common factors problem solving ks2

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Common Factors — Party Bag Problem Solving: Stretch (Year 6)

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This resource is suitable for the White Rose Maths Scheme of Learning, covering Autumn Term Block 2 (Addition, subtraction, multiplication and division), Step 2 (Common factors).

This party-bag problem solving worksheet is a great way for children to test their knowledge and understanding of common factors. Challenge children to use their skills to work out how many of each item should go in each party bag. There’s also an example question completed so children can see what they have to do — making it perfect for setting as homework too.

This worksheet is available in different levels. Please select 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 6 White Rose

• Key Stage: Key Stage 2
• Subject: Maths
• Topic: White Rose Maths | Autumn Term: Addition, Subtraction, Multiplication and Division | Small Step 2
• Topic Group: Calculations
• Year(s): Year 6
• Media Type: PDF
• Resource Type: Worksheet
• Last Updated: 25/10/2023
• Resource Code: M2WHT14217
• Curriculum Point(s): Identify common factors, common multiples and prime numbers. Solve problems involving addition, subtraction, multiplication and division.

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Factors, Multiples and Primes

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Common Factors Lesson

This Year 6 Common Factors lesson covers the prior learning of finding common factors using arrays, before moving onto the main skill of finding common factors.

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 Objective Mathematics Year 6: (6C5) Identify common factors, common multiples and prime numbers

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Lesson Slides

These lesson slides guide pupils through the prior learning of finding common factors using arrays, before moving onto the main skill of common factors. 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

Martin recaps what a factor is and then shows pupils how to find common factors of different numbers in this Common Factors Video Tutorial.

1 Prior Learning

This worksheet recaps prior learning of finding common factors using arrays, before moving onto the main skill of finding common factors.

Interactive Activity

This Year 5 Common Factors Game is designed to check pupils' understanding of common factors.

2 Practical Activities

Supporting Activities

This common factors supporting activities sheet contains suggestions for additional tasks you might wish to use to support pupils' understanding of the concepts taught in the lesson.

2 Varied Fluency

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

This Year 6 Common Factors Reasoning Practice checks your child's understanding of identifying common factors.

2 Reasoning & Problem Solving

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

This common factors extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the common factors lesson.

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of common factors.

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.

Interactive Challenge Activity

This Year 6 Common Factors Maths Challenge is designed to check pupils' ability to find common factors of two numbers.

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

2 Additional Activities

Consolidation Pack

This resource is aimed at Year 6 Expected and has been designed to give children the opportunity to consolidate the skills they have learned in the Autumn Block 2 Four Operations Block.

Learning Video Clip

Renata and Buzz are travelling into space in order to carry out important research. They will need to be able to work out the common factors of numbers in order to complete their mission.

Home Learning Pack

This Autumn week 4 Maths pack contains varied fluency, reasoning and problem solving worksheets.

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Problem-Solving Investigation: Multiples, factors & prime numbers (Year 6 Multiplication & Division)

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

4 October 2019

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Year 6 Multiplication and Division: Multiples, factors and prime numbers.

This in-depth Maths Investigation will develop maths meta-skills, and enable children to learn to think mathematically and articulate mathematical ideas.

In-depth Investigation: Magic Multiplication Squares Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square.

This problem-solving investigation is part of our Year 6 Multiplication and Division 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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Year 6 Multiplication and Division - Problem-Solving Investigations

These in-depth maths investigations are open-ended problem solving activities for Year 6 children. **In-depth Investigation: Magic Multiplication Squares** Children complete a magic multiplication square using their knowledge of number properties and relationships. They then explore factors and multiples to create a new multiplication magic square. **In-depth Investigation: The Eights Have It** Children multiply numbers starting with 9 by 9 and add single-digit numbers in a decreasing sequence. They identify and describe the patterns and start to explain them. **In-depth Investigation: Awesome Answers** Using a magic square to generate 3-digit numbers, children create divisions with dividends containing specified fractions. **In-depth Investigation: Stunning Squares** Children explore patterns in the squares of numbers with reversed digits to find pairs of ‘stunning squares’. **In-depth Investigation: Geometry Genius** Children use what they know about how to find the areas of triangles and parallelograms to find the areas of rhombi, kites and trapezia. **In-depth Investigation: Get to the Root** Children use their fluency in mental multiplication to explore the patterns of digital roots in multiplication. **In-depth Investigation: Riveting Reversals** Multiply 3-digit numbers with consecutive digits by a 2-digit number; reverse the 3-digit number and repeat. Find the difference between the two answers. **In-depth Investigation: Why is it so?** Children identify a pattern in the division of a total of six numbers created using the same 3 digits. They then use algebra to explain why it is so. These investigations will develop maths meta-skills, support open-ended questioning and logical reasoning, and enable children to learn to think mathematically and articulate mathematical ideas. These problem-solving investigations come from our [Year 6 Maths Blocks](https://www.hamilton-trust.org.uk/maths/year-6-maths/). Each Hamilton maths block contains a complete set of planning and resources to teach a term’s worth of objectives for one of the National Curriculum for England’s maths areas.

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Problem Solving

Connect 4 Factors

Playing solo: The player must fill the grid with the counters from both boxes. They must avoid lining up four numbers with a common factor (other than one).

Playing duo: Each player has a box of counters to choose from. Take it in turns to drop a counter into the game board. The winner is the first to line up four numbers with a common factor (other than one).

There are nine squares shown. The squares have side lengths of   1 ,  4 ,  7 ,  8 ,  9 ,  10 ,  14 ,  15  and  18  cm. They can be fitted together with no gaps and no overlaps to form a rectangle. How?

Factors and Multiples

The aim of the game is to try and make the longest chain possible by connecting factors and multiples.

Thinking Skills

In this activity your children will be working on capacity. They must create a given amount in one of the containers in the least amount of moves. Sounds simple eh?

The game has different levels to complete and will really get your children thinking.

Super for outside the box thinking.

Puppies Puzzle

The puppies need to go to sleep. There needs to be an even amount of puppies in each basket to make this happen. How many ways can they be sorted?

Broken Calculator

This is a great activity that encourage the children to use limited numbers and functions to make totals.

The children can progress through the levels to challenge themselves even further.

Pets Puzzle

Can you solve the Pet shop Puzzle? Mr Jones sells two kinds of animals and there are 44 animal legs in the shop. Over half of the pets are puppies. How many puppies and budgies are there in the pet shop?

River Puzzle

How can you safely bring the goat, wolf and cabbage  across the river?

The sum of each side of the triangle should equal the number in the centre of the triangular shape.

The first player to make a square on the grid wins. Encourage your children to think about developing winning strategies and movement patterns.

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Factors and Multiples Worksheets

Welcome to our Factors and Multiples Worksheets. Here you will find a wide range of free Math Worksheets which will help your child to learn to use multiples and factors at a 4th Grade/ 5th Grade level.

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Factors and Multiples Worksheet

These sheets have been designed to support your child with their learning of multiples and factors.

The sheets are graded in order of difficulty with the easiest sheet coming first in each section.

Using these sheets will help your child to:

• Know and understand what multiples and factors are;
• apply knowledge of multiples and factors to solve problems;
• Develop and practice their mental calculation skills.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

Quicklinks to ...

Multiples and Factors Help

Multiples worksheets, factors worksheets.

• Factors and Multiples Riddles
• Easier/Harder Worksheets
• More related resources

Factors and Multiples Online Quiz

If a number is a multiple of another number, it means that it can be made out of adding groups of the other number together.

12 is a multiple of 4 because 4 + 4 + 4 = 12 (or 4 x 3 = 12)

27 is a multiple of 9 because 9 + 9 + 9 = 27 (or 9 x 3 = 27)

17 is not a multiple of 4 because it cannot be made by adding groups of 4 together.

A factor is a number that divides into another number with no remainder.

In other words every number is divisible by each of its factors.

1 is a factor of every whole number, because every integer is divisible by one.

3 and 7 are both factors of 21 because 3 x 7 = 21

10 and 6 are both factors of 60 because 10 x 6 = 60

7 is not a factor of 24 because 24 is not divisible by 7 (24 ÷ 7 = 3 remainder 3).

Multiples and Factors are connected with each other:

• if we know that 3 is a factor of 12, then 12 is a multiple of 3
• if we know that 33 is a multiple of 11, then 11 is a factor of 33.
• also, if we know that 24 is not a multiple of 7, then 7 is not factor of 24.

The example below shows the relationship visually.

If we know that 3 is a factor of 24, then 24 must be a multiple of 3.

If we know that 24 is a multiple of 3, then 3 must be a factor of 24.

Multiples and Factors Worksheets

We have split our worksheets into 3 different sections:

• the first section contains only worksheets about Multiples
• the second section contains only worksheets about Factors
• the third section contains worksheets with both Factors and Multiples
• Multiples Sheet 4:1
• PDF version
• Multiples Sheet 4:2
• Multiples Sheet 4:3
• Multiples Sheet 4:4

We have two worksheets on finding Factor Pairs up to 100.

We have two worksheets which involve finding all the factors of different numbers.

• Factor Pairs Worksheet 1
• Factor Pairs Worksheet 2
• Factors Worksheet 4:1
• Factors Worksheet 4:2
• Factors and Multiples Worksheet 4:1
• Factors and Multiples Worksheet 4:2
• Factors and Multiples Worksheet 4:3

Factor and Multiples Riddles

Using riddles is a great way to get children to apply their knowledge of factors and multiples to solve problems.

It is also a good way to get children working collaboratively and talking about the language together.

Each riddle consists of some clues and a selection of possible answers.

Solving the clues gradually eliminates all the incorrect answers leaving just one solution.

• Factors and Multiples Riddles 1
• Factors and Multiples Riddles 2

Looking for some easier Multiples Sheets

The sheets in this section cover similar areas to the worksheets on this page but are at an easier level.

• round a number to the nearest 10, 100 or 1000;
• use the > and < symbols correctly for inequalities;
• use multiples and apply them to solve problems.
• Rounding Inequalities Multiples Worksheets

Looking for some harder Factors and Multiples Worksheets

We also have some more advanced worksheets about multiples and factors.

The worksheets below are more suitable for 6th graders and above.

• Greatest Common Factor Worksheets
• Least Common Multiple Worksheets
• Factor Tree Worksheets (easier)
• Prime Factorization Worksheets (harder)

More Recommended Math Resources

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

Divisibility Rules 1-10 Chart

We have a range of charts which can help you determine whether a number between 1 and 10 is a factor of a number.

• Divisibility Rules 1-10 Charts

Balancing Math Equations Worksheets

The sheets in this area will help your child understand the use and purpose of the equals sign (=) in an equation.

It will also help children learn to start manipulating and calculating numerical expressions so that they are equivalent.

This will stand them in good stead for when they start to learn algebra, and manipulate algebraic equations.

• Balancing Math Equations

Sieve of Erastosthenes

The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.

• Sieve of Eratosthenes page

Want to find out more about primes?

Take a look at our Prime Number page which clearly describes what a prime numbers is and what they are not.

There are also many different questions about prime numbers answered, as well as information about the density of primes.

• What is a Prime Number

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This quick quiz tests your knowledge and skill with factors and multiples here!

Fun Quiz Facts

• This quiz was attempted 1,569 times last academic year. The average (mean) score was 14.8 out of 20 marks.
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