problem solving factors year 6

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Year 6 Maths Worksheets UK Hub Page

Welcome to our Year 6 Maths Worksheets area.

Here you will find a wide range of free printable Year 6 Maths Worksheets for your child to enjoy.

Come and take a look at our rounding decimal pages, or maybe some of our adding and subtracting fractions worksheets. Perhaps you are looking for some worksheets about finding angles in a triangle, or need some ratio problem worksheets to help your child learn about ratio?

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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 6 Maths Learning

Here are some of the key learning objectives for the end of Year 6:

• know and use Place value up to 10 million
• Counting on and back in steps of powers of 10 from any number up to 10 million
• Round numbers to any given degree of accuracy.
• Count forwards and backwards through zero with positive and negative numbers.
• Read Roman numerals to 1000 and recognise years written in Roman numerals
• solve multi-step problems using addition and subtraction in a range of contexts
• identify multiples and factors including common factors
• multiply and divide up to 4-digit numbers by up to 2 digits
• Use their knowledge of the order of operations to carry out calculations involving the four operations.
• Identify common factors, common multiples and prime numbers.
• solve problems involving addition, subtraction, multiplication and division
• simplify fractions
• compare and order fractions including mixed numbers
• add and subtract fractions with different denominators including mixed numbers
• multiply simple fractions together and simplify the answer
• divide proper fractions by whole numbers
• recall and use equivalence between simple fractions, decimals and percentages.
• Multiply and divide whole numbers and decimals up to 3dp by 10, 100 or 1000
• read, write, order and compare numbers up to 3dp
• round decimals with up to 3dp to the nearest whole
• solve problems with numbers up to 3dp
• work out percentages of different amounts
• solve problems using percentages
• use simple formulae
• express missing number problems using algebra
• find pairs of numbers that satisfy equations with two variables
• solve problems involving simple ratios
• solve problems involving similar shapes where the scale factor is known
• use, read, write and convert between standard units of measure
• measure, compare and calculate using different measures
• know that shapes with the same area can have different perimeters
• find the area of parallelograms and right triangles
• find the volume of cubes and cuboids
• convert between miles and km
• name and understand the parts of circles - radius, diameter and circumference
• draw 2D shapes accurately using dimensions and angles
• compate and classify 2D shapes by a range of properties
• find missing angles in triangles, quadrilaterals and regular shapes
• use coordinates in all 4 quadrants
• draw and translate simple shapes in all 4 quadrants
• interpret and construct pie charts and line graphs
• calculate the mean as an average

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 6 is generally equivalent to 5th Grade in the US.

On this page you will find link to our range of math worksheets for Year 6.

Quicklinks to Year 6 ...

• Place Value Zone
• Mental Math Zone

Word Problems Zone

Fractions percents ratio zone.

• Percentages 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 6 number worksheets.

Here you will find a range of Free Printable Year 6 Number Worksheets.

Using these Year 6 maths worksheets will help your child to:

• use place value with numbers up to 10 million;
• use place value with up to 3 decimal places;
• understand how to use exponents (powers) of a number;
• understand and use parentheses (brackets);
• understand and use multiples and factors;
• extend their knowledge of prime and composite (non-prime) numbers up to 100;
• know and be able to use the PEMDAS (or PEDMAS) rule.
• Place Value Worksheets to 10 million
• Place Value to 3dp
• Ordering Decimals Worksheets
• PEMDAS Rule Support Page
• PEMDAS Problems Worksheets
• Balancing Math Equations
• Roman Numerals worksheets

Ordering Large Numbers and Decimals to 3dp

The sheets in this section involve ordering lists of decimals to 3 decimal places and also large numbers up to 100 million.

There are sheets with decimals up to 10, and also sheets with numbers from -10 to 10.

• Ordering Large Numbers up to 100 million
• Ordering Decimals to 3dp

Rounding Decimals

• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp
• Rounding Decimals Worksheet Challenges

Year 6 Decimal Counting Worksheets

Using these sheets will support you child to:

• count on and back by multiples of 0.1;
• fill in the missing numbers in sequences;
• count on and back into negative numbers.
• Counting By Decimals

Year 6 Mental Maths Zone

Each worksheet 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 quiz!

• Year 6 Mental Maths Tests

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Year 6 Addition Worksheets

• add decimals including tenths and hundredths mentally;
• add a columns of multi-digit numbers, including decimals.
• Decimal Addition Fact Worksheets
• 5th Grade Addition Worksheets BIG Numbers
• Decimal Column Addition Worksheets
• Money Worksheets (randomly generated)

Year 6 Subtraction Worksheets

Using these sheets will help your child to:

• subtract decimals including tenths and hundredths mentally;
• subtract multi-digit numbers, including decimals using column subtraction.
• Subtracting Decimals Worksheets (mental)
• Subtraction Worksheets up to Billions (columns)
• Column Subtraction with Decimals

Year 6 Multiplication Worksheets

• extend their knowlege of multiplication to decimals;
• use their multiplication tables to answer related facts, including decimals;
• multiply a range of decimals with up to 2 decimal places (2dp) by a whole number;
• multiply different money amounts by a whole number.
• Multiplying Decimals by 10 and 100
• Multiplication Fact Sheet Decimals
• Decimal Multiplication Worksheets to 1dp
• Decimal Multiplication Worksheets to 2dp
• Free Multiplication Worksheets (randomly generated)
• Multiply and Divide by 10 100 (decimals)
• Multiplication & Division Worksheets (randomly generated)
• Multiplication Word Problems

Division Worksheets 5th Grade

Using these Year 6 maths worksheets will help your child learn to:

• divide any whole number up to 10000 by a two digit number;
• express any division with a remainder in the form of a mixed number (a number with a fraction part).
• Long Division Worksheets (whole numbers)
• Long Division of Decimal Numbers
• Decimal Division Facts
• Division Facts Worksheets (randomly generated)

Year 6 Maths Problems

• apply their addition, subtraction, multiplication and division skills;
• apply their knowledge of rounding and place value;
• solve a range of problems including "real life" problems and ratio problems.

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

• Year 6 Math Problems (5th Grade)

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

• Year 6 Math Word Problems (5th Grade)

These sheets involve solving a range of ratio problems.

Year 6 Fraction Worksheets

Year 6 percentage worksheets, year 6 ratio worksheets.

• compare and order fractions;
• add and subtract fractions and mixed numbers;
• understand how to multiply fractions by a whole number;
• understand how to multiply two fractions together, including mixed fractions;
• understand the relationship between fractions and division;
• know how to divide fractions and mixed fractions;
• convert decimals to fractions.
• Comparing Fractions Worksheet page
• Adding Fractions Worksheets
• Adding Improper Fractions
• Subtracting Fractions Worksheets
• Adding Subtracting Fractions Worksheets
• Improper Fraction Worksheets
• Converting Decimals to Fractions Worksheets
• Fractions Decimals Percents Worksheets
• Multiplying Fractions Worksheets
• Dividing Fractions by Whole numbers
• Divide Whole numbers by Fractions
• Simplifying Fractions Worksheets
• Free Printable Fraction Riddles (harder)

Take a look at our percentage worksheets for finding the percentage of a number or money amount.

We have a range of percentage sheets from quite a basic level to much harder.

• Percentage of Numbers Worksheets
• Money Percentage Worksheets
• Percentage Word Problems

These Year 6 Ratio worksheets are a great way to introduce this concept.

We have a range of part to part ratio worksheets and slightly harder problem solving worksheets.

• Ratio Part to Part Worksheets
• Ratio and Proportion Worksheets

Year 6 Geometry Worksheets

• know how to find missing angles in a range of situations;
• learn the number of degrees in a right angle, straight line, around a point and in a triangle;
• know how to calculate the area of a triangle;
• know how to calculate the area of a range of quadrilaterals.
• learn the formulas to calculate the area of triangles and some quadrilaterals;
• write and plot coordinates in all 4 quadrants.
• (5th Grade) Geometry - Angles
• Area of Quadrilaterals
• 5th Grade Volume Worksheets
• Coordinate Worksheets (1st Quadrant)
• Coordinate Plane Worksheets (All 4 Quadrants)
• Parts of a Circle Worksheets

Measurement Zone, including Time & Money

Year 6 measurement worksheets.

Using these sheets will help your child understand how to:

• learn how to read a standard scale going up in different fractions: halves, quarters, eighths and sixteenths;
• learn how to read a metric scale going up in 0.1s, 5s, 10s, 25s, 50s & 100s;
• learn how to estimate a measurement of length, weight or liquid;
• convert temperatures in Celsius and Fahrenheit.
• (5th Grade) Measurement Worksheets

Time Puzzles - harder

Here you will find our selection of harder time puzzles.

• Time Word Problems Worksheets - Riddles (harder)

Using these sheets will help you to:

• find the mean of up to 5 numbers;
• find a missing data point when the mean is given.
• Mean Worksheets

Fun Zone: Puzzles, Games and Riddles

Year 6 maths games.

• Year 6 Math Games (5th Grade)

Year 6 Maths Puzzles

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

• Printable Math Puzzles

Math Salamanders Year 6 Maths Games Ebook

Our Year 6 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 6 Maths Games Ebook

Other UK Maths Worksheet pages

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

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Year levels.

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Expected level of development

Australian Curriculum Mathematics V9 : AC9M6N02

Numeracy Progression : Multiplicative strategies: P7

At this level, students learn to decompose composites into their prime factors and recognise primes as the building blocks of composite numbers. Students consolidate use of the distributive and commutative laws of multiplication to simplify calculations.

To build relational understanding, encourage students to make concrete and symbolic representations of numbers and ask students to describe their properties. For example, represent square numbers using counters or square tiles. Introduce and connect symbolic notation, for example, 3 x 3 = 3 2 , and explore patterns. 

Highlight how identifying factors can be used to simplify calculations. For example, 15 x 16 can be simplified into 5 x 3 x 4 x 4 and rearranged to 5 x 4 x 3 x 4 = 240 to make the calculation easier. The rearranging of these numbers contextualises the commutative and distributive properties of multiplication.

Build on the students’ existing strategies to locate factors and highlight students’ attempts at using a systematic approach. Use these as the basis to explicitly teach efficient strategies, such as modelling the use of a tree diagram to find the ‘prime factors’ of a given number through ‘prime factorisation’.

Build a shared understanding of the following terms:

• prime numbers: a whole number higher than 1 that is only divisible by itself and 1
• composite numbers: a whole number that is divisible by numbers other than itself and 1, for example, 4 is divisible by 2 as well as 1 and itself
• square numbers: numbers that are the product of a number which is multiplied by itself, for example, 3 x 3, which can be written as 3 2
• prime factors: the smallest possible factors of a number (that are also prime numbers), for example, the prime factors of 20 are 2 x 2 x 5.

Make explicit the value of using division to distinguish between prime and composite numbers. Dynamic software such as an interactive hundreds chart can help students see and describe patterns and determine rules for numbers with certain factors.

Provide opportunities to explore complex problems, such as: ‘What are all the numbers which have up to 3 factors?’ Encourage systematic thinking, such as trial and error, using combinations of only the first three prime numbers, actively notice patterns that emerge, and use these observations to make and test conjectures.

Teaching and learning summary:

• Provide investigative opportunities to explore properties of prime, square and composite numbers.
• Provide repeated opportunities to make sense of, simplify and solve multiplication problems.
• Present open-ended problem-solving opportunities where systematic thinking and strategies such as trial and error are required.

• identify and describe numbers as prime and composite numbers, and provide reasoning
• explain and express the characteristics of square numbers
• express a number as a product of its prime factors
• use known factors to flexibly solve multiplicative problems.

Some students may:

• incorrectly apply the distributive law when multiplying two or more numbers. For example, if multiplying 15 x 16, a common misconception is to multiply the tens (10 x 10) and then multiply the ones (5 x 6). To address this, encourage students to model the equation using an array to help them recognise why this strategy doesn’t work. Use explicit teaching when useful.
• make errors in their calculations. To address this, encourage students to solve the problem using multiple methods and notice whether the answer is the same in all instances. Another useful strategy is to ask students to estimate the total before calculating. Both approaches can help the student make sense of the multiplicative situation, recognise unrealistic solutions and resolve the problem themselves.

The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.

Learning intention:

• We are learning to investigate prime, square and composite numbers.

Why are we learning about this?

• Some numbers have special properties. These properties can be used to solve problems. For example, we use base 60 for our system of time instead of base 10.
• Open this interactive tool, Sieve of Eratosthenes . It shows the first 100 numbers arranged in a 10 x 10 grid called a hundreds chart.

Have a go at one of the following investigations.

• Explore using the Sieve of Eratosthenes tool. List the prime numbers found in the first 100 numbers. How does the Sieve of Eratosthenes help you identify prime numbers?
• Some numbers are highly composite, meaning that they have a lot of factors. Locate some of these on the hundreds chart.
• Some of the prime numbers under 100 can be written as the sum of two square numbers. How many can you find?
• There are more prime numbers in the first 50 numbers than there are in the next 50 numbers. True or false?

Success criteria:

• identify numbers as prime or composite numbers and explain why they are prime or not
• identify square numbers and be able to explain to others what characteristics make it a square number.

Please note:  This site contains links to websites not controlled by the Australian Government or ESA. More information  here .

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Teaching strategies.

A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well. 

Explicit teaching

Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.

Concrete, Representational, Abstract (CRA model)

The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.

Mathematics investigation

By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.

Multiple exposures

Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.

Teaching resources

A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.

Factors bingo

In this lesson we use the context of a bingo game to apply understanding of prime, composite and square numbers.

Two primes make one square

Use this task to spark curiosity about and explore properties of prime and square numbers.

Scrutinising square numbers

Use this open-ended challenge to connect and apply important number properties.

Primes and emirps

This activity is focused on exploring prime numbers.

Sieve of Eratosthenes

Use this task to investigate properties of multiples and see the connections between primes and multiples.

GeoGebra: Sieve of Eratosthenes

Use this dynamic software to explore prime and composite numbers to 100.

How many factors?

This activity is focused on finding factors of numbers.

Mathigon Polypad: Prime Factor Circles

Dynamic software that students can use in tandem with the Prime Factor Circles lesson.

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Problem-solving maths investigations for year 6.

Hamilton provide an extensive suite of problem-solving maths investigations for Year 6 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 6 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 6:

• Individually, they are incorporated into every unit in our Year 6 flexible maths blocks .
• Collectively, they appear on our resources page where you can explore all our in-depth problem solving investigations for Year 6 .

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Year 6 Identify Common Factors Reasoning and Problem Solving

Have you factored in reasoning and problem-solving opportunities for your children? This Year 6 Identify Common Factors worksheet includes everything you need to ensure that pupils fully understand the concept. With six engaging questions featuring a range of contents, children can demonstrate their understanding. Download now!

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National Curriculum Objectives

Identify common factors, common multiples and prime numbers

​​​This resource is available to download with a Premium subscription.

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Number Year 6 Block 2 Week 4 Division using factors

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 April 2022

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Division using factors for Year 6 from Block 2 - Week 4

Differentiated worksheets with reasoning and problem solving for the rest of this week can be found here: https://www.tes.com/teaching-resource/number-year-6-block-2-week-4-short-and-long-division-12181726

In this lesson, pupils will gain fluency practice when dividing using factors.

The resources are differentiated.

Answers are provided.

All lessons will fit in with White Rose planning.

Feedback is welcomed and appreciated.

Many more maths resources coming soon!

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