maths problem solving activity ks2

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Bead Numbers - Place Value

Bead Numbers is a place value investigation involving a tens and ones abacus. The game provides a good context for encouraging learners to think systematically.

Thinking of a Number

Guess the number by revealing the clues on the clouds one by one. Children will need knowledge of rounding, odd and even and tens and ones.

Tables Teaser

Can you work out which number goes in each row and column heading to make the interactive tables grid work? It is quite a challenge!

Mystic Numbers

Solve the number puzzles and collect the treasures.

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Maths problem solving questions – KS2 lesson plan

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The need to prepare children for their times tables test often means that we overlook building their reasoning and problem-solving skills. This is to allow time to develop number fluency and recall.

However, NRICH’s curriculum-linked activities enable your learners to become more fluent alongside developing their reasoning and problem-solving skills.

In this maths problem solving questions lesson you’ll work through NRICH’s Shape Times Shape worksheet to practise and develop some of these underused skills. 

Maths problem solving questions KS2 learning objectives

• Times tables facts  
• Reasoning skills  
• How to think about finding a way to a solution 
• The idea of a symbol (in this case a shape) representing a number 

Make sure all the children can see the Shape Times Shape worksheet. You could display it on the board or give out copies of the printable sheet.

Try to say very little as you introduce the task. Just review what the problem itself states, then give learners a few minutes to think on their own. 

NRICH is a maths outreach project, which is a collaboration between the Faculties of Education and Mathematics, based at the University of Cambridge. NRICH resources are free for teachers to use with their classes. 

Similar resources

• Money worksheets – Year 1 mats for teaching abstract concepts
• KS2 perimeter – Lesson plan based on real-life examples
• Written methods of multiplication – KS2 3-step traffic light method
• Negative numbers worksheet – KS2 resources and advice for teaching negative numbers
• Most and least worksheets – Free download for Early Years / KS1

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Play of the Wild

Education is an admirable thing, but it is well to remember from time to time that nothing that is worth knowing can be taught. -Oscar Wilde

Outdoor Problem Solving Activities KS2- Learning Maths

Outdoor Problem Solving Activities KS2 – Learning Maths Outdoors

These are some ideas for outdoor problem solving activities for KS2 to help children with learning maths outdoors. One of the most critical aspects of teaching and learning maths is to be able to solve problems. While teaching maths in school, I found that it can become easy to get overly focused on teaching the rules and procedures for doing maths. These are essential tools that everyone needs, but the actual point is to be able to apply those skills in real life. Therefore, children must be given opportunities to practice problem-solving and make it purposeful.

I hope you find these outdoor problem solving activities for KS2 useful, and perhaps they will also inspire you to try other ideas. If you would like some other ways to take learning maths outdoors, you may also want to see my post, Outdoor Maths Activities KS2 .

Nim is a mathematical strategy game where two players take turns removing objects from a pile. Each player must take at least one object per turn. The goal is to either take or avoid taking the last item from the stack. Children can play nim with a pile of sticks or rocks.

Ordering natural objects by different features

Children can place in order objects such as rocks or pinecones based on the characteristic(s) they decide upon. It might be longest to shortest, least to the greatest circumference or smallest to greatest volume.

Observing the sun & moon

Children can explore and investigate the sun and moon, including changes that take place over time. They can try to figure out some of the following questions, and ask some of their own questions as well.

• What time does the sun set and rise? Does this ever change? How do you know?
• Where on the horizon do you first/last see the sun or the moon? Does this change? How do you know?
• Can you observe the phases of the moon- how does it change? Are there any patterns that you notice?

Measuring circles

Children can measure circles (such as flower pots, tree stumps or other circular objects found outside). They can measure the circumference, radius and diameter and then investigate the relationship between radius/diameter and circumference. What do children notice? Is there a pattern? They may even be able to ‘discover’ pi.

How tall is a tree?

Measure / calculate the height of a tree with the shadow & calculation method, triangle method and/or clinometer method.  If children try more than one method, do they get the same results?  Which method might be more accurate?

(ex. Estimating by height, clinometer method, looking through legs method, pencil method, meter stick method)

Different ways children can help with planning in a garden

Children can figure out how much space is available in the garden and how many different types of plants can be planted. Can they figure out how many of one kind of plant will fit into one planter box? Can they figure out how many different sized plants fit into the same planter box? Children would need to use their measuring skills to calculate the surface area of the garden. Then they would need to find out how much space each plant requires (e.g. from seed packets) and then determine how many and which of the plants can be used.

If a new planter box is purchased, children can help work out how many bags of compost would be needed to fill it. (They would need to measure, calculate the size, etc.) Will there be any leftover soil from one of the bags? How do you know?

If children grow crops such as pumpkins, they can do things like ordering them from heaviest to lightest. This way they might see which is the ‘prize-winning pumpkin’ in a harvest festival.

They might also consider how much each pumpkin could be sold for.  This would involve calculating each pumpkin’s cost, based on a price of £1.00 per kilo, £2.00 per kilo (or whatever reasonable price is determined). They might also try to figure out if larger pumpkins (or other crops like corn) always weigh more than smaller ones? *The children will have to define what is the larger, longer, or wider circumference.

Children could get involved with selling the crops they grow.  This will give them plenty of opportunities to use mathematical skills and handle money in real-life contexts. They will also need to plan the pricing of different vegetables based on weight, the number of vegetables, or selling them in combinations. Children could even try to figure out the appropriate amount to charge for each crop based on the cost of the seeds, the growing time, grocery store costs or any other factors.

If they do sell some of what they grow after school or possibly at a market, then the children can apply their maths skills to figure out how much each customer will need to pay when buying any particular fruit or vegetable.  

Monitoring Plant Growth

See if children can figure out how quickly different plants grow. Can they determine the rate of growth (e.g. mm per week)? Which seedlings / plants grow fastest? Is it a steady rate of growth, or does it change?

*To take this further, children might also conduct an experiment to compare different groups. They might compare the growth or the growth rate of plants whose seeds have been frozen vs those that have not, or something else.  

Making Shapes

How many shapes can you make (including shapes within shapes) using a set number of sticks (ex. 6 large sticks and 6 small sticks)? Is there a way to make more or fewer shapes using the same number of sticks?

Planning and holding a bake sale

(Some parts of this activity take place inside and some outside. This activity can be linked further to learning maths outdoors if children use some ingredients grown from a school garden).

Baking for a bake sale is a great way to give children hands-on practice solving problems in real contexts. For a baking project they will need to follow recipes and accurately use measuring cups and weighing scales. They might also want to make larger quantities and scale up recipes by doubling, tripling, or quadrupling them. The children will need to plan ahead and calculate how much of each ingredient they need to buy to make a set number of cookies, cupcakes, etc. They must also determine how many batches would be needed to make 200 cupcakes if the recipe makes 2 dozen.

Then when they hold an actual sale they will be using their maths skills to calculate how much to charge people.  They must also learn how to give people the proper change (just like selling vegetables above). They can setup a stall outside of school and sell them after school one day. 

Organizing and running a track & field event

Children can get involved in organizing a sports day or track and field event. They can first decide which events to include and then figure out how much space is needed for each activity (e.g. measuring the appropriate length and width required). The children can then help measure and set up the activities.

Once races are held, that data can be used to make calculations. For example – for a jumping event, children can measure how far people jump, and after several tries, figure out if there is improvement and how much (finding the difference). Children can time how far it takes them to run certain distances, e.g. 500 meters versus ½ a mile. They can figure out how fast they are running. They might then calculate how fast they ran different races (e.g. miles per hour) and then figure out when they ran faster or slower.  

Finding ways to approximate measurements

See if children can find different ways to measure the approximate distance between two far points with a meter stick and string. This might be the length of the playground or the distance between two trees, etc. Children might compare different ways of measuring the approximate distance such as measuring the length it takes them to take one step and then counting the number of steps between two points. They might also use the string to go between the two points and measure the string’s length. See if they can find any other ways to find the approximate distances.

I hope that you find these outdoor problem solving activities for KS2 helpful and it helps you take teaching and learning maths outdoors!

Arithmetic , Gardening , Geometry , Maths , Measurement , Number & Place Value , School Age , Sticks

hands-on learning , Learning Outdoors , learning outside , outdoor learning , Sticks

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The 21 Best Maths Challenges At KS2 To Really Stretch Your More Able Primary School Pupils

Emily Weston

It won’t be long in your teaching career before you’re seeking out maths challenges at KS2 to stretch your more able pupils. Particularly once you get to Year 6, the maths challenges that may have previously kept them busy will no longer be stretching them. At least this is what I found out recently.

Every child deserves maths challenges that stretch them

You are not alone looking for ks2 maths challenges for high attainers, 1. i see reasoning uks2 – gareth metcalfe, 3. third space learning, 4. peter dickinson – reasoning club, 5. royal institute of science – maths masterclass, 7. nace (national association for able children in education) , 8. maths bot , 9. craig barton – same surface different deep, 10. dr frost maths , 21. mastering mixed ability maths, 12. parallel maths, 13. ted airplane riddle, 14. times tables app, 15. fibonacci rabbit sequence , 16. open middle, 17. daily rigour articles, 18. total maths , 19. maths in sport, 20. wild maths, 11. white rose, maths challenge books, where this list of mathematical challenges for able pupils came from.

Usually, applying knowledge and using transferable skills is enough to keep a class ticking over; extending their understanding beyond number. But in some cohorts there will be a child who completes the ‘challenges’ we set with relative ease; they aren’t taken out of their comfort zone or rarely make mistakes.

Some children will readily grasp the concepts being shown to them and will be ready to apply their strategies and understanding to further reasoning and problem solving questions.

This year I had a child like this in my class, and I found stretching his abilities a struggle as I didn’t have access to enough resources to give me, or him, variety.

I’d be helping one child grasp long multiplication – or something similar – when a shadow would loom over my shoulder. Turning around, he’d be there, telling me he had finished. Often, he had finished a year 6 maths challenge which I was sure would last for the whole lesson. Looking at the clock, 40 minutes of the lesson remained.

His abilities stretched beyond any child I had previously had in my class. So, I reached out to Twitter to discover some new ways to include maths challenges for more able pupils in my lessons.I was especially looking for work which he could pick up and use independently, if he had managed to complete the tasks already set.

After the responses on Twitter, it was clear to see I wasn’t not the only person left scratching my head in this kind of situation, wondering what resources I can turn to.

So, to help you find even more challenges for your greater depth pupils quickly and easily, we’ve put together this list of activities, categorised for ease of use.

You can find the original tweet here . It’s worth a read; the thread is packed with lots more ideas than I was able to include on this blog!

Top 6 Maths Challenges For Primary School Pupils

Prep: Find the activity you want, photocopy (and maybe some guillotine-ing!)

Who it’s for: Although this is the Upper Key Stage 2 version, it is available for Lower Key Stage 2 too!

Cost: You will need to purchase the ‘I See Reasoning’ resources.

This resource is full of a huge range of activities which push children to think beyond numbers and begin to use mathematical language to explain.

Each activity requires children to display their understanding of what they have already learnt, and build upon their knowledge in order to describe what they notice or know.

This document covers the whole of the maths curriculum, including not only problems relating to number, but also geometry, shape and statistics.

I also love that this really clearly includes the answers, which makes it so simple to use!

Each activity has its merits, but the three I find particularly useful are:

Explain the Mistakes

Children are shown mistakes and are required to explain why the diagrams/calculations are wrong.

They must use mathematical language and previous knowledge to first understand, then explain their thinking to show what would need to change in order for there to be a correct solution.

‘I know…so…’

This activity models to children how to link ideas and get them reasoning, building on what they know already.

Once they have seen this model in ‘I See Reasoning’ they will then begin to use this phrase within the classroom, not only when speaking to the teacher but also to their peers.

Different Ways 

This activity requires children to understand that their can be different variations. They can then explain how they know that these answers all work, and why.

Child Review: This was challenging as when you understand number so easily, it can be trickier to explain exactly how you know a fact is true. There was some element of challenge because of the range of different activities.

Link:  I See Reasoning

Prep: Just print and go! (Unless they’ve already done the challenge in a previous year group…!)

Who it’s for:  There are activities for all primary age ranges.

Cost: FREE!

I have to admit, this is my absolute go-to for mathematical challenges (as I’m sure it is for many of you out there!).

The huge range of challenges that are available can be easily searched so you can find the activity which is perfectly suited to the topic you’re doing,

They are also labelled with which age range the problem is most suited for (and can be adapted if you want to).

However, because Nrich is so popular I often find that the children have already accessed problems the previous year, meaning that inevitably they no longer pose any challenge to them, or it takes extra time to plan as you need to consult previous teachers.

My favourite challenge so far this year from Nrich is:

This activity really challenged my whole class. They worked in groups to discover the answer and there were cries of ‘noooo’ when we started running out of time for them to solve it (which inevitably led to another lesson being abandoned to let them have more time to work it out!)

This was an activity I thought would be completed quickly, but really challenged the all the children.

Child Review: This activity was really challenging as it used lots of logic. You had to use what you knew about number, use trial and error and really understand how the strategy works! I like these types of problems as they make me think.

Link:  Nrich

Prep: Access to a computer and a headset.

Who it’s for: Years 2 to 7

Cost: Bespoke to each school, on average £15 per pupil per week.

Some of you might already be using Third Space Learning’s one-to-one online maths interventions with your lower attaining pupils or as part of your Pupil Premium budget. But these interventions can also be an excellent way of further stretching most able pupils.

Third Space’s highly targeted initial diagnostic assessment identifies maths strengths as well as weaknesses. With higher attaining pupils, Third Space tutors can create lesson plans aimed at engaging and developing these strengths, introducing them to concepts and topics that will challenge and motivate them.

Third Space also provides an online Maths Hub  full of premium and free maths resources , such as the one below, that you can use in lessons to continue challenging your more able pupils.

Child Review: “ I enjoy coming here every Friday to do Third Space Learning! It makes me happy every time I come to school!” – Katie, Third Space pupil

Link:  Find out about the maths interventions (or call 0203 771 0095)

108 Greater Depth Questions for KS2 Maths Mastery

Download our set of 108 Greater Depth Maths Mastery questions for some free additional stretch and challenge for your more able pupils.

Prep: Print and go!

Who it’s for:  Year 5 and 6.

Cost: There is a cost for these resources. You will need to contact Peter directly to enquire.

Peter Dickinson has created a range of reasoning resources which really require children to think and apply their knowledge.

Each challenge explicitly targets a different aspect of maths, as well as requiring the children to transfer a range of different skills to help them solve the problem.

For example, in the ‘Multiplication Square’ children have to not only use multiplying knowledge, but also that of decimals and place value.

I’ve found that these reasoning word problems cover a lot of the curriculum, particularly number, which allow a really wide range of maths challenge for the class.

The best part of these, is that it’s really useful to laminate them within the classroom in order to use over and over again; because of the level of challenge, sometimes they don’t get finished and it enables the child to continue another time before passing them on to someone else.

Child Review: I really like that these are usually laid out in familiar ways and full of lots of different types of challenges. Some of them really make me think and use lots of logic – I enjoy that they actually challenge me!

Link:  Peter can be found on Twitter at @2358Peter

Prep: There are quite a few downloads to prepare for the session, but they also have PowerPoints to help with you explanation.

Who it’s for:  Year 5 and 6, although they may also link to some topic work in a lesser capacity lower down.

I was really disappointed I hadn’t come across these resources before (thanks for the suggestion @Glazgow/@racheldorris1)!

They cover a range of topics including (but not limited to!) fractions, shape, number patterns and reflections.

Each of these are also linked to a science element (and in some cases, some history or art too!) providing a range of curricular links you can also build into your lessons.

Each ‘off the shelf’ lesson is fully planned and resourced for you, which means it is easy to prep for the children (although I do recommend reading through it all first – some lessons have quite a few downloads you need to use whereas some need equipment!).

The topics are all very interesting and are some you may not come across or think of having not discovered them on the Royal Institute of Science site. One example of this is creating colours through using fractions and proportion.

These sorts of cross-curricular activities are also excellent evidence to show off during Ofsted inspections !

Child Review: These challenges are really interesting because they involve different parts of the curriculum too! We have only done one of these, but I really look forward to doing more!

Link:  Royal Institution Maths Masterclasses

Prep: Some printing may be required!

Who it’s for:  KS2 – there are a range of different challenges.

This resource was kindly suggested by @ianr73 and I am very glad it was! Transum has a range of features which are really useful to use in class.

Firstly, they have a range of daily challenges which are puzzles for the children to complete and challenge a different area of their maths knowledge each day.

In this example, it focuses on time and has a range of different examples for them to work on. I have this on my board at some point each day to expose the class to new ideas and maths puzzles!

Also, as you might expect, they have a range of maths challenges on their site too. There are a wide range of problems to choose from – I found them to be quite like Nrich in their style which meant they were easy to begin using in the classroom.

There were also the options of outdoor maths, riddles and a range of online maths games to use too!

Child Review: I really enjoy the daily maths puzzle that we can have as it shows lots of different types of maths I might not otherwise get to see. The challenges are fun, and can be done in different ways too.

Link:  Transum

Favourite Maths Challenges Recommended By Primary School Teachers

Gone through all of the challenges above and still need more? These are some of the other maths challenges that were recommended on the Twitter thread:

What it is: An association which specifically focuses on how to challenge more able children in a range of different ways.

What it is: These are a range of maths challenges in different formats (including exam style questions) which can be used in different year groups (as well as going through Secondary).

What it is: These problems are based around the concept that children should be revisiting different areas of maths constantly. If they do problems based around just the topic being studied they aren’t effectively applying their knowledge.

A range of problem solving activities which children can use to extend their reasoning understanding.

What it is: A free Third Space Learning resource with 8 mastery-based maths activities, all designed to be ‘low threshold/high ceiling’ – relatively easy to pick up, but with lots of room to stretch more able pupils.

Link: Mastering Mixed Ability Maths Resource

What it is: These are challenges which are used to stretch children. They are aimed for Year 7 up, but might be used to stretch children in Year 6 as an extra ‘weekly challenge’ if the topic matches!

What is is: A riddle which children will need to apply their knowledge and maths logic to solve the problem.

What it is: A challenging app to speed up times table recall knowledge, which can be done on a phone or tablet.

What it is: This is using mathematical discovery (trial and error) rather than allocation of knowledge. It is a really good challenge for children (especially Year 5/6 )

What it is: A site that promotes problem solving over worksheets, allowing children to work in a more practical manner.

What it is: This is a free newspaper that puts maths problems into a real life context. It is full of interesting ideas to get children using challenge!

What it is: Tara Loughran (@MathsMummy) is a maths consultant who has created a range of problem sheets which stretch children across a range of topics in the maths curriculum.

What it is: A range of maths problems which are also linked to sport. Curated by University of Cambridge, it covers KS1 and KS2!

What it is: This is a similar site to Nrich which has a range of activities, stories and maths puzzles to challenge your children.

What it is: A scheme of work which moves from fluency to reasoning in all areas of the maths curriculum.

A few books were suggested for Maths Challenges too!

• Maths No Problem
• Kjartan Poskit books – Murderous Maths
• Alex’s Adventures in Numberland – Alex Bellos
• The Number Detective: 100 Number Puzzles to Test Your Logical Thinking

These KS2 maths challenges have really allowed me to go deeper with certain children within maths lessons (and even during particular topics!) within the classroom.

Having a wider range of maths challenge resources makes it much easier to ensure that you are deepening maths mastery in a way that is meaningful and encourages children to use logic.

To find more challenges you can use with the greater depth children in your class, check out these other TSL blogs:

• How To Stretch And Challenge More Able Pupils In KS2 Maths
• What Does Greater Depth Look Like In KS2 Maths?
• 108 Greater Depth Questions For Maths Mastery
• Ready To Progress Criteria

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Maths Problem Solving Booklets

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

23 August 2022

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Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability.

Designed to be printed as A5 booklets.

Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten. I am a maths problem magpie and collect maths problems wherever I find them. All I have done is bundled these ones up to make it convienent.

If you find a problem that is yours and you don’t want it used please comment and I’ll remove it - cheers.

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Very impresses. Ta.

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Excellent resource

Great resource to use at KS3

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Just what I have been looking for. Thanks so much!

Good resources. Thanks you!

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KS2 Resources & Worksheets > KS2 Mathematics Resources & Worksheets >

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Year 4 Read and Write Numbers up to 10,000 Discussion Problem

Are you looking for ways to challenge children's understanding of place value? Then look no further! This Year 4 Read and Write Numbers up to 10,000 Discussion Problem includes an engaging task featuring digit cards for pupils to complete.

Year 6 Compare Numbers up to 10,000,000 Discussion Problem

This Year 6 Compare Numbers up to 10,000,000 Discussion Problem has been designed to give children the opportunity to work in groups or partners to complete complex problems using their previous learning.

Year 4 Read and Write Numbers up to 10,000 Reasoning and Problem Solving

Children can develop their understanding of numbers written as numerals and words in this Year 4 Read and Write Numbers up to 10,000 Reasoning and Problem Solving worksheet.

Year 3 Multiples of 50 Reasoning and Problem Solving

Children will have plenty of opportunities to apply their place value knowledge with this Year 3 Multiples of 50 Reasoning and Problem Solving resource.

Year 4 Represent Numbers up to 10,000 Discussion Problem

Challenge children's understanding of representing 4-digit numbers with this Year 4 Represent Numbers up to 10,000 Discussion Problem.

Year 4 Read and Write Numbers up to 10,000 Fluency Matrix

Are you in need of place value resources that cover 4-digit numbers? Then look no further! This Year 4 Read and Write Numbers up to 10,000 Fluency Matrix resource includes a gradual progression of skills across the questions.

Year 6 Read and Write Numbers up to 10,000,000 Reasoning and Problem Solving

With this Year 6 Read and Write Numbers up to 10,000,000 Reasoning and Problem Solving resource, children have several opportunities to practise their skills with numbers up to ten million.

Year 5 Order Numbers up to 100,000 Varied Fluency

Develop children's place value knowledge with this Year 5 Order Numbers up to 100,000 Varied Fluency resource. It includes a range of questions featuring a variety of representations such as bar models, place value counters and part-whole models.

Year 5 Order Numbers up to 100,000 Reasoning and Problem Solving

Once children are secure in how to order numbers they can move on to applying their understanding. This Year 5 Order Numbers up to 100,000 Reasoning and Problem Solving worksheet includes plenty of opportunities for pupils to demonstrate their skills.

Year 5 Compare Numbers up to 100,000 Discussion Problem

Pupils can practise their knowledge of place value and comparing two 5-digit numbers in a fun, engaging way with this Year 5 Compare Numbers up to 100,000 Discussion Problem.

Year 3 Multiples of 50 Discussion Problem

Are you looking for an activity to further challenge children's place value knowledge? If so, this Year 3 Multiples of 50 Discussion Problem is perfect! It includes two questions designed to promote deeper thinking.

Year 3 Multiples of 50 Supporting Activity

Develop children's understanding of place value with this Year 3 Multiples of 50 Supporting Activity

Year 4 Represent Numbers up to 10,000 Reasoning and Problem Solving

Embed pupils' understanding of representing 4-digit numbers with this Year 4 Represent Numbers up to 10,000 Reasoning and Problem Solving resource. Children will represent 4-digit numbers using Base 10, place value counters and digit cards.

Year 4 Represent Numbers up to 10,000 Practical Activities

This Year 4 Represent Numbers up to 10,000 Practical Activities resource includes two activities.

Year 5 Order Numbers up to 100,000 Fluency Matrix

Develop children's confidence when ordering numbers with this Year 5 Order Numbers up to 100,000 Fluency Matrix. It features a range of questions which graduate in challenge enabling progression in learning.

Year 5 Order Numbers up to 100,000 Supporting Activity

Develop children's place value knowledge with this Year 5 Order Numbers up to 100,000 Varied Fluency resource. It Learning in a practical way can be fun and engaging for pupils.

Year 5 Order Numbers up to 100,000 Discussion Problem

This Year 5 Order Numbers up to 100,000 Discussion Problem includes an open-ended question for children to solve.

Year 4 1,000 More or Less Reasoning and Problem Solving

Children can use and apply their place value skills with this Year 4 1,000 More or Less Reasoning and Problem Solving worksheet.

Year 4 1,000 More or Less Discussion Problem

If you're in need of a challenge activity to further develop children's understanding of place value, then look no further! This Year 4 1,000 More or Less Discussion Problem offers an open-ended question for children to solve.

Year 4 1,000 More or Less Homework

This Year 4 1,000 More or Less Homework resource features two fluency questions and a reasoning question for children to demonstrate their understanding.

Year 4 1,000 More or Less Fluency Matrix

If you would like to asses your pupils' fluency skills when adding or subtracting 1,000, then look no further! This Year 4 1,000 More or Less Fluency Matrix is the resource for you!

Year 4 1,000 More or Less Varied Fluency

Develop children's place value skills with this Year 4 1,000 More or Less Varied Fluency worksheet. There are 6 questions for pupils to complete featuring different representations such as place value charts and Base 10 equipment.

Compare Calculations Teaching PowerPoint

These lesson slides guide pupils through the prior learning of completing multi-step addition and subtraction problems, before moving on to the main skill of comparing calculations without focusing on their answers.

Find Missing Numbers Teaching PowerPoint

These lesson slides guide pupils through the prior learning of using the inverse operation, before moving on to the main skill of finding missing numbers.

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Problem Solving

 A selection of resources containing a wide range of open-ended tasks, practical tasks, investigations and real life problems, to support investigative work and problem solving in primary mathematics.

Problem Solving in Primary Maths - the Session

Quality Assured Category: Mathematics Publisher: Teachers TV

In this programme shows a group of four upper Key Stage Two children working on a challenging problem; looking at the interior and exterior angles of polygons and how they relate to the number of sides. The problem requires the children to listen to each other and to work together co-operatively. The two boys and two girls are closely observed as they consider how to tackle the problem, make mistakes, get stuck and arrive at the "eureka" moment. They organise the data they collect and are then able to spot patterns and relate them to the original problem to find a formula to work out the exterior angle of any polygon. At the end of the session the children report back to Mark, explaining how they arrived at the solution, an important part of the problem solving process.

In a  second video  two maths experts discuss some of the challenges of teaching problem solving. This includes how and at what stage to introduce problem solving strategies and the appropriate moment to intervene when children find tasks difficult. They also discuss how problem solving in the curriculum also helps to develop life skills.

Cards for Cubes: Problem Solving Activities for Young Children

Quality Assured Category: Mathematics Publisher: Claire Publications

This book provides a series of problem solving activities involving cubes. The tasks start simply and progress to more complicated activities so could be used for different ages within Key Stages One and Two depending on ability. The first task is a challenge to create a camel with 50 cubes that doesn't fall over. Different characters are introduced throughout the book and challenges set to create various animals, monsters and structures using different numbers of cubes. Problems are set to incorporate different areas of mathematical problem solving they are: using maths, number, algebra and measure.

Problem solving with EYFS, Key Stage One and Key Stage Two children

Quality Assured Category: Computing Publisher: Department for Education

These three resources, from the National Strategies, focus on solving problems.

  Logic problems and puzzles  identifies the strategies children may use and the learning approaches teachers can plan to teach problem solving. There are two lessons for each age group.

Finding all possibilities focuses on one particular strategy, finding all possibilities. Other resources that would enhance the problem solving process are listed, these include practical apparatus, the use of ICT and in particular Interactive Teaching Programs .

Finding rules and describing patterns focuses on problems that fall into the category 'patterns and relationships'. There are seven activities across the year groups. Each activity includes objectives, learning outcomes, resources, vocabulary and prior knowledge required. Each lesson is structured with a main teaching activity, drawing together and a plenary, including probing questions.

Primary mathematics classroom resources

Quality Assured Collection Category: Mathematics Publisher: Association of Teachers of Mathematics

This selection of 5 resources is a mixture of problem-solving tasks, open-ended tasks, games and puzzles designed to develop students' understanding and application of mathematics.

Thinking for Ourselves: These activities, from the Association of Teachers of Mathematics (ATM) publication 'Thinking for Ourselves’, provide a variety of contexts in which students are encouraged to think for themselves. Activity 1: In the bag – More or less requires students to record how many more or less cubes in total...

8 Days a Week: The resource consists of eight questions, one for each day of the week and one extra. The questions explore odd numbers, sequences, prime numbers, fractions, multiplication and division.

Number Picnic: The problems make ideal starter activities

Matchstick Problems: Contains two activities concentrating upon the process of counting and spotting patterns. Uses id eas about the properties of number and the use of knowledge and reasoning to work out the rules.

Colours: Use logic, thinking skills and organisational skills to decide which information is useful and which is irrelevant in order to find the solution.

GAIM Activities: Practical Problems

Quality Assured Category: Mathematics Publisher: Nelson Thornes

Designed for secondary learners, but could also be used to enrich the learning of upper primary children, looking for a challenge. These are open-ended tasks encourage children to apply and develop mathematical knowledge, skills and understanding and to integrate these in order to make decisions and draw conclusions.

Examples include:

*Every Second Counts - Using transport timetables, maps and knowledge of speeds to plan a route leading as far away from school as possible in one hour.

*Beach Guest House - Booking guests into appropriate rooms in a hotel.

*Cemetery Maths - Collecting relevant data from a visit to a local graveyard or a cemetery for testing a hypothesis.

*Design a Table - Involving diagrams, measurements, scale.

Go Further with Investigations

Quality Assured Category: Mathematics Publisher: Collins Educational

A collection of 40 investigations designed for use with the whole class or smaller groups. It is aimed at upper KS2 but some activities may be adapted for use with more able children in lower KS2. It covers different curriculum areas of mathematics.

Starting Investigations

The forty student investigations in this book are non-sequential and focus mainly on the mathematical topics of addition, subtraction, number, shape and colour patterns, and money.

The apparatus required for each investigation is given on the student sheets and generally include items such as dice, counters, number cards and rods. The sheets are written using as few words as possible in order to enable students to begin working with the minimum of reading.

NRICH Primary Activities

Explore the NRICH primary tasks which aim to enrich the mathematical experiences of all learners. Lots of whole class open ended investigations and problem solving tasks. These tasks really get children thinking!

Mathematical reasoning: activities for developing thinking skills

Quality Assured Category: Mathematics Publisher: SMILE

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education