problem solving shapes ks2

• Number Bonds
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• Knowing Tables – 2x, 3x, 4x, 5x, 10x
• All Tables – Choosable
• All Tables – Random
• Division Facts
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• Primes, Factors & Square numbers
• 2D & 3D Shapes
• Direction, Movement & Logo
• Reflection Only
• Rotation Only
• Coordinates
• Mixed Symmetry
• Angles – Measuring
• Measurement
• Problem solving
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• Fractions – Problem Solving
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Maths Games and Learning Activties for Fun

Category: 2d shape, quadrilaterals – snappy maths.

Quadrilaterals – Snappy Maths Answer as many questions as you can. Use the ‘Enter’ key or press ‘Go’ to submit each answer. Your time starts after you answer the first one.  

Tangrams – ABC YA

Complete the puzzle by moving and rotating the seven shapes. A fun way to work problem solving and visual spatial skills. App Features 3 levels offering increased challenge Click on a shape or drag it to select it Use the Read More …

Virtual Pattern Blocks – NCTM

Virtual Pattern Blocks – NCTM Pattern blocks can be used for problem solving and reasoning with fractions as children investigate the relationships between various parts and wholes. Typically Yellow Hexagon = 1 whole Red trapezium = 1/2 Blue parallelagram = Read More …

Polygon Explorer – Visnos

Polygon Explorer – Visnos Create and manipulate polygons, examine how the interior and exterior angles change as the number of sides increase. Drag vertices, use a protractor or ruler to measure angles and length properties

Geoboard – Math Learning Center

Geoboard is a tool for exploring a variety of mathematical topics introduced in the primary school. Children stretch bands around the pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more. Open Activity

The quadrilateral sorter – David Hellam

Properties of all quadrilaterals – click to read properties.

Shapes – David Hellam

Use the mouse to make your character pick up the shapes and take them to the right box – matching word and image – but do not get caught by the robots.

Making Rectangles – NVLM

Combine pentominoes to make different rectangles

Matho Geometry – AplusMath

Maths Bingo using flashcard and recoignising properties of shapes

Polygons shape sorter – Crick

sort polygons into quads and not quads, regular and irregular. Note – wrong answer not accepted so can be done without thought. KS2

Shifting shapes – ICT Games

Recognise the 2D shape – Yr1

Shapes 1 – David Hellam

Pelmanism – match each regular 2D shape to its name

Quadrilaterals 1 – David Hellam

Pelmanism – Match quadrilateral’s name to its shape Yr 6

Shape sorting – NNS

Sort 2D shapes into 3 boxes according right angles. Only correct sorting possible.

Polygon matching – Math Playground

turn cards to match shapes with names

Sorting Shapes – Venn DIagram – MathsFrame

Sort a variety of 2D shapes on a Venn diagram. Sort by one or two conditions.

Shape sorter – DFES

sort shapes by rectangles and red in a Carroll diagram. No errors possible.

Sorting 2D Shapes – NNS

Sort 2D shapes into 3 boxes according right angles. Only correct sorting possible.      

Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

Maths Problem Solving At KS2: Strategies and Resources For Primary School Teachers

John Dabell

Maths problem solving KS2 is crucial to succeeding in national assessments. If your Key Stage 2 pupils are still struggling with reasoning and problem solving in Maths, here are some problem solving strategies to try with your classes; all aligned to Ofsted’s suggested primary school teaching strategies.

Reasoning and problem solving are widely understood to be one of the most important activities in school mathematics. As far back as 1982,  The Cockcroft Report , stated:

‘The ability to solve problems is at the heart of mathematics. Mathematics is only “useful” to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name “problem solving”. […] At each stage […] the teacher needs to help pupils to understand how to apply the concepts and skills which are being learned and how to make use of them to solve problems. These problems should relate both to the application of mathematics to everyday situations within the pupils’ experience, and also to situations which are unfamiliar.’

Thirty plus years later and problem solving is still the beating heart of the Maths curriculum and – along with fluency and reasoning – completes the triad of aims in the 2014 New National Curriculum.

Ofsted’s view on problem solving in the Maths curriculum

Despite its centrality, Ofsted report that ‘ problem solving is not emphasised enough in the Maths curriculum ’. Not surprisingly, problem solving isn’t taught that well either because teachers can lack confidence, or they tend to rely on a smaller range of tried and tested strategies they feel comfortable with but which may not always ‘hit home’. If you’re looking to provide further support to those learners who haven’t yet mastered problem solving, you probably need a range of different strategies, depending on both the problem being attempted and the aptitude of the pupil.

We’ve therefore created a free KS2 resource aimed at Maths Coordinators and KS2 teachers that teaches you when and how to use 9 key problem solving techniques:  The Ultimate Guide to Problem Solving Techniques

The context around KS2 problem solving

According to Jane Jones, former HMI and National Lead for Mathematics, in her presentation at the Jurassic Maths Hub:

• Problems do not have to be set in real-life contexts, beware pseudo contexts.
• Providing a range of puzzles and other problems helps pupils to reason strategically to approach problems, sequence unfolding solutions, and use recording to help their mathematical thinking for next steps.
• It is particularly important that teachers and TAs stress reasoning, rather than just checking whether the final answer is correct.
• Pupils of all ability need to learn how to solve problems – not just the high attainers or fastest workers.

The Ultimate Guide to Problem Solving Techniques

9 ready-to-go problem solving techniques with accompanying tasks to get KS2 reasoning independently

How to approach KS2 maths problems

So what do we do? Well Ofsted advice is pretty clear on what to do when teaching problem solving. Jane Jones says we should:

• Set problems as part of learning in all topics for all pupils.
• Vary the ways in which you pose problems.
• Try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.
• Make sure you discuss alternative approaches with pupils to help develop their reasoning.
• Ensure that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

Perhaps more than most topics in Maths, teaching pupils how to approach problem solving questions effectively requires a systematic approach. Pupils can face any number of multi-step word problems throughout their SATs and they will face them without our help. To truly give pupils the tools they need to approach problem solving in Maths we must ingrain techniques for  approaching  problems.

With this in mind, below are some methods and techniques for you to consider when teaching problem solving in your KS2 Maths lessons. For greater detail and details on how to teach this methods, download the  Ultimate Guide to Problem Solving Techniques

Models for approaching KS2 problem solving

Becoming self-assured and capable as a problem solver is an intricate business that requires a range of skills and experience. Children need something to follow. They can’t just pluck a plan of attack out of thin air which is why models of problem solving are important especially when made memorable. They help establish a pattern within pupils so that, when they see a problem, they feel confident in taking the steps towards solving it.

Find out how we encourage children to approach problem solving independently in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils.

The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely:

• Understand the problem
• Devise a strategy for solving it
• Carry out the strategy
• Check the result

Many models have followed the Polya model and use acronyms to make the stages stick. Which model you use can depend on the age of the children you are teaching and sometimes the types of word problems they are trying to solve. Below are several examples of Polya model acronyms:

C – Circle the question words U – Underline key words B – Box any key numbers E – Evaluate (what steps do I take?) S – Solve and check (does my answer make sense and how can I double check?)

R – Read the problem correctly. I – Identify the relevant information. D – Determine the operation and unit for expressing the answer. E – Enter the correct numbers and calculate

I – Identify the problem D – Define the problem E – Examine the options A – Act on a plan L – Look at the consequences

R – Read and record the problem I – Illustrate your thinking with pictures, models, number lines etc C – Compute, calculate and check E – Explain your thinking

R – Read the question and underline the important bits U – Understand: think about what to do and write the number sentences you will need C –  Choose how you will work it out S – Solve the problem A – Answer C – Check

Q – Question – read it carefully U – Understand – underline or circle key elements A – Approximate – think about the size of your answer C – Calculate K – Know if the answer is sensible or not

T – Think about the problem and ponder E – Explore and get to the root of the problem A – Act by selecting a strategy R – Reassess and scrutinise and evaluate the efficiency of the method

The idea behind these problem solving models is the same: to give children a structure and to build an internal monitor so they have a business-like way of working through a problem. You can choose which is most appropriate for the age group and ability of the children you are teaching.

The model you choose is less important than knowing that pupils can draw upon a model to follow, ensuring they approach problems in a systematic and meaningful way. A far simpler model – that we use in the   Ultimate Guide to KS2 Problem Solving Techniques  – is UCR: Understand the problem, Communicate and Reflect.

You then need to give pupils lots of opportunities to practice this! You can find lots of FREE White Rose Maths aligned maths resources, problem solving activities and printable worksheets for KS1 and KS2 pupils in the Third Space Learning Maths Hub .

You might also be interested in:

• 25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)
• 30 Problem Solving Maths Questions And Answers For GCSE
• Why SSDD Problems Are Such An Effective Tool To Teach Problem Solving At KS3 & KS4

What’s included in the guide?

After reading the  Ultimate Guide to KS2 Problem Solving Techniques , we guarantee you will have a new problem solving technique to test out in class tomorrow. It provides question prompts and activities to try out, and shows you step by step how to teach these 9 techniques

• Open ended problem solving
• Using logical reasoning

Working backwards

Drawing a diagram

Drawing a table

Creating an organised list

Looking for a pattern

Acting it out

Guessing and checking

Cognitive Activation: getting KS2 pupils in the lightbulb zone

If you need more persuasion, pupils who use strategies that inspire them to think more deeply about maths problems are linked with higher Maths achievement. In 2015 The  National Education Research Foundation  (NFER) published ‘ PISA in Practice: Cognitive Activation in Maths ’. This shrewd report has largely slipped under the Maths radar but it offers considerable food for thought regarding what we can do as teachers to help mathematical literacy and boost higher mathematical achievement.

Cognitive Activation isn’t anything mysterious; just teaching problem solving strategies that pupils can think about and call upon when confronted by a Maths problem they are trying to solve. Cognitive It encourages us as teachers to develop problems that can be solved in more than one way and ‘may require different solutions in different contexts’. For this to work, exposing children to challenging content and encouraging a culture of exploratory talk is key. As is:

• Giving pupils maths problem solving questions that require them to think for an extended time.
• Asking pupils to use their own procedures for solving complex problems.
• Creating a learning community where pupils are able to make mistakes.
• Asking pupils to explain how they solved a problem and why they choose that method.
• Presenting pupils with problems in different contexts and ask them to apply what they have learned to new contexts.
• Giving pupils problems with no immediately obvious method of solution or multiple solutions.
• Encouraging pupils to reflect on problems.

Sparking cognitive activation is the same as sparking a fire – once it is lit it can burn on its own. It does, however, require time, structure, and the use of several techniques for approaching problem solving. Techniques, such as open-ended problem solving, are usually learned by example so we advise you create several models to go through with pupils, as well as challenge questions for independent work. Many examples exist and we encourage you to explore more (e.g. analysing and investigating, creating a tree diagram, and using simpler numbers).

Read these:

• How to develop maths reasoning skills in KS2 pupils
• FREE CPD PowerPoint: Reasoning Problem Solving & Planning for Depth
• KS3 Maths Problem Solving

That time, effort, and planning will – however – be well spent. Equipping pupils with the tools to solve problems they have never seen before is more akin to teaching for life than teaching for Maths. The skills they gain from being taught problem solving successfully will be skills they use and hone for the rest of their life – not just for their SATs.

For a range of problem solving techniques, complete with explanations, contextual uses, example problems and challenge questions – don’t forget to download our free  Ultimate Guide to KS2 problem solving and reasoning techniques  resource here.

KS2 problem Solving FAQs

Here are some techniques to teach problem solving to primary school pupils: Open ended problem solving Using logical reasoning Working backwards Drawing a diagram Drawing a table Creating an organised list Looking for a pattern Acting it out Guessing and checking

Ofsted say that teachers can encourage problem-solving by: Setting problems as part of learning in all topics for all pupils. Varying the ways in which you pose problems. Trying to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations. Making sure you discuss alternative approaches with pupils to help develop their reasoning. Ensuring that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

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2D shape match

A super KS2 card sort activity to help children to match up 2D shapes and their properties. An ideal resource to be used as the beginning or end of a teaching sequence on 2-D shapes.

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2d shape problem solving activity

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18 November 2011

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Millennials have a fresh take on the FIRE movement, and it's less about taking it easy in retirement

At age 36, Jace Mattinson is already over retirement . Four years ago, he sold his lumber company for seven figures, and he had enough saved that he never needed to work again.

He said that was an enticing idea after five "extremely tough" years of owning a business. During that time, he was away from his home in Austin a few nights a week and hustling to run the 135-year-old company he'd acquired. After selling the company, he needed a long break from anything laborious.

"I was golfing three, four times a week. I was going to the lake. I was doing all my hobbies that I really cared about and enjoyed, ones that for the greater part of a decade I didn't have as much time to do," Mattinson told Business Insider.

But after eight months, he decided retirement was not nearly as fulfilling as he'd imagined. He returned to a job in lumber distribution and revived his financial podcast. He said he wanted to continue to model a good work ethic for his kids.

Mattinson has all the trappings of someone in the FIRE movement . The acronym, which stands for financial independence, retire early, was coined in the 1990s in the book "Your Money or Your Life" and popularized on blogs like Mr. Money Mustache and the investment site Motley Fool. The idea was to work hard, ideally with multiple income streams, live a life of austerity, invest prudently, and build a big enough nest egg to walk away from work well before the average retirement age of 64.

But millennials, including Mattinson, who finds himself happiest when he has a balance of work and leisure, said they're not as interested in early retirement — and are creating their own versions of life after work.

Millennials often want the FI without the RE

Devotees of the FIRE movement often save or invest the majority of their income . Some take on extra jobs or delay major life milestones like marriage or having kids.

It's an exclusive club, and many hungry millennials are eager to join it. ChooseFI's Facebook group has over 108,000 members, while the r/financialindependence subreddit has 2.2 million members. But for some FIRE wannabes, the "FI" part of the equation is the biggest focus, and the "RE" half seems to be less of a foregone conclusion.

A popular rule of thumb among this group is the "4% rule," which says you should aim to save 25 times your annual expenses so you can withdraw 4% of your funds each year after you quit working. Some FIRE participants told BI that their target savings goal is between $1.5 million and $2.5 million, though many are working toward more for even greater security.

To be sure, early retirees are a small slice of the population. According to Business Insider's analysis of American retirees, just 2.2% are 50 or younger. Less than 1% are below age 35. Just 0.75% of all Americans over 18 and under 50 are retired. Still, many BI spoke with retire unofficially or partially retire, taking on less responsibility at a company or moving to a lower-stakes position.

BI spoke to a dozen millennials who have achieved or are on track to achieve financial independence. While some have retired and told BI they're enjoying it, most feel retirement is pointless and still want to build their careers or give back to their communities.

"The thing I have noticed shift most is the emphasis on FI and less on RE," Scott Rieckens, the executive producer of the film " Playing With FIRE ," said. "I think it's awesome to see, as it signals that financial independence is the key motive, which it is, and that work and purpose are actually really important. Retiring early to nothing is a bad idea."

Brad Barrett, the host of the "ChooseFI" podcast, said "vanishingly few" people with the wherewithal to reach financial independence are retiring early. To him, reaching financial independence allows someone to live the life they want, but retiring early signifies turning away from everything you've worked toward.

For many, financial freedom goes beyond quitting a job you don't like. Some said it's the ability to spend on travel or leisure without much stress — which has become even more important after the pandemic's peak. Others said it helps them lead a life of purpose, whether that means educating people on a podcast or leading charity efforts.

The problem with retirement seems to be that people want to add value to their communities and within their own lives — and they believe work is the way to do that. As Bill Schaninger, a speaker, author, and thought leader on the future of work, found in research he conducted with Naina Dhingra for McKinsey , 70% of people who were surveyed said they define their purpose through work.

"Many people figured out one of the things that I get a lot of validation from is being clever, solving problems, participating, and working on something bigger than me," Schaninger told BI.

COVID-19 may have amplified this, he added. "The fragility of our condition, I think, was brought home in a way that maybe many of us had taken for granted," he said. "And so now it's like, 'Well, if I'm going to do this, it has to matter.'"

The millennial version of early retirement

Mitch, 37, said he is about to quit his high-stress job and take a mini-retirement — he has a 22-stop national parks trip planned this summer.

The Minnesota resident and vice president of a building-maintenance company, who asked that only his first name be used because of an ongoing job transition, has a net worth of about $2 million but said he's only planning to take a few months off before returning to the workforce in a lower-stress position. All the sources BI spoke with provided documentation of their net worth.

Mitch said he stumbled into the online personal-finance community in his early 30s, which inspired him and his wife to increase their savings to at least 75% of their income by avoiding spending on luxury items. He said even his high savings won't affect his decision to quit working.

"I think a lot of traditional retirees lack purpose — they take a year or two of retirement and hate it because they do whatever and lose purpose," Mitch said. "The ones that volunteer, continue to coach and consult, or do whatever it is to sharpen their brain and really have a purpose tend to be some of the happiest retirees."

Brian Luebben, a financially independent millennial , described having a panic attack shortly after he hit FI and quit his sales job.

"If you have anxiety, financial freedom is not going to solve it," he said. "If you have depression, financial freedom is not going to solve it. Be careful of the mountaintop moments. When you become a millionaire, when you become financially free, when you do all this stuff, no mariachi band follows you around and performs."

He argued that achieving financial independence and hitting a specific number is "the simplest part." After all, there's a playbook for wealth-building strategies like investing in real estate or building an e-commerce business.

"The most difficult part is figuring out what you do when you have nothing to do all day," he said. "What do you choose to work on?"

Luebben, who hosts a podcast and runs the entrepreneur resource The Action Academy to help other people achieve financial freedom, said people should think through four core questions before they're even close to achieving financial independence: "What does the perfect day look like? What does the perfect week look like? Who was with you? And where?"

Going through that exercise can help ensure that your identity doesn't become wrapped up in achieving FIRE, which is something that Grant Sabatier, who took a year and a half off from work after achieving financial independence, struggled with.

"I defined myself by the pursuit of financial independence," Sabatier, the author of " Financial Freedom ," said. "Then, once I reached it, it was like, now I no longer had to do that thing, so what am I going to do? I encourage people on the path to do that inner work. Don't delay figuring out what you really want, why you're pursuing financial independence, and what you want to do after."

Balancing work and fun

Instead of a traditional retirement, many financially independent millennials are finding a balance between work and leisure that works for them.

For Sabina Horrocks, 41, becoming a millionaire was "quite boring." She and her husband worked in six-figure managerial positions, recently achieving a net worth of about $2 million, then had a daughter in 2021. They "plowed money into investments early on," kept daily expenditures low, and purchased rental properties they eventually sold.

She quit her sales operations job but has no intention of stopping work. She's a stay-at-home mom and plans to continue her blog The Moneyaires ; she'd also like to become a financial coach or planner.

Blogging and coaching were common post-FI pursuits among the would-be early retirees BI spoke to. Michelle Schroeder-Gardner, 34, runs the blog Making Sense of Cents , and over the past decade, she and her husband have lived mostly in an RV or a sailboat.

By 2017, their blog, advertising sales, and a course they created called Making Sense of Affiliate Marketing had generated nearly $1.2 million in revenue. By 2018, they had achieved financial independence. After years of 100-hour workweeks, she now spends 10 hours a week on her business, which generates $600,000 a year.

"I'm able to travel whenever I want. I can work whenever I want. Nothing's really dependent on my work hours," she said. "My plan is pretty much to continue doing this while I like it and continue to make a little bit more money and save as much as I can."

Lauren and Steven Keys, who quit their full-time jobs in their 20s , have a similar outlook.

Steven does freelance work for his former employer but spends much of his time on an online-tutoring service called CramBetter that he cofounded in 2023. Lauren has one social-media client she works with a couple of hours a month. They also run a financial-independence blog, Trip of a Lifestyle , and earn rental income from a fully paid-off investment property.

"There's this misconception about early retirement that you'll never make another penny ever again and just sit on the beach all day for the rest of your life," Steven said. "We're never going to stop making any money whatsoever."

Are you part of the FIRE movement or living by some of its principles? Reach out these reporters at [email protected] or [email protected] .

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