is a key part of maths lessons in Key Stage 2, and these free worksheets (six weeks’ worth in total) help children improve their reasoning skills. Each worksheet comes with around three questions based on Year 4 maths topics, example answers, and even step-by-step explanations to help pupils break down how to get to an answer. 

Download  Rapid Reasoning (Year 4) Weeks 1-6

Year 4 Maths Test: Times Tables

Knowing their multiplication tables is one of the key maths skills every child should have by the time they leave primary school, and Year 4 children will have this skill tested through the new multiplication tables check . 

These times tables practice tests provide a quick and clear way to help children practise, and spot any gaps in their knowledge. No more worries about getting caught out on the 7x table!

Download the Times Tables Packs

Year 4 Maths Worksheets for times tables: Tarsia Puzzles Mixed Times Tables Pack

These times tables worksheets are a fun way to practise times tables facts and related division facts independently and develop mental arithmetic skills.  

Download the Tarsia Puzzles Mixed Times Tables Pack

Year 4 Maths Worksheets for place value: All Kinds of Word Problems

This worksheet contains ten increasingly difficult questions about number and place value. A great choice whether you want to help a child revise this topic, or give a high achiever something more challenging to do as homework!

Download  All Kinds of Word Problems on Number and Place Value (Year 4)

Year 4 Maths Worksheets for addition and subtraction: Let’s Practise Using the Bar Model

These worksheets focus on word problems involving addition and subtraction of up to 4-digit numbers. It is important for children to experience a range of question types, especially in a topic where they may feel more confident. 

Download Year 4 addition and subtraction worksheets: Let’s Practise Using the Bar Model

Year 4 Maths Worksheets for addition and subtraction: Worked Examples

While children will have looked at formal column addition and subtraction, there are many common mistakes that even the most experienced amongst them can make. This worksheet highlights the common errors when using formal written methods, estimating and identifying related facts for addition and subtraction calculations. 

Download Year 4 Worked Examples Addition and Subtraction

Year 4 Maths Worksheets for addition and subtraction: Maths Code Crackers

Sometimes a simple set of fluency questions can be engaging. This worksheet focuses on calculations including up to 4-digit numbers add 4-digit numbers and up to 4-digit numbers subtract 4-digit numbers, all with the aim of finding answers and the punchline to a halloween themed joke. 

Download Year 4 Code Crackers: Addition and Subtraction

Year 4 Maths Worksheets for addition and subtraction: All Kinds of Word Problems 

These worksheets provide children with an opportunity to solve a wide range of addition and subtraction word problems. The problems range from missing digits to adding money and measures.

Year 4 Maths Worksheets for multiplication: All Kinds of Word Problems 

In Year 4, children are not only expected to know their times tables facts up to 12 x 12, they also need to know how to multiply 3-digit numbers by a 1-digit number. This workbook covers problems involving factors, missing numbers, multiplying 3-digit numbers by 1-digit numbers as well as times table facts. 

Download All Kinds of Word Problems: Multiplication 

Year 4 Maths Worksheets for multiplication: Let’s Practise Using the Bar Model

These worksheets include a range of word problems that can be solved using bar models. The questions cover times tables up to 12 x 12 as well as 2-digit numbers multiplied by 1-digit numbers. 

Download Year 4 Let’s Practise Using the Bar Model Multiplication Worksheets

Year 4 Maths Worksheets for division: Short and Long Division Worksheets

Long division is one of the most difficult parts of the primary maths curriculum, and learning long division requires a good understanding of short division to start with. While a Year 4 child won’t have learnt long division yet, these worksheets include short division questions at the beginning, helping children sharpen their division skills in preparation for the next step.

Download our Free Year 4 Division Worksheets

Year 4 Maths Worksheets for multiplication and division: Code Crackers

A fun way for children to get some more practise in: every question’s answer is part of the punchline of a joke. Solve them all and you solve the joke! The questions themselves cover all of the new things pupils have learned about the topic, so it’s easy to identify where any gaps are. 

Download  Maths Code Crackers Year 4: Multiplication and Division

Year 4 Maths Worksheets for multiplication and division: Worked Examples 

Children love to be the teacher. This worksheet gives children an opportunity to check work that has already been completed, explain any errors and develop reasoning skills. The worksheet covers a range of multiplication and division topics, including multiplying three 1-digit numbers together and dividing a 2-digit number by a 1-digit number.

Download Year 4 Worked Examples Multiplication and Division 

Year 4 Maths Worksheets on decimals: Independent Recap

This small collection of four worksheets covers tenths, hundredths, and dividing 1- and 2-digit numbers by 10 and 100 – all topics covered in Year 4 maths.

As independent working activities, they are specifically designed to be completed by children even if they can’t get access to online tools, or parent support.

Download the Year 4 Decimals Independent Recap Worksheets

Year 4 Maths Worksheets on decimals: Worked Examples 

Decimals are first formally introduced to children in Year 4. This worksheet focuses on a range of topics including understanding the value of the digits in a decimal number, dividing by 10 and converting between fractions and decimals. As decimals is a new topic to Year 4, there are several common errors pupils could make and this worksheet aims to address these misconceptions. 

Download Year 4 Worked Examples Decimals

Year 4 Maths Worksheets on decimals: Maths Code Crackers Year 4 Decimals

This worksheet focuses on the value decimals, ordering decimals and adding decimals to make a whole in a fun way. Children need to answer the questions to solve the answer to a topical joke. 

Download Maths Code Crackers Year 4 Decimals

Year 4 Maths Worksheets on area: Code Crackers

Area is a new and more complicated Year 4 topic, moving away from the number facts and arithmetic-based work children will have been used to from previous years. Our Code Crackers worksheet on area gives them the chance to test their understanding of this more complex topic, and have fun at the same time. Answers for all questions are included with the pack. 

Download  Maths Code Crackers Year 4: Area

Year 4 Maths Worksheets on area: Year 4 Worked Examples Area

When covering the topic of area, it is important that children understand not only what area is but what a 2-D shape is. This worksheet covers the required content for this year group while also addressing common misconceptions that can form when the new topic of area is introduced. Children will focus on counting the squares to calculate areas as well as compare areas while they check and explain incorrect answers. 

Download Year 4 Worked Examples Area

Year 4 Geometry worksheets

Year 4 maths worksheets for properties of shape: independent recap.

Children have been learning about shapes since Year 1, but that does not mean the content is easy to understand. These worksheets cover identifying angles (including the names of angles and measurements in degrees), comparing and ordering angles as well as properties of 2d shapes, classifying triangles and quadrilaterals and identifying lines of symmetry  and completing symmetrical figures. 

Download Year 4 properties of shapes worksheets: Independent Recap  

Year 4 Maths Worksheets for properties of shape: Code Crackers

This properties of shape worksheet focuses on recapping all the learning from this block of work. With a range of retrieval questions to answer, children need to answer the questions correctly to find the answer to a Wimbledon related joke. 

Download Year 4 properties of shape worksheets: Code Crackers

Year 4 Maths Worksheets for properties of shape: Worked Examples

There are several different aspects of properties of shape that children need to know in Year 4. This worksheet recaps some of the key language in the topic (for example, obtuse angle, rhombus) as well as some key concepts (for example, classification of triangles, lines of symmetry), while including opportunities to develop reasoning skills. 

Download Year 4 Properties of Shapes Worksheets: Worked Examples

Year 4 Maths Worksheets for fractions: Code Crackers

Finding fractions of numbers is a maths skill that becomes more and more important the later a child gets in their maths learning, but the basics are covered in Key Stage 2. This fractions for kids worksheet helps children become better at solving these types of problems without making it seem (too much) like work. 

Download  Maths Code Crackers Year 4: Fractions

Year 4 Maths Worksheets for fractions: Independent recap 

These worksheets recap adding and subtracting fractions with the same denominator and calculating fractions of quantities. Children will have been introduced to both of these topics in Year 3, however it is important that they have a strong understanding of the concepts before moving on to more complex fraction work. These worksheets encourage completely independent work. 

Download Year 4 Fractions Independent Recap

Year 4 Maths Worksheets for fractions: Year 4 Worked Examples

The topic of ‘fractions’ is very broad. In this worksheet, the focus is on 5 different areas of the fractions block that children in Year 4 often find confusing (adding three or more fractions, finding a fraction of an amount, subtracting from a whole, equivalent fractions and counting in fractions). 

Download Year 4 Worked Examples Fractions

Year 4 Maths Worksheets for statistics: Worked Examples

In Year 4, children are expected to be able to read and interpret a range of graphs and tables. This worksheet focuses on reading a table, bar chart and line graph. Children should be familiar with tables and bar charts but will have been introduced to line graphs for the first time in Year 4.  

Download Year 4 Maths Worksheets for statistics: Worked Examples

Year 4 Maths Worksheets for statistics: Independent Recap

These worksheets focus on answering questions about bar charts, tables and line graphs. As line graphs are new to Year 4, one of the worksheets in this pack encourages children to use data to draw their own line graphs. 

Download Year 4 Maths Worksheets for statistics: Independent Recap

Year 4 Maths Worksheets for statistics: Code Crackers

This worksheet encourages children to read and interpret a range of graphs to answer retrieval, comparison and sum questions about a range of different graphs and tables. 

Download Year 4 Maths Worksheets for statistics: Code Crackers

A great way to get an overall idea of a Year 4 child’s maths learning – two tests (one arithmetic, one reasoning) of about an hour each, with answer sheets included. Please remember that children may not have covered every topic on this test, so they may not be able to answer some questions.

Download our free Year 4 Assessment Pack

Also in this series…

• Year 2 Maths Curriculum Toolkit for 6 & 7 Year Olds
• Year 2 Maths Worksheets
• Year 3 Maths Curriculum Toolkit for 7 & 8 Year Olds
• Year 3 Maths Worksheets
• Year 5 Maths Curriculum Toolkit for 9 & 10 Year Olds
• Year 5 Maths Worksheets
• Year 6 Maths Curriculum Toolkit for 10 & 11 Year Olds
• Year 6 Maths Worksheets

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Reasoning/Problem Solving Maths Worksheets for Year 4 (age 8-9)

This category is all about children choosing the most appropriate method to achieve a quick and accurate answer and to be able to explain their methods and reasoning.

Problem solving: finding the missing digits in 4-digit numbers. Tricky!

Problem solving: finding the values of missing counters. Logical thinking and careful work needed here!

Reasoning about numbers on a number line and rounding numbers.

More reasoning about number and place value.

Not only do the questions have to be answered, but explanations given. These pages really show how well children understand what they are doing.

More written explanations on which operation to use and whether the question should be done mentally or on paper.

Lots of questions, most of which can be done mentally. The important thing is to explain how they were tackled.

Decide which operation is needed (add, subtract, multiply, divide) and whether a calculator, or pencil and paper are needed, or whether it can be done, 'in your head'.

Solving problems

A selection of problem solving activities and word problems.

Here are some problems written in words. Fairly straightforward as they require just one mathematical step to work out the answer

Some word problems that need at least two steps to find the answer. This makes them much harder, so careful thinking is needed.

5 pages of word problems, all involving money. Some are suitable for calculator work as they are specially written to make the process the most important factor: it is no use having a calculator if you don't know what calculation to carry out!

A range of number and money problems, typical of those found in KS2 test papers.

More number and money problems, typical of those found in KS2 test papers.

Tricky word problems involving time and money.

More word problems; this time on measurement of length, mass and capacity. These really test children's understanding of when to use addition, subtraction, multiplication or division to solve a problem.

Time problems are especially tricky, especially when finding lengths of time that cross the hour boundary. A good knowledge of the number of days in each month is also needed.

Not many problems on a page, but there is an awful lot within each question. Each is a mini investigation, which can be explored in depth.

Number patterns, remainders, number machines and much more in this mixed selection of problems.

Working out the missing value.

More working out missing values.

Using the instructions on the packet what is the maximum number of bulbs that can be grown in the garden?

Using the instructions on the packet what is the maximum number of seeds that can be sown in the garden?

Using the instructions on the packet what is the maximum number of vegetables that can be grown in the garden?

An addition challenge suitable for year 4 on.

The fish are all called numbers. Can you work out their names by solving the clues?

Investigations

More open ended activities where children choose the approach to the task.

Making rules for sequences is an early step towards understanding algebra, and an important part of Year 5 maths. More 'How would you...?' type questions as well.

How many different three course meals can Sam choose?

Investigate patterns made by placing consecutive numbers in a number square.

A great little investigation which has plenty of extension possibilities.

Fun addition investigation using the date: 22.02.2022.

Some thoughts on how important this area of maths is.

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Resources tagged with: NC Yr 4

There are 51 NRICH Mathematical resources connected to NC Yr 4 , you may find related items under NC .

Satisfying Four Statements

Can you find any two-digit numbers that satisfy all of these statements?

Representing Numbers

Find as many different ways of representing this number of dots as you can.

Ordering Journeys

How would you put these journey lengths in order?

What Distance?

Can you use addition and subtraction to answer these questions about real-life distances?

Count Me In

How do you know whether you will reach these numbers when you count in steps of six from zero?

Dicey Operations in Line

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Seeing Squares

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Reasoned Rounding

Four strategy dice games to consolidate pupils' understanding of rounding.

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Let Us Divide!

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Bryony's Triangle

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Sorting Logic Blocks

This activity focuses on similarities and differences between shapes.

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

A task which depends on members of the group noticing the needs of others and responding.

What Shape?

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

Counters in the Middle

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Table Patterns Go Wild!

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Times Tables Shifts

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Reflector ! Rotcelfer

Can you place the blocks so that you see the reflection in the picture?

Nice or Nasty

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

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Four-digit Targets

You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Venn Diagrams

How will you complete these interactive Venn diagrams?

Eight Hidden Squares

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Shape Times Shape

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Multiplication Square Jigsaw

Can you complete this jigsaw of the multiplication square?

Twice as Big?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Multiples Grid

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Coordinate Challenge

Use the clues about the symmetrical properties of these letters to place them on the grid.

Torn Shapes

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Take Your Dog for a Walk

Use the interactivity to move Pat. Can you reproduce the graphs and tell their story?

Fractional Wall

Using the picture of the fraction wall, can you find equivalent fractions?

Stringy Quads

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Nine-pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

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?

Andy's Marbles

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

How Big Are Classes 5, 6 and 7?

Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.

Fractional Triangles

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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.

Symmetry Challenge

How many symmetric designs can you make on this grid? Can you find them all?

Let Us Reflect

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

A Cartesian Puzzle

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Shapes on the Playground

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

Round Decimals: Reasoning and Problem Solving

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Hundredths as Decimals Year 4 Decimals Resource Pack

Step 8: Hundredths as Decimals Year 4 Spring Block 4 Resources

Hundredths as Decimals Year 4 Resource Pack includes a teaching PowerPoint and differentiated varied fluency and reasoning and problem solving resources for Spring Block 4.

Free Home Learning Resource

Download for print Save to G-drive Answers and Guidance

Additional questions are available for Premium members.

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What's included in the pack?

This pack includes:

• Hundredths as Decimals Year 4 Teaching PowerPoint.
• Hundredths as Decimals Year 4 Varied Fluency with answers.
• Hundredths as Decimals Year 4 Reasoning and Problem Solving with answers.

National Curriculum Objectives

Mathematics Year 4: (4F6b) Recognise and write decimal equivalents of any number of tenths or hundredths

Differentiation:

Varied Fluency Developing Questions to support recognising hundredths as a decimal (in numbers smaller than one where there are always digits in the tenths and hundredths columns, excluding zero), with visual support. Expected Questions to support recognising hundredths as a decimal (in numbers smaller than one where there where there are always digits in the tenths and hundredths columns, including using zero as a placeholder), with some visual support. Greater Depth Questions to support recognising hundredths as a decimal (in numbers greater than one where there are always digits in the tenths and hundredths columns, including using zero as a placeholder), with no visual support.

Reasoning and Problem Solving Questions 1, 4 and 7 (Reasoning) Developing Explain which statement is correct using decimals smaller than one. Expected Explain which statement is correct using decimals smaller than one and zero as a place holder. Greater Depth Explain which statement is correct using decimals greater than one and zero as a place holder.

Questions 2, 5 and 8 (Problem Solving) Developing Use three digit cards to make three decimals less than one, demonstrating understanding by including equivalent fractions. Zero given in ones. Expected Use four digit cards to make three decimals less than one, demonstrating understanding by including equivalent fractions. Greater Depth Use six digit cards to make three decimals greater than one, demonstrating understanding by including equivalent fractions.

Questions 3, 6 and 9 (Reasoning) Developing Explain whether an inequality statement is correct using decimals less than one, some visual support. Expected Explain whether an inequality statement is correct using decimals less than one with zero as a place holder. Greater Depth Explain whether an inequality statement is correct using decimals greater than one with zero as a place holder.

This resource is available to download with a Premium subscription.

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