year 3 fractions on a number line problem solving

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Fraction Number Line Sheets

Welcome to our Fraction Number Line Worksheets.

We have a range of number line resources, including support sheets and worksheets to help your child understand how to place fractions on a number line and understand fraction equivalence.

We have some resource sheets available in color and also in landscape as well as portrait.

These sheets are aimed at 3rd and 4th graders.

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• Fraction Number Line 0 to 1 Printables (portrait)
• Fraction Number Line 0 to 1 Printables (landscape)
• Fraction Number Line Worksheets
• Mixed Fraction Number Line Worksheets
• More related Math resources

Fraction Number Line Online Quiz

Fraction number line, number line fraction resources.

Here you will find a selection of printable Fraction lines designed to help your child understand visually how much fractions are worth.

The support sheets are also great for learning about equivalent fractions.

Using these sheets will help your child to:

• develop an understanding visually of how much fractions are worth.
• compare two fractions;
• begin to learn about fraction equivalence.

Fraction Number Line Printables: 0 to 1 Portrait Support Sheets

• Fraction Number Line 0 to 1 Sheet 1a
• PDF version
• Fraction Number Line 0 to 1 Sheet 1b
• Empty Fraction Number Line 0 to 1 Sheet 1c
• Fraction Lines 0 to 1 in simplest form
• Fraction Number Lines 1 to 2

Fraction Number Line Printables: 0 to 1 Landscape Support Sheets

• Fraction Number Line 0 to 1 Landscape Sheet 1a
• Fraction Number Line 0 to 1 Landscape Sheet 1b
• Fraction Number Line 0 to 1 Landscape Sheet 1c

Fraction Number line Worksheets

Here you will find a selection of free fraction worksheets designed to help your child understand the value of fractions.

• understand visually how much fractions are worth;
• understand how to work out the next fraction in a simple sequence.

The first set of worksheets is all about filling in the missing fractions between 0 and 1.

The second set of worksheets involves working out different mixed numbers greater than 1.

Number Line Fraction Worksheets 0 to 1

• Fraction Number Line Worksheets 1a
• Fraction Number Line Worksheets 1b
• Fraction Number Line Worksheets 1c
• Fraction Number Line Worksheets 1d

Number Line Fraction Worksheets - Mixed Numbers > 1

• Fraction Lines Sheet 2
• Sheet 2 Answers
• Fraction Lines Sheet 3
• Sheet 3 Answers
• Fraction Lines Sheet 4
• Sheet 4 Answers

More Recommended Math Worksheets

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

• Decimal Number Lines

Here is our collection of decimal number lines.

• see visually the order of decimal numbers in a number line;
• understand place value of decimals.

Fractions of shapes

Before you learn about finding fractions of numbers, you should be confident with fractions as parts of a whole.

Here you will find a selection of Fractions of Shapes Worksheets designed to help your child understand fractions of shapes as parts of a whole.

• develop an understanding of fractions as parts of a whole;
• work out the fractions of shapes.
• Fractions of Shapes Worksheets

Fractions of Numbers

Often when we are talking about and using fractions, we are looking at fractions of numbers or quantities.

To find a fraction of a number or quantity, we need to first divide the number or quantity by the denominator. Then multiply this by the numerator to give the answer.

The printable learning fractions page below contains more support, examples and practice finding fractions of numbers.

• Unit Fraction of Numbers
• Fraction of a Whole Number

Learning Fractions Math Help Page

Here you will find the Math Salamanders free online Math help pages about Fractions.

There is a wide range of help pages including help with:

• fraction definitions;
• equivalent fractions;
• converting improper fractions;
• how to add and subtract fractions;
• how to convert fractions to decimals and percentages;
• how to simplify fractions.
• Learning Fractions Support

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This quick quiz tests your understanding and skill at recognising and understanding fractions on a number line.

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Fractions on a number line Online practice for grades 3-5

Practice marking fractions on a number line with this interactive exercise. You will be shown a number line, and you drag a dot to the correct place to represent the given fraction (standard CCSS.3.NF.A.2).

You can choose to work with proper or improper fractions and/or mixed numbers. Proper fractions are the easiest, whereas placing an improper fraction on a number line probably requires you to change it to a mixed number first. You also have the option of practicing with positive or negative fractions, or both.

Free Printable Fractions on a Number Line Worksheets for 3rd Year

Math Fractions on a Number Line: Discover our collection of free printable worksheets for Year 3 students, designed to help them understand and master fractions using number lines effectively.

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Explore printable Fractions on a Number Line worksheets for 3rd Year

Fractions on a Number Line worksheets for Year 3 are an excellent resource for teachers looking to enhance their students' understanding of fractions and their applications in mathematics. These worksheets provide a variety of engaging activities that help students visualize and manipulate fractions using number lines. By working with Fraction Models, students can develop a deeper comprehension of the relationships between different fractions, as well as their equivalencies and comparisons. Teachers can use these worksheets to supplement their existing math curriculum, providing additional practice and reinforcement of key concepts. With a focus on Year 3 math standards, these worksheets are specifically designed to support the development of essential fraction skills in young learners. Fractions on a Number Line worksheets for Year 3 are a valuable tool for any teacher looking to strengthen their students' foundation in fractions.

Quizizz offers a fantastic platform for teachers to create interactive and engaging worksheets, including those focused on Fractions on a Number Line for Year 3 students. With Quizizz, teachers can easily design customized worksheets that incorporate Fraction Models and other visual aids to help students grasp complex math concepts. In addition to worksheets, Quizizz also provides a wide range of other educational resources, such as quizzes, flashcards, and interactive games, all designed to support learning in a fun and engaging way. By utilizing Quizizz's extensive library of resources, teachers can ensure their Year 3 students receive a well-rounded education in math, fractions, and beyond. The platform's user-friendly interface and customizable features make it an ideal choice for educators seeking to enhance their students' learning experience in an innovative and effective manner.

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Fractions on a Number Line Lesson

This Year 3 Fractions on a Number Line lesson covers the prior learning of making equal parts, before moving onto the main skill of using a number line to count forwards and backwards in fractions.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

National Curriculum Objectives

Mathematics Year 3: (3F1c) Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

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Interactive activities for children

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Lesson Slides

These lesson slides guides pupils through the prior learning of making equal parts, before moving onto the main skill of fractions on a number line. There are a number of questions to check pupils' understanding throughout.

Modelling PowerPoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

Video Tutorial

In this Fractions on a Number Line (up to one whole) Video Tutorial, Aaron shows pupils how to identify fractions on a number line. He uses key vocabulary including quarters, equal parts and whole.

In this Fractions on a Number Line (over 1) Video Tutorial, Aaron shows pupils how to identify fractions greater than one on a number line using bar models. He uses key vocabulary including thirds, equal parts and whole.

1 Prior Learning

This worksheet recaps prior learning of making equal parts, before moving onto the main skill of using a number line to count forwards and backwards in fractions.

Interactive Activity

This Year 2 Make Equal Parts Game checks pupils’ understanding of recognising equal parts of shapes or quantities.

This Year 2 Recognise a Half Game checks pupils’ understanding of recognising half of a shape or set of objects.

This Year 2 Recognise a Quarter Game checks pupils’ understanding of recognising a quarter of different shapes.

This Year 2 Recognise a Third Game is designed to checks pupils’ understanding of recognising thirds using a variety of representations.

2 Varied Fluency

This differentiated worksheet includes varied fluency questions for pupils to practise the main skill of this lesson.

This Fractions on a Number Line Greater Than 1 Game checks pupils’ understanding of representing fractions that are beyond one whole on a number line.

This Fractions on a Number Line Less Than 1 Game checks pupils’ understanding of finding fractions on a number line no greater than 1.

2 Reasoning & Problem Solving

This fractions on a number line extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the fractions on a number line lesson.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of fractions on a number line.

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

This Year 3 Fractions on a Number Line Maths Challenge checks pupils’ knowledge of counting forwards and backwards using fractions.

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Consolidation Pack

These Fractions worksheets are fantastic at helping your pupils practice their reasoning and problem solving skills. This pack contains two different question types for Year 3 Spring Block 5.

Home Learning Pack

This Summer week 1 Maths pack contains varied fluency, reasoning and problem solving worksheets

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Year 3: Fractions

New Maths Curriculum (2014): Year 3 objectives.

Pupils should connect tenths to place value and decimal measures, not restricted to decimals between 0 and 1 inclusive and to division by 10. 

They should begin to understand unit and non-unit fractions as numbers on the number line, and deduce relations between them, such as size and equivalence. They should go beyond the [0, 1] interval, and 1/4 + 3/4 = 1 for example, relating this to measure. 

Pupils should understand the relation between unit fractions as operators and division by integers. 

They should continue to recognise fractions in the context of parts of a whole, numbers, measurements, a shape, or unit fractions as a division of a quantity.

Pupils should practise adding and subtracting fractions with the same denominator through a variety of increasingly complex problems to improve fluency.  

Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10

Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators, recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators, recognise and show, using diagrams, equivalent fractions with small denominators, add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7), compare and order unit fractions, and fractions with the same denominators, solve problems that involve all of the above.

What your child will learn

Understand and count in tenths.

In Year 3, your child will learn to count in tenths. They will understand that finding a tenth is the same as dividing by ten (by dividing objects, sets of objects, and numbers into ten equal parts).

This will help them to keep seeing the connection between fractions and division. It is possible that your child will start to be introduced to decimals at this stage, too.

Find fractions of a set of objects

Your child will learn to find and write fractions of a given number of objects. For example:

Find     of 15.   First, your child can find   of 15 by dividing the total by the denominator : 15 ÷ 5 = 3.   Then, they can multiply this result by the numerator to find the correct fraction: If   of 15 is 3, then    of 15 is 3  × 2 = 6.     of 15 is therefore 6.

Your child will be able to do this with unit and non-unit fractions. They will learn that:

Use fractions as numbers

Your child will be able to do this with unit and non-unit fractions:

Show equivalent fractions using diagrams

They’ll show their understanding of equivalent fractions by drawing diagrams like this:

Your child will also learn to use objects and  fraction walls  to show equivalent fractions.

Add and subtract fractions with the same denominator

Compare and order fractions

Solve problems that involve all of the above.

Finally, your child will learn to put all this learning into practice by solving problems involving fractions.

They will be able to relate fractions to division, count in fractional steps (for example, counting up and down in tenths), compare fractions, understand  unit  and  non-unit fractions , understand equivalent fractions, find fractions of amounts, and add and subtract fractions with the same denominator.

How to help at home

There are lots of everyday ways you can help your child to understand fractions. Here are just a few ideas.

1. Make fraction snowflakes

Paper folding can be a great way to explore fractions.

Decorate a piece of paper or card and then ask your child to fold the paper into different equal parts. For example, they could fold the paper into fifths by creating five equal sections. Ask them to show you a fifth, two-fifths, three-fifths, four-fifths, and five-fifths, which they can see is equivalent to a whole.

Challenge your child by giving the paper a value and asking them to work out what the fractions would be worth. What would one fifth represent if the whole paper had a value of 10? As they fold, they may like to cut patterns into the paper to make a ‘snowflake’ and watch the pattern develop as they fold further.

2. Have fun with food

Cake, pizza, or any foods with a regular shape can help children understand what fractions are and how they work. Ask your child questions like, ‘If I cut our cake into 8 pieces, what fraction will each piece be?’

Foods that people eat lots of can help your child understand how to find fractions of amounts. For example:

‘We have 12 fish fingers in the packet. There are 4 of us. What fraction of the fish fingers can we each have? How many fish fingers would that be?’

Activity: Cupcake fractions

3. Compare fractions together

In Year 3, your child will compare  unit fractions  and fractions with the same  denominator  by saying which fraction is bigger or smaller – and explaining how they know.

4. Fraction countdown

‘Would you prefer it if I cut this cake into ten equal pieces and gave you a piece, or if I cut the cut into two equal pieces and gave you a piece?’

Print out the  Fraction Match activity sheet and cut out each fraction card. Take a selection of cards and see if your child can put them all in order, either from largest to smallest or smallest to largest. Are there any equivalent fractions? See if your child can match them up.

Activity: Fraction Match

5. Make a fraction wall

Equivalent fractions are different fractions that have the same value. In Year 3, your child will learn about equivalent fractions with small denominators using drawings and diagrams.

Why not try making a fraction wall with your child? You could investigate using the computer to make your fraction wall by creating a table and splitting each row into the equal number of parts you need. For example, to represent fifths, you would have to split the whole row into five equal parts.

Alternatively, you can download our fraction wall below.

Fraction wall

6. Adding and subtracting fractions

Try adding and subtracting fractions with the same denominator with your child. Try to do this within a whole, i.e. make sure that the sum uses numbers less than one, including the answer.

Using drawings or diagrams can help your child visualise adding and subtracting fractions. For example:

 +   =    This could be calculated using a diagram like this:     Y our child will first split the whole into five equal parts. Your child can then shade one box to represent   and two boxes to represent  . They will then be able to see that the total is  .

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Published 2013 Revised 2019

Exploring Fractions

• The first group  gives you some starting points to explore with your class, which are applicable to a wide range of ages.  The tasks in this first group will build on children's current understanding of fractions and will help them get to grips with the concept of the part-whole relationship. 
• The second group of tasks  focuses on the progression of ideas associated with fractions, through a problem-solving lens.  So, the tasks in this second group are curriculum-linked but crucially also offer opportunities for learners to develop their problem-solving and reasoning skills.   

• are applicable to a range of ages;
• provide contexts in which to explore the part-whole relationship in depth;
• offer opportunities to develop conceptual understanding through talk.

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Counting Fractions on a Number Line Problems: Foundation (Year 3)

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This resource is suitable for the White Rose Maths Scheme of Learning, covering Spring Term Block 3 (Fractions A), Step 8 (Count in Fractions on a number line).

Using this worksheet children will be asked to solve the number line fraction problems. Can they decide which number line statements are correct, and explain why, and identify the correct placements of fractions on number lines?

An answer sheet is included.

This worksheet is available in different levels. Please see the drop-down menu to select another level.

This resource is also available in a handy Lesson Pack, containing a selection of brilliant worksheets for this small step.

View Lesson Pack    See all Year 3 White Rose

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: White Rose Maths | Spring Term: Fractions A | Small Step 8
• Topic Group: Fractions, Decimals and Percentages
• Year(s): Year 3
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 27/02/2024
• Resource Code: M2WFT16689
• Curriculum Point(s): Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators.

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