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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

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Home > Learning Resources

KS1 and KS2 Maths – Problem solving

• Author: Mike Askew
• Main Subject: CPD
• Subject: Maths
• Date Posted: 20 June 2012

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If children use well worn techniques to solve problems without understanding or modelling the context, their maths skills won't fully evolve

Children, from birth, are proficient problem solvers. By the age of two or three they have solved what are probably life’s two biggest problems - how to walk and how to talk. As they get older they solve practical problems, such as sharing a bag of sweets fairly with others, long before they’ve heard of division. In this article, I look at how we can build on this natural propensity to solve problems in teaching mathematics.

Routine and non-routine problems

Routine problems are problems children know how to solve based on their previous experiences. The sort of thinking required by routine problems can be described as reproductive: the child only needs to recall or reproduce a procedure or method they have previously learnt. A problem like ‘Apples’, for example (see below), is likely to be a routine problem for most children at the upper end of primary school; they know to multiply the two numbers together without having to think deeply about what operation to use.

• Apples on a supermarket shelf are in bags of eight. • If Jane buys six bags, how many apples is that?

In contrast, non-routine problems are where the learner does not immediately have a solution tucked under his belt. The problem solver has to put some effort into understanding the problem and creating, rather than recalling, a solution strategy. Non-routine problems engage learners in productive thinking.

We often think of non-routine problems as needing to be unusual or not having, to us as adults, an immediately obvious method of solution. ‘Stamps’ is typical of this type of non-routine problem.

• Clearing out a desk draw I found a collection of 5p and 6p stamps. • I have a parcel to post that needs 58p worth of stamps on it. • Can I create this exactly using the stamps I found? • If so, is there more than one way of doing this?

In choosing problems to work with, we need to decide whether or not we think a problem will be routine or non-routine for the particular children working on it. In the rest of this article, the problems chosen are being treated as though they are non-routine problems for the children working on them. That’s not to say that I don’t think routine problems have a place in the curriculum - they do. Here, however, I want to deal with some of the issues around teaching and learning non-routine problems.

The importance of context

• Four hungry girls share three pizzas equally. • Eight hungry boys share six pizzas equally. • Does each girl get more pizza than each boy, less or the same?

As a routine problem, the ‘story’ of pizzas and hungry children doesn’t serve any real purpose: children quickly learn to disregard the context, to strip out the mathematics and to work some procedure. The problem could just as easily have been put in the context of builders sharing bricks and many learners would happily say each builder would get 3/4 of a brick, without stopping to question the near impossibility of sharing out bricks.

We can, however, treat ‘Pizzas’ as a non-routine problem and use it to introduce children to thinking about fractions and equivalences. The context of hungry children and pizzas then becomes important. It is not chosen simply to be window-dressing for a fraction calculation. Nor are pizzas chosen because children are intrinsically motivated by food, making the unpalatable topic of fractions digestible. No, the context s chosen because children know about fair shares and slicing up pizzas - they can solve this problem without any formal knowledge of fractions. As the researcher Terezhina Nunes once pointed out, young children would not be able to solve the ‘bald’ calculation 3 divided by 4 but, “show me four young children who, given three bars of chocolate to share out fairly, hand the bars back saying ‘it can’t be done.”

Children have ‘action schemas’ for solving problem like ‘Pizzas’ - they can find ways to solve this with objects, pictures, diagrams and, eventually, symbols. Teaching can then build on the children’s informal solutions to draw out the formal mathematics of fractions. From being one of 20 ‘problems’ on a worksheet to complete in a lesson, ‘Pizzas’ can become a ‘rich task’ taking up the best part of a lesson, if children work on it in pairs and carefully selected solutions are then shared with the class.

Creating mathematical models

Part of the productive thinking in working on rich, non-routine problems requires children to create mathematical models, and we can teach to support this.

• At the supermarket Myprice, milk costs £1.08 per litre. • This is 7 pence less per litre than milk costs at Locost. • How much does 5 litres of milk cost at Locost?

What is missing from this approach is attention to setting up an appropriate model of the problem. Ultimately this could be a mental model of the problem context, but it helps initially to encourage children to put something on paper that can be shared and discussed. In problems involving quantities, like ‘Milk’, simple bar diagrams can help children create the appropriate model. These help children examine the relationships between the quantities (as opposed to simply fixing on specific numbers and keywords).

Setting up a diagrammatic model begins with creating a representation of what is known in the situation. In this example, we know milk at Myprice costs £1.08, so a diagram for this would look like:

MYPRICE £1.08

This provides the basis for talking about what the picture for the price of milk at Locost is going to be. Will the bar be longer or shorter? Where is the bar for the 7 pence to be drawn?

Two different models can be set up and children asked to describe the relationship between the prices at the two supermarkets, to see which diagram fits with the information in the problem. If the diagram for the price at Locost is shorter by 7, then two statements can be made:

MYPRICE £1.08p LOCOST     7p

• Myprice milk costs 7 pence more than milk at Locost.

• Locost milk costs 7 pence less than milk at Myprice.

In comparison, making the bar for milk at Locost longer by 7 gives different comparative statements:

MYPRICE £1.08p 7p LOCOST    

• Myprice milk costs 7 pence less than milk at Locost.

• Locost milk costs 7 pence more than milk at Myprice.

Children can then talk about which of these situations fits with the wording in the problem.

Having established that Locost milk must be £1.15 a litre, children can go on to produce the bar diagram model for this.

Supporting non-routine problem solving

Where the problems were played out as non-routine, three factors identified are worth noting. First, in choosing the tasks, the teachers made sure they would build on learners’ prior knowledge - as I suggest a problem like ‘Pizzas’ can. Second, in contrast to focusing on getting the answer, the researchers observed what they called ‘sustained pressure for explanation and meaning’. In other words, the teachers pressed for children to explain what and why they were doing what they were doing rather than simply focusing on whether or not they had got the correct answer. Third, the amount of time children were allowed to work on the problem was neither too long or too short: children need enough time to ‘get into’ a problem, but too much time can lead to a loss of engagement.

Share good practice

Gather together a collection of problems covering all the years of education in your school (or ask teachers to each contribute two or three problems).

Working together in small groups, teachers sort the problems into three groups:

1. Problems they think would be routine for the children they teach 2. Problems they think would be non-routine for their children 3. Problems they think would be much too difficult for their age group

Everyone agrees to try out a problem from group 2 with their class. Discuss how too much focus on getting the answer can reduce the challenge and stress the importance of pressing children to explain their working. At a subsequent meeting, people report back, focusing in particular on strategies they used to keep the problem solving non-routine.

About the author

Mike Askew is Professor of Primary Education at Monash University, Melbourne. Until recently, he was Professor of Mathematics Education at King’s College, University and Director of BEAM.

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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 .

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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.

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Fluency, reasoning and problem solving in primary maths

Australia and new zealand, primary maths, tes resources team.

Develop fluency, reasoning and problem solving in Maths with the mastery approach

The skills of fluency, reasoning and problem solving are well-known to all primary Maths teachers, and in mastery teaching they play an essential role. To help you develop your mastery approach, we have hand-picked this selection of Maths resources, with everything from reasoning lessons and problem solving worksheets, to daily fluency questions and independent investigations. So, why not take a look?

To find out more about Maths mastery explore Teaching for mastery in primary maths .

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Problem Solving Teaching Resources

This collection of problem-solving teaching resources provides students with materials and strategies to guide them when learning to solve numeracy word problems. Learning to decipher word problems and recognise the correct operation to use in order to solve the problem correctly, is an important skill for students to learn. Use these educational games, activities, worksheets, posters, PowerPoint presentations and word problem cards to assist your students when they are learning to problem-solve. Also included are daily maths word problems which can be used as warm-up activities at the beginning of each numeracy lesson.

• Teaching Resource 47
• Lesson Plan 1
• Task Cards 16
• Worksheets 14
• Teaching Presentations 7
• Match-Up Games 4
• Templates 2
• Bookmarks 1
• Classroom Displays 1
• Labels, Signs & Decorations 1
• Foundation Stage 3
• Key Stage 1 19
• Lower Key Stage 2 28
• Upper Key Stage 2 20
• Key Stage 3 4

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File formats.

• Printable PDF 43
• Microsoft PowerPoint (.pptx) 10
• Microsoft Word (.docx) 6
• Adobe Reader (.pdf) 4
• Google Slides 3
• Teach Starter Publishing 48

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• Problem Solving Worksheets
• Problem Solving for Key Stage 1
• Problem Solving for Key Stage 2 - Lower
• Problem Solving for Key Stage 2 - Upper

Problem-Solving

Jabberwocky

Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically.

Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions.

Problem-solving involves three basic functions:

Seeking information

Generating new knowledge

Making decisions

Problem-solving is, and should be, a very real part of the curriculum. It presupposes that students can take on some of the responsibility for their own learning and can take personal action to solve problems, resolve conflicts, discuss alternatives, and focus on thinking as a vital element of the curriculum. It provides students with opportunities to use their newly acquired knowledge in meaningful, real-life activities and assists them in working at higher levels of thinking (see Levels of Questions ).

Here is a five-stage model that most students can easily memorize and put into action and which has direct applications to many areas of the curriculum as well as everyday life:

Expert Opinion

Here are some techniques that will help students understand the nature of a problem and the conditions that surround it:

• List all related relevant facts.
• Make a list of all the given information.
• Restate the problem in their own words.
• List the conditions that surround a problem.
• Describe related known problems.

It's Elementary

For younger students, illustrations are helpful in organizing data, manipulating information, and outlining the limits of a problem and its possible solution(s). Students can use drawings to help them look at a problem from many different perspectives.

Understand the problem. It's important that students understand the nature of a problem and its related goals. Encourage students to frame a problem in their own words.

Describe any barriers. Students need to be aware of any barriers or constraints that may be preventing them from achieving their goal. In short, what is creating the problem? Encouraging students to verbalize these impediments is always an important step.

Identify various solutions. After the nature and parameters of a problem are understood, students will need to select one or more appropriate strategies to help resolve the problem. Students need to understand that they have many strategies available to them and that no single strategy will work for all problems. Here are some problem-solving possibilities:

Create visual images. Many problem-solvers find it useful to create “mind pictures” of a problem and its potential solutions prior to working on the problem. Mental imaging allows the problem-solvers to map out many dimensions of a problem and “see” it clearly.

Guesstimate. Give students opportunities to engage in some trial-and-error approaches to problem-solving. It should be understood, however, that this is not a singular approach to problem-solving but rather an attempt to gather some preliminary data.

Create a table. A table is an orderly arrangement of data. When students have opportunities to design and create tables of information, they begin to understand that they can group and organize most data relative to a problem.

Use manipulatives. By moving objects around on a table or desk, students can develop patterns and organize elements of a problem into recognizable and visually satisfying components.

Work backward. It's frequently helpful for students to take the data presented at the end of a problem and use a series of computations to arrive at the data presented at the beginning of the problem.

Look for a pattern. Looking for patterns is an important problem-solving strategy because many problems are similar and fall into predictable patterns. A pattern, by definition, is a regular, systematic repetition and may be numerical, visual, or behavioral.

Create a systematic list. Recording information in list form is a process used quite frequently to map out a plan of attack for defining and solving problems. Encourage students to record their ideas in lists to determine regularities, patterns, or similarities between problem elements.

Try out a solution. When working through a strategy or combination of strategies, it will be important for students to …

Keep accurate and up-to-date records of their thoughts, proceedings, and procedures. Recording the data collected, the predictions made, and the strategies used is an important part of the problem solving process.

Try to work through a selected strategy or combination of strategies until it becomes evident that it's not working, it needs to be modified, or it is yielding inappropriate data. As students become more proficient problem-solvers, they should feel comfortable rejecting potential strategies at any time during their quest for solutions.

Monitor with great care the steps undertaken as part of a solution. Although it might be a natural tendency for students to “rush” through a strategy to arrive at a quick answer, encourage them to carefully assess and monitor their progress.

Feel comfortable putting a problem aside for a period of time and tackling it at a later time. For example, scientists rarely come up with a solution the first time they approach a problem. Students should also feel comfortable letting a problem rest for a while and returning to it later.

Evaluate the results. It's vitally important that students have multiple opportunities to assess their own problem-solving skills and the solutions they generate from using those skills. Frequently, students are overly dependent upon teachers to evaluate their performance in the classroom. The process of self-assessment is not easy, however. It involves risk-taking, self-assurance, and a certain level of independence. But it can be effectively promoted by asking students questions such as “How do you feel about your progress so far?” “Are you satisfied with the results you obtained?” and “Why do you believe this is an appropriate response to the problem?”

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		: : Investigations & Puzzles (Naomi Hass) (Bayswater School) Algebra Challenges (Carole Buscombe) (Phil Rhodes) (Phil Rhodes) (Phil Rhodes) (Cherie Rothery) (Cherie Rothery) (Jennifer Orgill) (Kim Pitchford) Solving Equations (Paul Williams) Algebra (Carole Buscombe) Algebra (Paul Cogan) Introduction to Algebra (Lynne Hawkins) Algebra 1 (Cherie Rothery) Algebra 2 (Cherie Rothery) Equations - Reversing Operations (Cherie Rothery)   Click how you can : this site with Custom Search - - - Resources you can trust Problem solving - number If your class is struggling with problem solving, then we’ve got the solution. Year 5 Problem solving – number  comprises differentiated activities based upon the number problem-solving objectives in the year 5 maths curriculum. Activities include scaffolded word problems and investigations alongside explanations, teaching notes and answers. What's included? 9 comprehensive activities differentiated to three levels teaching notes, explanations and step-by-step answers space for workings. Topics featured: place value problems addition and subtraction problems, including money multiplication and division problems, including factors, squares, scaling fractions, decimals and equivalence. What's inside? Unit 1 - Place value number problems (pages 5-20) Place value number problems introduction Place value number problems questions Place value number problems answers Unit 2 - Place value practical problems (pages 21-32) Place value practical problems introduction Place value practical problems questions Place value practical problems answers Unit 3 - Addition and subtraction problems (pages 33-59) Addition and subtraction problems introduction Addition and subtraction problems questions Addition and subtraction problems answers Unit 4 - Length, perimeter and area (pages 60-80) Length, perimeter and area introduction Length, perimeter and area questions Length, perimeter and area answers Unit 5 - Multiplication and division, factors and squares (pages 81-98) Multiplication and division, factors and squares introduction Multiplication and division, factors and squares questions Multiplication and division, factors and squares answers Unit 6 - Multiplication and division operations (pages 99-113) Multiplication and division operations introduction Multiplication and division operations questions Multiplication and division operations answers Unit 7 - Multiplication and division - scaling (pages 114-120) Multiplication and division - scaling introduction Multiplication and division - scaling questions Multiplication and division - scaling answers Unit 8 - Fractions and decimal places (pages 127-151) Fractions and decimal places introduction Fractions and decimal places questions Fractions and decimal places answers Unit 9 - Fractions equivalence - fractions, decimals and percentages (pages 152-167) Fractions equivalence - fractions, decimals and percentages introduction Fractions equivalence - fractions, decimals and percentages questions Fractions equivalence - fractions, decimals and percentages answers You might also like Problem solving - measurement, geometry and statistics . 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STEM Bins® Speed Builds STEM Activities (Morning Work, Early Finishers, Centers) Classroom Calm Down Corner Kit | Identifying Feelings Emotional Regulation 15 Working Memory Brain Games: Improve executive function in 5 minutes a day! Place Value Mystery Pictures Math Logic Puzzles: 5th grade Enrichment - [Digital & Printable PDF] STEM Bins® Hashtag Blocks Speed Builds BUNDLE - STEM Activities, Fast Finishers Math Logic Puzzles: 4th grade ENRICHMENT - [Digital & Printable PDF] STEM Index Card Tower Challenge Easy Prep Project & Elementary Team Building CUBES Math Strategy Poster Display | EDITABLE Measurement Activities Project 2nd Grade, Nonstandard 1st Measuring Length Craft (Educator Guide) A Little SPOT of Feelings & Emotions Math Logic Puzzles: 3rd grade Enrichment - [Digital and Printable PDF] STEM Challenge Bucket Tower Problem-Solving Learning Activity Upper Elementary Circle of Control Activities Inside vs. Outside of Our Control Lesson STEM Bins® Plastic Snowflakes / Brainflakes Speed Builds: STEM Activities SET 1 100th Day of School Activities STEM Activities Size of the problem behavior task cards worksheets social skills visual scenario Quadrilateral Robots - Great Project Based Learning Math Activity (PBL) Size Of The Problem And Reaction Activities For SEL & School Counseling Lessons Math Logic Puzzles: 2nd grade Enrichment - [Digital & Printable PDF] We're hiring Help & FAQ Privacy policy Student privacy Terms of service Tell us what you think Center for Teaching Teaching problem solving. Print Version Tips and Techniques Expert vs. novice problem solvers, communicate. Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand. If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem. In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding. When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics) Encourage Independence Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles. Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others Be sensitive Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill. Encourage Thoroughness and Patience Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process. Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline . The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving. Teaching Guides Quick Links Services for Departments and Schools Examples of Online Instructional Modules Building Problem-Solvers: Engaging Maths Challenges & Playful Games for Primary Students Table of Contents Building Problem-Solvers: Incorporating challenging maths puzzles and games into primary education is a powerful strategy for developing problem-solving skills in young learners. We recognise the importance of engaging pupils with interactive tasks that not only stimulate their mathematical abilities but also build their confidence in tackling complex challenges. By designing diverse mathematical exercises that range from simple to complex, we create opportunities for children to develop fluency as mathematical thinkers and problem solvers, a skill set that is essential in today’s fast-paced, ever-evolving world. It’s crucial to foster a supportive maths culture within the classroom, one that encourages risk-taking and persistence in overcoming obstacles. Education in primary mathematics should not only focus on procedural fluency but also on the understanding of fundamental mathematical concepts . Tools and strategies such as visual representations and heuristic approaches can be invaluable in promoting this kind of deep comprehension. By integrating these techniques with a varied set of maths puzzles and games, we make learning mathematics an engaging and dynamic experience. Key Takeaways Developing problem-solving skills in maths is essential for primary education. Diverse and challenging puzzles enhance mathematical thinking. A supportive learning environment encourages perseverance and growth in maths. Understanding the Fundamentals of Maths In our pursuit of developing proficient problem solvers, it’s essential to start with a strong foundation in mathematics. We focus on building an understanding of numbers and operations, as well as recognising the significance of patterns and relationships. These components are vital in nurturing a comprehensive mathematical mindset. Number and Operations At the core of mathematical understanding are numbers and operations . This involves grasping how numbers work and interact with one another through basic operations : addition, subtraction, multiplication, and division. For example: Addition: It’s combining quantities to increase the total. Subtraction: It’s determining how much one quantity is greater than another Multiplication : It simplifies repeated addition. Division: It’s finding out how many times a number can be subtracted from another in equal parts. Understanding these operations enables children to solve real-world problems effectively. Patterns and Relationships Patterns and relationships form the building blocks for higher-level mathematical thinking. They involve seeing connections and predicting what comes next, based on a sequence or rule. Patterns: These may be numerical or geometric, allowing us to anticipate the next element in a sequence. 1, 2, 4, 8 … (Doubling each time) Relationships: Understanding that certain pieces of information are related, and using this to solve problems, is key to mathematical reasoning . An example might be in understanding that if a car covers more distance in an hour at a faster speed, there’s a direct relationship between speed and distance. In fostering these fundamental skills, we offer our learners not just theory but engaging challenges through mathematical puzzles and games that reinforce these concepts. By participating in such activities, children can apply these foundational maths skills, making connections between theory and practice in a dynamic and enjoyable way. Teaching Mathematics Effectively In our quest to develop sharp problem solvers and creative thinkers, we must focus on how mathematics is taught in primary schools. Our approach bridges the gap between traditional teaching and innovative, engaging methods . Role of Teachers We, as educators, play a pivotal role in moulding students into proficient problem-solvers. By incorporating a variety of maths puzzles and games into our classrooms, we make abstract concepts tangible and accessible. We believe in adapting our teaching styles to meet individual learning needs, devising strategies that make mathematics more than just a subject – instead, a captivating journey of discovery. Curriculum Integration The curriculum should not solely dictate our teaching, but serve as a dynamic framework that integrates real-world problem-solving and logical reasoning through mathematical activities . It is essential we weave challenging exercises with relevant contexts into lessons, thus aligning with our commitment to a broad and balanced education where every child flourishes. The Importance of Problem-Solving Skills Problem-solving skills are integral to learning mathematics, as they enable children to approach complex problems strategically and with confidence. Our goal is to harness these skills through puzzles and games that challenge and engage primary school children. Developing Critical Thinking We understand that critical thinking is the foundation of effective problem-solving. Our puzzles and games are designed to stimulate students’ thinking and reasoning processes , encouraging them to make connections and derive solutions based on logical deduction. Cultivating Patience and Persistence Throughout the problem-solving journey, we foster a sense of patience and persistence in our young learners. Recognising that solutions are not always immediate or straightforward, our resources teach children the value of perseverance and resilience in the face of challenging tasks. Engaging Pupils with Interactive Maths Games Interactive maths games are a brilliant way for us to make mathematics appealing and accessible to primary school pupils. By selecting the right games and integrating 21st-century technology, we can transform the learning experience into an interactive adventure that captivates our young learners. Selecting Appropriate Games When choosing maths games, we must ensure that they are appropriately challenging and aligned with the curriculum. The games should be designed to encourage pupils to think critically and develop their problem-solving skills. We often look for options that offer multiple levels of difficulty, which enables us to cater to the diverse abilities within a classroom. The aim is to select games that not only educate but also genuinely engage the students, making the learning process both enjoyable and effective. Integrating ICT in Maths Games In today’s digital age, integrating Information and Communication Technology (ICT) in maths games is not just innovative; it’s essential. We leverage ICT to provide simulations and virtual environments where pupils can explore mathematical concepts. This interactive technology helps to create immersive experiences that make abstract ideas more concrete. Using ICT, we can give pupils the chance to practise and hone their maths skills through fun, tech-driven games, fostering a more dynamic and interactive learning environment. Incorporating interactive maths games within the classroom is a testament to our commitment to engaging and educating our pupils in a way that resonates with their experiences and interests. Through careful selection and the use of modern ICT, we are able to provide a learning experience that is both enriching and exciting. Designing Challenging Maths Puzzles In our pursuit to build effective problem-solvers, we focus on introducing maths puzzles that are engaging and non-routine, designed to foster natural curiosity in learners. Creating Non-Routine Tasks We believe that the essence of problem-solving lies in the ability to tackle non-routine tasks. These are not your everyday textbook problems, but instead, they present a scenario that requires students to apply concepts in ways they might not have anticipated. In constructing these tasks, it’s vital to strike a balance—too easy and they won’t push the envelope; too hard and they might discourage learners. For example, a puzzle involving pattern recognition might ask pupils to identify the underlying rule of a sequence and predict the next set of numbers. Fostering Curiosity Through Puzzles Curiosity drives us to explore the unknown, and with maths puzzles, it translates into learners venturing beyond their comfort zones. We craft puzzles that inherently provoke students’ interest and pique their natural inquisitiveness. A well-thought-out puzzle can act as an open inquiry, where the journey to the solution is as valuable as the solution itself. Consider a jigsaw arithmetic puzzle that requires learners to not only solve for missing pieces but also to understand why those pieces fit together as they do. Incorporating Diverse Mathematical Tasks When we introduce a variety of mathematical tasks to primary students, we lay the foundation for robust problem-solving skills. By engaging in an assortment of challenges , children can develop a deeper understanding of numbers, spatial awareness, and logical reasoning. Exploration and Investigation We believe that learning should be an adventure, where exploration and investigation play pivotal roles. By offering tasks that encourage students to explore, we open up opportunities for hands-on learning and inquisitive thinking. For instance, we might ask them to investigate the number of ways to reach a total of 10 using only red and blue counters. This simple task invites them to explore addition and the concept of combinations. Measurement and Geometry Measurement and geometry are two areas where children can apply maths to real-world scenarios. We often ask our students to measure lengths and widths of classroom objects, using rulers and other tools to relate the numbers to physical attributes. Then, we might move on to explore geometric shapes by examining and constructing models , allowing for a tangible understanding of edges, faces, and vertices. This hands-on experience is invaluable for cementing their conceptual knowledge. Overcoming Obstacles in Problem Solving Engaging with maths puzzles and games in primary education can sometimes present challenges. It’s essential we understand these stumbling blocks and employ effective strategies to help our children become confident problem solvers. Identifying Common Mistakes Often, obstacles in problem solving arise from common misunderstandings or repeated mistakes . We might see children rush through a problem without fully understanding it, or they may become fixed on one approach and not consider alternative methods. Documenting these mistakes offers us a chance to address them directly. Rushing : Not taking enough time to understand the problem. Fixation on one strategy : Failing to consider different angles. Overlooking details : Missing out on crucial information within the problem. Strategies to Overcome Challenges After pinpointing the typical mistakes, our strategies should focus on overcoming these barriers and reinforcing effective problem solving habits. Encourage thorough reading : Urge pupils to read problems several times. Promote multiple approaches : Introduce a variety of methods to tackle a single problem. Detail orientation : Teach children to pay attention to all the information given. Remember, practice makes perfect, and providing children with a mixture of puzzles and games can build their resilience and adaptability in maths. Creating a Supportive Maths Culture At the heart of nurturing future problem-solvers is the establishment of a supportive maths culture . This means creating an environment where every child feels valued and capable of mastering mathematical challenges . Encouraging Open Communication We recognise the importance of open communication in the classroom. It’s crucial to foster an atmosphere where pupils feel comfortable to express their ideas, ask questions, and share their experiences. In our classroom, we encourage learners to articulate their thought processes and reasoning. This not only clarifies their understanding but also enriches peer learning, as students learn from each other’s perspectives. Such a culture not only enhances their communication skills but also demystifies complex concepts, making maths more approachable . Building Confidence and Growth Mindset We strive to infuse our pupils with confidence and a growth mindset . To do this, we emphasise the belief that abilities can be developed through dedication and hard work. This contrasts with a fixed mindset, where children might believe their skills are static and unchangeable. By celebrating effort rather than innate ability , we inspire our students to embrace challenges and learn from mistakes—an approach that is pivotal for fostering resilient problem solvers . Our aim is to show that mathematics is not about being ‘right’ all the time; instead, it’s about the adventure of learning and improving. Assessing and Enhancing Problem-Solving Capabilities In our quest to build adept problem-solvers through maths puzzles and games , it’s vital that we effectively assess and enhance primary students’ problem-solving capabilities. This not only involves gauging their current skill levels but also providing constructive feedback to aid their growth. Conducting Meaningful Assessments When it comes to assessing problem-solving activities, our approach is to create evaluations that are as engaging as the learning experiences themselves. We believe that a student’s problem-solving skills are best understood by observing them during actual problem-solving activities. Such assessments might involve practical tasks where pupils apply heuristics or use visual representations to tackle mathematical problems, as highlighted by Developing Mathematical Problem-Solving Skills . These tasks are designed to mirror ‘real life’ scenarios, requiring students to think critically and creatively. Providing Constructive Feedback Feedback is a powerful tool in our educational arsenal—it informs students about their performance and provides guidance on how they can improve. Our feedback is specific, timely, and always focused on strategies that students can use to enhance their problem-solving abilities. Whether it’s encouraging greater representational fluency or exploring diverse strategies, we ensure that our feedback helps students reflect and grow as problem solvers. By drawing on resources such as the Real Engagement in Active Problem Solving (REAPS) model, we support teachers in offering feedback that fosters creative problem solving in mathematics. In all of our endeavours at LearningMole, we strive to provide learning experiences that not only educate but also excite. We’re dedicated to fostering environments where every student can become a confident and proficient problem solver. Resources for Primary Maths Education We know that the right resources can make all the difference in empowering primary maths education. So, let’s explore some excellent materials that you can access for free, as well as delve into the treasures offered by NRICH to enrich our young learners’ mathematical journey. Free Teaching Materials We pride ourselves on providing a variety of free teaching materials designed to make maths engaging and fun . You’ll find interactive tutorials , activity sheets , and articles, all tailored for the curious minds of primary children. These resources are not only educational, but they also allow children to absorb key maths concepts in a way that feels like play. Interactive Tutorials : Engage with our step-by-step guides that bring clarity to complex maths problems. Articles : Discover insights and tips targeted at enhancing the teaching experience. Activity Sheets : Download and print these for hands-on practice that reinforces mathematical understanding. One platform we admire is LearningMole , which offers a wealth of content to help children discover the joy of maths through various fun and creative resources. Utilising NRICH Resources When it comes to using NRICH resources , we’re looking at a treasure trove of maths puzzles and activities that are perfect for primary pupils. NRICH aims to challenge and excite young minds with games that are both intriguing and highly educational. Challenging Puzzles : They stimulate strategic thinking and offer varying degrees of difficulty to suit all levels. Classroom Activities : Carefully crafted to promote collaborative problem-solving among students. These resources from NRICH not only complement our teaching but also bring a new dimension to primary maths, making our lessons more dynamic and effective. Frequently Asked Questions In this section, we’ll address some of the most common inquiries related to enhancing problem-solving skills through mathematics puzzles and games in primary education. What are some engaging activities that can enhance problem-solving abilities in primary school children? Children in primary school can greatly benefit from activities such as building structures using different shapes or collaborative tasks where they devise solutions to “real life” scenarios. These activities encourage them to apply mathematical concepts in practical ways. Can you suggest some games that improve problem-solving skills for young learners? Certainly! Games like chess, Sudoku, and even certain board games that require strategic thinking can improve problem-solving skills . These games challenge young minds to think ahead and plan their moves carefully. How can puzzles be effectively used to develop mathematical problem-solving competencies in children? Puzzles can be used in teaching by posing them as interesting challenges that are mathematically meaningful . Puzzles such as tangrams, magic squares, and logic puzzles encourage children to use mathematical reasoning and pattern recognition. In what ways can teachers incorporate problem-solving exercises into their primary classroom curriculum? Teachers can introduce problem-solving in the classroom by integrating puzzles and games into lesson plans. They might also ask thought-provoking questions that lead to problem-solving discussions or use differentiated instruction to cater to various learning styles. Which hands-on group activities can help children build teamwork and problem-solving skills concurrently? Group activities that involve building projects from common objects like blocks or recycled materials allow children to work together. They can also participate in team-based challenges that require collective problem-solving and decision-making. What types of maths challenges are suitable for primary students to promote critical thinking and reasoning? Suitable challenges include pattern identification , sequencing tasks, basic arithmetic puzzles, and solving mathematical puzzles . These can be tailored to match the students’ age and proficiency level, ensuring the tasks remain engaging and appropriately challenging. Leave a Reply Cancel reply Your email address will not be published. Required fields are marked * Save my name, email, and website in this browser for the next time I comment. Related Posts Digital Portfolios as a Reflection Tool in Education: Enhancing Student Learning Paths Leveraging Digital Portfolios to Enhance Parent-Teacher Interactions Digital Portfolios for Group Projects: Enhancing Teamwork and Evaluation Techniques 1st Edition Problem Solving in Primary Mathematics Learning to Investigate! Taylor & Francis eBooks (Institutional Purchase) Opens in new tab or window Description Problem Solving in Primary Mathematics is an essential text designed to support new and experienced teachers in guiding pupils through mathematical investigations and problem solving, offering a framework that children themselves can begin to adopt as they progress to greater metacognitive awareness. Underpinned by the latest international research and theory, it examines how individual pupils think and act differently and offers guidance on how to promote independence and autonomy in the classroom. It examines key topics such as: Preparing for mathematical learning Designing learning material Assessing and evaluating learning Identifying key points for intervention What to do when learning is stalled Critical numeracy for real-world problem solving Mental Model Theory and the Mental Model Mode Different approaches to problem solving and investigating Aimed at new and experienced educators, particularly those with a maths specialism, and illustrated with investigations and activities, Problem Solving in Primary Mathematics demonstrates how frameworks can be used in key mathematical areas and assists students in progressing towards more meaningful problem solving. Table of Contents Christine Edwards-Leis is Senior Lecturer in Primary Mathematics at St Mary’s University, Twickenham, UK. Previously she was lecturer and researcher at University of South Australia, Australia. Her research interests are Mental Model Theory and how children use problem-solving strategies in mathematics and design and technology. Debbie Robinson is Head of Primary Mathematics and Senior Lecturer in Primary Mathematics at St Mary’s University, Twickenham, UK. She has extensive experience as both classroom teacher and advisory teacher in both primary and secondary schools. She provided INSET for qualified teachers for BEAM Publications and Education Authorities and her research interests are the use of practical activities, contexts and images to engage learners in mathematics. About VitalSource eBooks VitalSource is a leading provider of eBooks. Access your materials anywhere, at anytime. Customer preferences like text size, font type, page color and more. Take annotations in line as you read. Multiple eBook Copies This eBook is already in your shopping cart. If you would like to replace it with a different purchasing option please remove the current eBook option from your cart. Book Preview The country you have selected will result in the following: Product pricing will be adjusted to match the corresponding currency. The title Perception will be removed from your cart because it is not available in this region. Skip to main content Skip to secondary menu Skip to primary sidebar Skip to footer Geeky Gadgets The Latest Technology News Solving the Battery Problem 1:58 pm September 12, 2024 By Julian Horsey The transition to a zero-carbon economy is heavily dependent on the development and implementation of effective energy storage solutions. Wind and solar energy, currently the most affordable forms of primary energy, are crucial in driving this shift towards sustainability. However, the intermittent nature of these renewable sources presents a significant challenge, necessitating the deployment of reliable storage systems to ensure a steady supply of energy. This is where thermal batteries, a promising technology that could solve the battery problem, developed by Dr. Justin Briggs and his company, Antora , come into play. These innovative batteries are designed to store excess energy generated from renewable sources, making it readily available on demand. Battery Problem TL;DR Key Takeaways : Transitioning to a zero-carbon economy requires effective energy storage solutions. Wind and solar energy are crucial but need reliable storage due to their intermittent nature. Thermal batteries, developed by Antora, store excess renewable energy for on-demand use. These batteries are efficient for industrial heat storage but less so for converting heat back to electricity. Energy storage is a major challenge, with ethical and environmental concerns in mineral extraction. Autonomous underwater robots offer a responsible alternative for selective mineral harvesting. Renewable energy adoption can significantly reduce greenhouse gas emissions and enhance energy independence. There is bipartisan support and increasing investments in renewable technologies. Ethical resource extraction and minimizing environmental impact are critical in the clean energy transition. Technological innovations like thermophotovoltaics and autonomous robots are key to addressing storage and extraction challenges. Thermal Batteries and the Clean Energy Transition The clean energy transition is not only about reducing carbon emissions but also about reindustrializing regions like the American heartland. Wind and solar energy offer a sustainable alternative to fossil fuels, providing a pathway to economic growth and energy independence. However, efficiently harnessing this energy is a complex task. Thermal batteries are a key component in addressing this challenge, allowing the storage of energy during periods when production exceeds demand. This stored energy can then be used to assist industrial operations and reduce reliance on non-renewable sources, ensuring a consistent and reliable power supply. Antora’s thermal battery technology employs a simple yet effective design, using solid blocks of carbon that are heated resistively to store energy. This method has proven to be highly efficient for industrial heat storage, although the process of converting stored heat back into electricity is less efficient. Despite this limitation, the technology offers a viable solution for industries that require high-temperature processes, effectively bridging the gap between energy production and consumption. Overcoming Challenges in Energy Storage and Resource Extraction Energy storage remains one of the most significant hurdles in the renewable energy landscape. Many current storage systems struggle to provide reliable, on-demand power, hindering the widespread adoption of renewable energy sources. Additionally, the extraction of minerals required for battery production poses ethical and environmental challenges. Traditional mining practices can be destructive, leading to habitat destruction and social disruption in vulnerable communities. To address these concerns, innovative solutions like autonomous underwater robots, developed by Impossible Metals, are emerging as responsible alternatives. These robots enable selective mineral harvesting, minimizing environmental impact and ensuring ethical resource extraction. The adoption of renewable energy and advanced storage solutions has the potential to yield substantial economic and environmental benefits. By reducing greenhouse gas emissions and dependence on fossil fuels, these technologies contribute to long-term sustainability and efficient resource management. Moreover, the transition to clean energy can drive economic growth, creating new jobs and fostering energy independence. Thermal batteries store excess renewable energy, making it available on demand Clean energy transition reindustrializes regions and reduces reliance on fossil fuels Antora’s thermal batteries efficiently store industrial heat, bridging energy production and consumption Autonomous underwater robots enable responsible mineral extraction for battery production Renewable energy and advanced storage solutions drive economic growth and sustainability Here are a selection of other articles from our extensive library of content you may find of interest on the subject of batteries : Why Does My iPhone Have a Yellow Battery How to Finally Fix Battery Drain in iOS  snapVCC super-efficient regulator for your 9V battery or power How to improve Android 14 battery life iOS 18 Battery Life: Early Results and Expectations How to Fix iOS 17 Battery Drain Envisioning a Sustainable Future The vision of a reindustrialized American heartland powered by clean energy is rapidly becoming a reality. Bipartisan support for renewable energy underscores its potential to drive economic growth and achieve energy independence. Favorable market dynamics and increasing investments in renewable technologies are accelerating the adoption of clean energy solutions, fostering a sustainable and prosperous future. Ethical considerations are at the forefront of the clean energy transition. The use of abundant and ethically sourced materials, such as carbon, is essential in minimizing environmental impact and protecting vulnerable communities. Innovative technologies , like autonomous underwater robots, exemplify the commitment to responsible mineral extraction, ensuring that the pursuit of clean energy aligns with ethical standards. Continued technological advancements in energy conversion and storage are vital to the success of the clean energy transition. Thermophotovoltaics, for example, offer a promising avenue for efficient energy conversion, enhancing the overall efficiency of storage systems. As these technologies evolve and mature, they will collectively support the shift towards a sustainable, zero-carbon economy, addressing both energy storage and ethical resource extraction challenges. In conclusion, advanced energy storage solutions like thermal batteries are pivotal in addressing climate change and allowing the transition to a clean energy future. By supporting industrial growth, ensuring ethical resource extraction, and driving technological innovation, these technologies pave the way for a sustainable and prosperous zero-carbon economy. The path ahead is clear, and with continued investment, research, and commitment to ethical practices, we can achieve a brighter, cleaner future for generations to come. Media Credit: Freethink About Geeky Gadgets Advertise On Geeky Gadgets Contact Geeky Gadgets Disclosure Policy Free Newsletter Geeky Gadgets Logo Privacy Policy Further Reading Apple iPhone Camera News Concepts & Design Design News Entertainment News Geeky Stuff Mobile Phone News Tablet News 468 COMMENTS Primary Resources: Maths: Solving Problems: Word and Real Life Problems Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers. Primary Resources: Maths: Solving Problems: Investigations & Puzzles Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers. Primary Resources: Maths: Solving Problems: Money Problems Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers. Problem Solving 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. 100+ KS1 Maths Problem Solving Perfect for KS1 students, our maths problem-solving primary resources test a range of skills, from addition and subtraction to remainders and number order! We've included challenging topics like negative numbers, using inverse numbers, and remainders, to ensure these primary resources on problem-solving test your students' maths knowledge. Problem Solving Mathematical Problem Solving in the Early Years. This article describes how the NRICH Early Years resources aim to further develop young children's natural problem-solving abilities in the context of mathematics. Problem solving This collection of teaching resources aims to help children develop maths problem solving skills. 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To help you develop your mastery approach, we have hand-picked this selection of Maths resources, with everything from reasoning lessons and problem solving worksheets, to daily fluency questions and independent investigations. So, why not take ... Problem Solving Teaching Resources This collection of problem-solving teaching resources provides students with materials and strategies to guide them when learning to solve numeracy word problems. Learning to decipher word problems and recognise the correct operation to use in order to solve the problem correctly, is an important skill for students to learn. Problem Solving Resources Problem-solving is the ability to identify and solve problems by applying appropriate skills systematically. Problem-solving is a process—an ongoing activity in which we take what we know to discover what we don't know. It involves overcoming obstacles by generating hypo-theses, testing those predictions, and arriving at satisfactory solutions. Primary Resources: Maths: Solving Problems: Simple Algebra Primary Resources - free worksheets, lesson plans and teaching ideas for primary and elementary teachers. Problem-solving: number Help your year 5 children master problem-solving number skills with these differentiated activities based on the maths curriculum. Primary Teachers The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. NRICH is part of the family of activities in the ... 100+ KS1 Maths Problem Solving Perfect for KS1 students, our maths problem-solving primary resources test a range of skills, from addition and subtraction to remainders and number order! We've included challenging topics like negative numbers, using inverse numbers, and remainders, to ensure these primary resources on problem-solving test your students' maths knowledge. Free Math Worksheets Khan Academy is a nonprofit whose resources are always free to teachers and learners - no ads, no subscriptions. Printing math worksheets use up a significant amount of paper and are hard to distribute during virtual learning. Khan Academy practice requires no paper and can be distributed whether your students are in-person or online. Problem solving resources Browse problem solving resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources. Teaching Problem Solving Make students articulate their problem solving process. In a one-on-one tutoring session, ask the student to work his/her problem out loud. This slows down the thinking process, making it more accurate and allowing you to access understanding. When working with larger groups you can ask students to provide a written "two-column solution.". Building Problem-Solvers: Engaging Maths Challenges & Playful Games for Building Problem-Solvers: Incorporating challenging maths puzzles and games into primary education is a powerful strategy for developing problem-solving skills in young learners. We recognise the importance of engaging pupils with interactive tasks that not only stimulate their mathematical abilities but also build their confidence in tackling complex challenges. By designing diverse ... PDF Problem-solving activities: ideas for the classroom Problem-solving activities: ideas for the This resource was developed by teachers within the Royal Society Schools Network Problem Solving in Primary Mathematics Learning to Investigate! Description Problem Solving in Primary Mathematics is an essential text designed to support new and experienced teachers in guiding pupils through mathematical investigations and problem solving, offering a framework that children themselves can begin to adopt as they progress to greater metacognitive awareness. What is Problem Solving? Steps, Process & Techniques The Problem-Solving Process In order to effectively manage and run a successful organization, leadership must guide their employees and develop problem-solving techniques. Finding a suitable solution for issues can be accomplished by following the basic four-step problem-solving process and methodology outlined below. Solving the Battery Problem Solving the Battery Problem 1:58 pm September 12, 2024 By Julian Horsey The transition to a zero-carbon economy is heavily dependent on the development and implementation of effective energy ... assignment essay homework paper phd report resume speech thesis