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Working Systematically at KS2 - Primary Teachers

This page has been superseded by our Working Systematically - Primary Teachers page

Scroll down to see our complete collection of KS2 problems that require children to work systematically, or explore the two sub-collections focusing on important aspects of systematic working.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Finding All Possibilities Upper Primary

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Ordered Ways of Working Upper Primary

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Sitting Round the Party Tables

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Beads and Bags

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

What could the half time scores have been in these Olympic hockey matches?

School Fair Necklaces

How many possible symmetrical necklaces can you find? How do you know you've found them all?

Nine-pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

Five More Coins

Could Ben have any amount of money between 5p and £2 in his pocket if he has five coins?

What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Fifteen Cards

Can you use the information to find out which cards I have used?

Guess the Dominoes

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Greater Than or Less Than?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Coded Hundred Square

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Multiply Multiples 1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Buying a Balloon

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Can you replace the letters with numbers? Is there only one solution in each case?

A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Cubes Here and There

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Finding Fifteen

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Through the Window

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

This Pied Piper of Hamelin

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Two Primes Make One Square

Can you make square numbers by adding two prime numbers together?

Sealed Solution

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Prison Cells

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Display Boards

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Button-up Some More

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

The Dice Train

This dice train has been made using specific rules. How many different trains can you make?

Curious Number

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Counting Cards

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Cover the Tray

These practical challenges are all about making a 'tray' and covering it with paper.

5 on the Clock

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Ribbon Squares

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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KS2 - Problem Solving and Reasoning Questions

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

10 March 2023

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ozzyshortstop34

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bonniegraham

Great! i will use these :) THanks for sharing.

Just the type of problems I was looking for.

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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

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!

Fluency, Reasoning and Problem Solving: What This Looks Like In Every Maths Lesson

Neil Almond

Fluency reasoning and problem solving have been central to the new maths national curriculum for primary schools introduced in 2014. Here we look at how these three approaches or elements of maths can be interwoven in a child’s maths education through KS1 and KS2. We look at what fluency, reasoning and problem solving are, how to teach them, and how to know how a child is progressing in each – as well as what to do when they’re not, and what to avoid.

The hope is that this blog will help primary school teachers think carefully about their practice and the pedagogical choices they make around the teaching of reasoning and problem solving in particular.

Before we can think about what this would look like in practice however, we need to understand the background tothese terms.

What is fluency in maths?

Fluency in maths is a fairly broad concept. The basics of mathematical fluency – as defined by the KS1 / KS2 National Curriculum for maths – involve knowing key mathematical facts and being able to recall them quickly and accurately.

But true fluency in maths (at least up to Key Stage 2) means being able to apply the same skill to multiple contexts, and being able to choose the most appropriate method for a particular task.

Fluency in maths lessons means we teach the content using a range of representations, to ensure that all pupils understand and have sufficient time to practise what is taught.

Read more: How the best schools develop maths fluency at KS2 .

What is reasoning in maths?

Reasoning in maths is the process of applying logical thinking to a situation to derive the correct problem solving strategy for a given question, and using this method to develop and describe a solution.

Put more simply, mathematical reasoning is the bridge between fluency and problem solving. It allows pupils to use the former to accurately carry out the latter.

Read more: Developing maths reasoning at KS2: the mathematical skills required and how to teach them .

What is problem solving in maths?

It’s sometimes easier to start off with what problem solving is not. Problem solving is not necessarily just about answering word problems in maths. If a child already has a readily available method to solve this sort of problem, problem solving has not occurred. Problem solving in maths is finding a way to apply knowledge and skills you have to answer unfamiliar types of problems.

Read more: Maths problem solving: strategies and resources for primary school teachers .

We are all problem solvers

First off, problem solving should not be seen as something that some pupils can do and some cannot. Every single person is born with an innate level of problem-solving ability.

Early on as a species on this planet, we solved problems like recognising faces we know, protecting ourselves against other species, and as babies the problem of getting food (by crying relentlessly until we were fed).

All these scenarios are a form of what the evolutionary psychologist David Geary (1995) calls biologically primary knowledge. We have been solving these problems for millennia and they are so ingrained in our DNA that we learn them without any specific instruction.

Why then, if we have this innate ability, does actually teaching problem solving seem so hard?

Mathematical problem solving is a  learned skill

As you might have guessed, the domain of mathematics is far from innate. Maths doesn’t just happen to us; we need to learn it. It needs to be passed down from experts that have the knowledge to novices who do not.

This is what Geary calls biologically secondary knowledge. Solving problems (within the domain of maths) is a mixture of both primary and secondary knowledge.

The issue is that problem solving in domains that are classified as biologically secondary knowledge (like maths) can only be improved by practising elements of that domain.

So there is no generic problem-solving skill that can be taught in isolation and transferred to other areas.

This will have important ramifications for pedagogical choices, which I will go into more detail about later on in this blog.

The educationalist Dylan Wiliam had this to say on the matter: ‘for…problem solving, the idea that pupils can learn these skills in one context and apply them in another is essentially wrong.’ (Wiliam, 2018)So what is the best method of teaching problem solving to primary maths pupils?

The answer is that we teach them plenty of domain specific biological secondary knowledge – in this case maths. Our ability to successfully problem solve requires us to have a deep understanding of content and fluency of facts and mathematical procedures.

Here is what cognitive psychologist Daniel Willingham (2010) has to say:

‘Data from the last thirty years lead to a conclusion that is not scientifically challengeable: thinking well requires knowing facts, and that’s true not simply because you need something to think about.

The very processes that teachers care about most—critical thinking processes such as reasoning and problem solving—are intimately intertwined with factual knowledge that is stored in long-term memory (not just found in the environment).’

Colin Foster (2019), a reader in Mathematics Education in the Mathematics Education Centre at Loughborough University, says, ‘I think of fluency and mathematical reasoning, not as ends in themselves, but as means to support pupils in the most important goal of all: solving problems.’

In that paper he produces this pyramid:

This is important for two reasons:

1)    It splits up reasoning skills and problem solving into two different entities

2)    It demonstrates that fluency is not something to be rushed through to get to the ‘problem solving’ stage but is rather the foundation of problem solving.

In my own work I adapt this model and turn it into a cone shape, as education seems to have a problem with pyramids and gross misinterpretation of them (think Bloom’s taxonomy).

Notice how we need plenty of fluency of facts, concepts, procedures and mathematical language.

Having this fluency will help with improving logical reasoning skills, which will then lend themselves to solving mathematical problems – but only if it is truly learnt and there is systematic retrieval of this information carefully planned across the curriculum.

Performance vs learning: what to avoid when teaching fluency, reasoning, and problem solving

I mean to make no sweeping generalisation here; this was my experience both at university when training and from working in schools.

At some point schools become obsessed with the ridiculous notion of ‘accelerated progress’. I have heard it used in all manner of educational contexts while training and being a teacher. ‘You will need to show ‘ accelerated progress in maths ’ in this lesson,’ ‘Ofsted will be looking for ‘accelerated progress’ etc.

I have no doubt that all of this came from a good place and from those wanting the best possible outcomes – but it is misguided.

I remember being told that we needed to get pupils onto the problem solving questions as soon as possible to demonstrate this mystical ‘accelerated progress’.

This makes sense; you have a group of pupils and you have taken them from not knowing something to working out pretty sophisticated 2-step or multi-step word problems within an hour. How is that not ‘accelerated progress?’

This was a frequent feature of my lessons up until last academic year: teach a mathematical procedure; get the pupils to do about 10 of them in their books; mark these and if the majority were correct, model some reasoning/problem solving questions from the same content as the fluency content; set the pupils some reasoning and word problem questions and that was it.

I wondered if I was the only one who had been taught this while at university so I did a quick poll on Twitter and found that was not the case.

I know these numbers won’t be big enough for a representative sample but it still shows that others are familiar with this approach.

The issue with the lesson framework I mentioned above is that it does not take into account ‘performance vs learning.’

What IS performance vs learning’?

The premise is that performance in a lesson is not a good proxy for learning.

Yes, those pupils were performing well after I had modeled a mathematical procedure for them, and managed to get questions correct.

But if problem solving depends on a deep knowledge of mathematics, this approach to lesson structure is going to be very ineffective.

As mentioned earlier, the reasoning and problem solving questions were based on the same maths content as the fluency exercises, making it more likely that pupils would solve problems correctly whether they fully understood them or not.

Chances are that all they’d need to do is find the numbers in the questions and use the same method they used in the fluency section to get their answers – not exactly high level problem solving skills.

Teaching to “cover the curriculum” hinders development of strong problem solving skills.

This is one of my worries with ‘maths mastery schemes’ that block content so that, in some circumstances, it is not looked at again until the following year (and with new objectives).

The pressure for teachers to ‘get through the curriculum’ results in many opportunities to revisit content just not happening in the classroom.

Pupils are unintentionally forced to skip ahead in the fluency, reasoning, problem solving chain without proper consolidation of the earlier processes.

As David Didau (2019) puts it, ‘When novices face a problem for which they do not have a conveniently stored solution, they have to rely on the costlier means-end analysis.

This is likely to lead to cognitive overload because it involves trying to work through and hold in mind multiple possible solutions.

It’s a bit like trying to juggle five objects at once without previous practice. Solving problems is an inefficient way to get better at problem solving.’

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Fluency and reasoning – Best practice in a lesson, a unit, and a term

By now I hope you have realised that when it comes to problem solving, fluency is king. As such we should look to mastery maths based teaching to ensure that the fluency that pupils need is there.

The answer to what fluency looks like will obviously depend on many factors, including the content being taught and the year group you find yourself teaching.

But we should not consider rushing them on to problem solving or logical reasoning in the early stages of this new content as it has not been learnt, only performed.

I would say that in the early stages of learning, content that requires the end goal of being fluent should take up the majority of lesson time – approximately 60%. The rest of the time should be spent rehearsing and retrieving other knowledge that is at risk of being forgotten about.

This blog on mental maths strategies pupils should learn in each year group is a good place to start when thinking about the core aspects of fluency that pupils should achieve.

Little and often is a good mantra when we think about fluency, particularly when revisiting the key mathematical skills of number bond fluency or multiplication fluency. So when it comes to what fluency could look like throughout the day, consider all the opportunities to get pupils practicing.

They could chant multiplications when transitioning. If a lesson in another subject has finished earlier than expected, use that time to quiz pupils on number bonds. Have fluency exercises as part of the morning work.

Read more: How to teach times tables KS1 and KS2 for total recall .

What about best practice over a longer period?

Thinking about what fluency could look like across a unit of work would again depend on the unit itself.

Look at this unit below from a popular scheme of work.

They recommend 20 days to cover 9 objectives. One of these specifically mentions problem solving so I will forget about that one at the moment – so that gives 8 objectives.

I would recommend that the fluency of this unit look something like this:

LY = Last Year

This type of structure is heavily borrowed from Mark McCourt’s phased learning idea from his book ‘Teaching for Mastery.’

This should not be seen as something set in stone; it would greatly depend on the needs of the class in front of you. But it gives an idea of what fluency could look like across a unit of lessons – though not necessarily all maths lessons.

When we think about a term, we can draw on similar ideas to the one above except that your lessons could also pull on content from previous units from that term.

So lesson one may focus 60% on the new unit and 40% on what was learnt in the previous unit.

The structure could then follow a similar pattern to the one above.

Best practice for problem solving in a lesson, a unit, and a term 

When an adult first learns something new, we cannot solve a problem with it straight away. We need to become familiar with the idea and practise before we can make connections, reason and problem solve with it.

The same is true for pupils. Indeed, it could take up to two years ‘between the mathematics a student can use in imitative exercises and that they have sufficiently absorbed and connected to use autonomously in non-routine problem solving.’ (Burkhardt, 2017).

Practise with facts that are secure

So when we plan for reasoning and problem solving, we need to be looking at content from 2 years ago to base these questions on.

Now given that much of the content of the KS2 SATs will come from years 5 and 6 it can be hard to stick to this two-year idea as pupils will need to solve problems with content that can be only weeks old to them.

But certainly in other year groups, the argument could be made that content should come from previous years.

You could get pupils in Year 4 to solve complicated place value problems with the numbers they should know from Year 2 or 3. This would lessen the cognitive load, freeing up valuable working memory so they can actually focus on solving the problems using content they are familiar with.

Read more: Cognitive load theory in the classroom

Increase complexity gradually.

Once they practise solving these types of problems, they can draw on this knowledge later when solving problems with more difficult numbers.

This is what Mark McCourt calls the ‘Behave’ phase. In his book he writes:

‘Many teachers find it an uncomfortable – perhaps even illogical – process to plan the ‘Behave’ phase as one that relates to much earlier learning rather than the new idea, but it is crucial to do so if we want to bring about optimal gains in learning, understanding and long term recall.’  (Mark McCourt, 2019)

This just shows the fallacy of ‘accelerated progress’; in the space of 20 minutes some teachers are taught to move pupils from fluency through to non-routine problem solving, or we are somehow not catering to the needs of the child.

When considering what problem solving lessons could look like, here’s an example structure based on the objectives above.

Fluency, Reasoning and Problem Solving should NOT be taught by rote 

It is important to reiterate that this is not something that should be set in stone. Key to getting the most out of this teaching for mastery approach is ensuring your pupils (across abilities) are interested and engaged in their work.

Depending on the previous attainment and abilities of the children in your class, you may find that a few have come across some of the mathematical ideas you have been teaching, and so they are able to problem solve effectively with these ideas.

Equally likely is encountering pupils on the opposite side of the spectrum, who may not have fully grasped the concept of place value and will need to go further back than 2 years and solve even simpler problems.

In order to have the greatest impact on class performance, you will have to account for these varying experiences in your lessons.

Read more: 

• Maths Mastery Toolkit : A Practical Guide To Mastery Teaching And Learning
• Year 6 Maths Reasoning Questions and Answers
• Get to Grips with Maths Problem Solving KS2
• Mixed Ability Teaching for Mastery: Classroom How To
• 21 Maths Challenges To Really Stretch Your More Able Pupils
• Maths Reasoning and Problem Solving CPD Powerpoint
• Why You Should Be Incorporating Stem Sentences Into Your Primary Maths Teaching

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

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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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TES Maths Investigations Collection

Engaging investigation ideas to inspire creative thinking in your classroom

Since the abolition of maths coursework, there is no formal requirement to carry out investigations with your students. However, it is only through investigative work that students of all ages and abilities can start to appreciate the true beauty of the subject. They can hypothesise, be creative, challenge themselves, work with other students and potentially discover things that have never been discovered before.

At our school, we do an investigation with each year group every half term. They may last 20 minutes or five lessons. Here is a selection of the best investigations that the TES Maths community has to offer.

I really hope you and your students find them useful, enjoyable and stimulating.

Craig Barton, TES Maths adviser

• Creativity in maths This useful guide is worth reading before embarking upon any maths investigation. What does it mean to be creative and how can you provide opportunities for creativity in your classroom? It comes complete with five puzzles in a ready-to-print format.
• Maths investigations A collection of over 20 maths problems, puzzles, games and investigations that are designed for KS2, but which could easily be used to extend the learning and problem solving skills of younger KS3 students.
• More maths investigations This resource contains lots of ideas for real-life maths investigations, covering number, algebra, shape, space and measure. Again, while they are aimed at KS2 pupils, they could be adapted for use with KS3 students as well.
• Even more maths investigations! These starter sheets introduce a topic for investigation and come with levelled guidance to help students to self- and peer-assess as they progress through it. Although they are targeted at Year 7, these are suitable for year groups at both KS2 and KS3.
• Investigative lesson presentations A collection of classic maths investigations, including chessboards and tetrahedron towers, presented as PowerPoint presentations with learning objectives and level expectations.
• Challenging ideas for KS4 and Post-16 This was one of my TES Maths Resources of 2014 and it’s easy to see why. These investigations are ideal for gifted and talented GCSE and sixth form students and include everything from code-breaking and Goldbach’s conjecture to the Riemann hypothesis and game theory.
• Diagonals of rectangles This may be one of my own resources, but it is one of my all-time favourites as it’s so versatile. It can be accessed by Year 6 students, while still challenging the most able Year 11s. The concept is so simple, but the potential depth is great.
• Investigating circle theorems Some of the best investigations are topic-specific and this activity is no exception. It uses the free dynamic geometry package, GeoGebra, to help students derive, identify and better understand all of the key circle theorems.
• Prison cells investigation The famous investigation about the numbers on prison cell doors is well-presented, has a really clear structure and some fantastic ideas for differentiation.
• Pentominoes Pentominoes are a superb, versatile teaching resource that can be used for investigating many aspects of shape. This resource takes you through lots of ideas for making the most of them.
• Mathemagic These maths magic tricks are engaging way of presenting a problem to your KS3 pupils, before challenging them to investigate how and why they work. Better still, can they go on to design their own?
• Noughts and crosses investigation Who would have thought you could get so much maths goodness from a game of noughts and crosses?  This game will appeal to secondary students of all ages.

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I See Problem-Solving - LKS2

The ebook i see problem-solving - lks2 helps to break down problem-solving for all children. build-up tasks, support prompts and worked examples enable children to develop understanding. there are also a range of extension tasks and reasoning prompts that allow children to explore ideas at greater depth. the ultimate resource for teaching problem-solving in y3/4.

I See Problem-Solving - LKS2 Sample provides 5 free sample tasks. Most tasks have a build task, main question , a support prompt and  explain and extend features to deepen the challenge. There are sometimes practise questions too. The  worked examples  model the solutions to the main tasks step-by-step - download below for free. The 54 tasks span all areas of the LKS2 maths curriculum. The purchase price is £30 (£25 + £5 VAT) for the PDF digital download.

I See Problem-Solving - LKS2 Worked Examples (PowerPoint)

I See Problem-Solving - LKS2 Worked Examples (PDF)

Each task starts with a  build prompt to introduce the key concepts, generate discussion and activate prior learning. Here are two example build tasks: 

Now the children are ready for the main task . Often, complex mathematical concepts are explored with relatively small numbers. For many tasks there are multiple possible answers: some children will work to find an answer, whereas for others the challenge is knowing that they have found all possible answers. Here are two examples of the task prompt:

Some children will need extra guidance to help them to complete a task. They can access the support prompt, which may give a useful visual representation or it might focus children's thinking on one particular aspect of the question, leading them to the key thought process. This allows children to access help whilst maintaining a feeling of independence. 

Each task also has a range of  explain and extend tasks to allow children to explore the same ideas at greater depth. Children will need to find multiple answers, explain their thinking fully or apply their knowledge in a new way. These prompts step up the challenge and really deepen the thinking!

The 54 tasks of I See Problem-Solving - LKS2 cover all areas of the LKS2 curriculum (children aged 7-9). The sale price is £30. When ordered, the PDF file is emailed direct to your inbox for your use.

To purchase, click on the link below. If you need assistance ordering, please read the Frequently Asked Questions below or email [email protected].

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