nrich problem solving year 5

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Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
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• Coordinates, Functions and Graphs

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• Angles, Polygons, and Geometrical Proof
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About NRICH

NRICH is an innovative collaboration between the Faculties of Mathematics and Education at the University of Cambridge which focuses on problem solving and on creating opportunities for students to learn mathematics through exploration and discussion. NRICH provides thousands of free online mathematics resources for ages 3 to 18, covering all stages of early years, primary and secondary school education - completely free and available to all. We aim to:

• Enrich and enhance the experience of the mathematics curriculum for all learners
• Develop mathematical thinking and problem-solving skills
• Offer challenging, inspiring and engaging activities
• Show rich mathematics in meaningful contexts
• Work in partnership with teachers, schools and other educational settings to share expertise

Developing confident, resilient problem-solvers

Supporting teachers, putting research into practice.

The Joint Mathematical Council of the United Kingdom

Addressing the five ‘big questions’ in problem-solving with NRICH

The importance of ensuring learners acquire the problem-solving skills which will enable them to thrive both socially and economically in their increasingly automated world is widely recognised (Luckin et al., 2017). Nevertheless, government inspectors have reported serious concerns about the quality and quantity of problem-solving in our schools (Ofsted, 2015). This summer schools were challenged to reflect on ‘Five big questions for problem-solving’ (EEF, 2021). In this blog, we will consider each of those five questions and explore the ways that the NRICH team is supporting schools to address them.

Question one: Do teachers in your school select genuine problem-solving tasks for which pupils do not already have a ready-made method available?

Too often, learners are presented with routine word problems which merely require the application of a known algorithm. ‘Genuine’ problems enable them to make their own problem-solving decisions by choosing their own strategies and enabling them to compare their approach with those of other learners, thus developing their problem-solving efficiency and flexibility. At NRICH , our award-winning activities allow learners to develop these key skills alongside the confidence to tackle genuine problems. Moreover, our ‘ low threshold, high ceiling ‘ approach enables everyone to get started on the problem while ensuring a suitable level of challenge too, making them ideal for whole-class teaching.

Question two: Are pupils given the opportunity to see – through multiple worked examples – to use, and to compare different approaches to solving a problem?

Many problems can be explored in more than one way. Working flexibly, making connections between different areas of the curriculum and reflecting on various problem-solving approaches are key steps towards becoming a more fluent mathematician. NRICH encourages learners to develop these skills in these two ways:

Our primary , secondary and post-16 Live Problems invite learners to explore and submit their ideas to the team. We review each submission that we receive and publish a selection on our website showcasing different approaches and the reasoning behind them.

Our NRIC H online activities sometimes feature ‘hide and reveal’ buttons showcasing different starting points towards a solution for learners to explore further for themselves. This approach enables learners to widen their range of strategies for solving unfamiliar problems and develop alternative approaches to explore when they get stuck using their first-choice strategy.

Question three: Are pupils encouraged to use visual representations to support them to solve a problem?

One of the most important approaches towards solving an unfamiliar problem is drawing a good diagram. Learning to draw diagrams is a skill which we encourage learners of all ages to develop alongside their other mathematical skills and knowledge. From sketching graphs to drawing a bar model, good diagrams can help learners clarify their understanding and identify possible ways forward.

Our four steps towards problem-solving feature highlights the importance of drawing a diagram to enable young learners to get started on a problem. We often highlight a useful diagram, table or sketch graph in the solutions chosen for publication. As learners progress through their learning, the team model more specific drawing skills, such as sketching a graph to help solve a STEP problem.

Question four: Are pupils supported to monitor, reflect on, and communicate their reasoning and choice of strategies, possibly through the use of prompt questions?

NRICH  encourages learners to reflect on their learning using this approach inspired by the Strands of Mathematical Proficiency model introduced by Kilpatrick et al. (2001).

Our approach uses child-friendly language that teachers and parents can share with students five key ingredients that characterise successful mathematicians. At NRICH , we believe that learning mathematics is about much more than just learning topics and routines. Successful mathematicians understand the curriculum content and are fluent in mathematical skills and procedures, but they can also solve problems, explain their thinking and have a positive attitude about themselves as learners of mathematics.

With this in mind, we have created  this self assessment tool  to help learners recognise where their mathematical strengths and weaknesses lie. We hope learners will explore NRICH activities and then take time to reflect on their own mathematical capabilities using our model.

Question 5: Is professional development time allocated to develop teachers’ pedagogical understanding of problem-solving, with particular support for early career teachers?

NRICH supports teachers to maximise the potential of our activities by offering free, regular professional development for teachers .  Each session is delivered online, enabling teachers to access the support wherever they are based, reducing teacher travel and cover costs for schools. We also record the sessions and upload them to our website so that schools can access them for future professional development days or staff/department meetings in their settings.

The live sessions are led by NRICH team members and they link directly to our latest primary , secondary and post-16 Live Problems. This approach enables teachers to consider the possibilities of the activities with the NRICH team before exploring them the next day with their own classes. Later, they are invited to share their classwork with our team for possible publication on the NRICH website.

The five ‘big questions’ provide excellent starting points for evaluating the teaching and learning of problem-solving in different settings. I hope that this blog shares an insight into the different ways that NRICH can support schools to address the five questions for themselves by engaging with our activities, Live Problems and teacher webinars.

Dr Ems Lord FCCT

Director of NRICH

Centre for Mathematical Sciences

University of Cambridge

Selected references

EEF. (2021). EEF Blog: Integrating evidence into maths teaching – guiding problem-solving. Accessed from https://educationendowmentfoundation.org.uk/news/eef-blog-integrating-evidence-into-mathematics-guiding-problem-solving /

Kilpatrick, J. Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics (Vol. 2101). J. Kilpatrick, & National research council (Eds.). Washington, DC: National Academy Press.

Luckin, R., Baines, E., Cukurova, M., Holmes, W., & Mann, M. (2017). Solved! Making the case for collaborative problem-solving. Accessed from http://oro.open.ac.uk/50105/1/solved-making-case-collaborative-problem-solving.pdf

Ofsted. (2015). Better Maths Conference Spring Keynote 2015. Accessed here https://www.slideshare.net/Ofstednews/better-mathematics-keynote-spring-2015

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• Nrich Problem Solving Schools Programme

Sign up to NRICH’s Problem-solving Schools programme

NRICH, a trusted provider of free problem-solving resources and teacher support, is launching the Problem-solving Schools programme.

Register for free to enhance problem-solving provision across your school and sign up to the Problem-solving Schools Charter.

Why is problem-solving so important?

With the rise of AI, problem-solving skills are more important than ever for students.

To thrive both inside and outside of the classroom, they need to develop resilience, be able to work collaboratively, and think creatively and flexibly. And, perhaps most importantly, they will need to be able to solve problems.

Problem solving opens up a world of possibilities. Students have to apply their knowledge, think laterally, and use their creativity to solve challenges.

Not only does problem solving serve a longer-term purpose of empowering students for the future, it is also a crucial part of helping them to discover the joy of mathematics.

Imagine only engaging with football through practice drills and never seeing Messi score, or learning music through scales and never hearing an orchestra play…

Problem solving is the light bulb moment for students when it comes to maths. They start to see the value in what they are doing.

Once they really understand its value, that’s when they become engaged and motivated to learn!

Highlighted by Ofsted

A new Ofsted report, published in July 2023, said that the teaching of mathematical problem solving remains an area “of weakness across many schools”, and emphasised the importance of teaching skills that “equip [pupils] for the next stage of education, work and life”.

As well as asking schools to teach specific problem-solving strategies, they want students to have plenty of opportunities to put these strategies into practice and choose the best one for each situation.

What is NRICH doing to support schools?

NRICH’s core mission is to develop confident, resilient problem-solvers who value and enjoy working mathematically. With that mission in mind, we are launching the Problem-solving Schools programme.

The aim of this new initiative is to help embed problem-solving in classrooms by providing:

• Targeted problem-solving resources
• Dedicated teacher CPD on how best to use them
• Advice on engaging parents so they can support their children at home
• A dedicated schools Charter to sign up for, demonstrating your school’s commitment to put problem solving at the heart of maths learning.

The programme is open to all schools with resources and CPD available for key stages 2–4.

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Year 5 Column Subtraction Worksheets (differentiated) and Other Resources

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

30 May 2022

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Resources on Column Subtraction for Year 5:

• Year 5 column subtraction worksheets (differentiated to 4 levels and with the answers)
• a link to an nrich problem-solving activity involving missing numbers in a column addition calculation (this is different to the higher level worksheet questions)
• a PowerPoint presentation
• a page with the steps for column subtraction
• success criteria

There is a PDF version and an editable version of each file.

Click here to see how people have rated other resources that we have on TES.

Other Year 5 Maths resources: https://www.tes.com/teaching-resource/-12160846 - Numbers in Words https://www.tes.com/teaching-resource/-12160851 - Place Value (Whole Numbers) https://www.tes.com/teaching-resource/-12160854 - Ordering Whole Numbers https://www.tes.com/teaching-resource/-12160859 - Rounding Whole Numbers https://www.tes.com/teaching-resource/-12160861 – Place Value (Decimals) https://www.tes.com/teaching-resource/-12161134 – Complements to 1 https://www.tes.com/teaching-resource/-12163410 – Comparing Decimals and Fractions https://www.tes.com/teaching-resource/-12163418 – Decimal Sequences https://www.tes.com/teaching-resource/-12163429 – Rounding Decimals https://www.tes.com/teaching-resource/-12163439 – Comparing and Ordering Decimals https://www.tes.com/teaching-resource/-12163443 – Multiply and Divide by 10, 100 & 1,000 https://www.tes.com/teaching-resource/-12163455 – Column Addition https://www.tes.com/teaching-resource/-12163587 – Column Subtraction https://www.tes.com/teaching-resource/-12163589 – Column Addition and Subtraction https://www.tes.com/teaching-resource/-12163592 – Add and Subtract By Partitioning https://www.tes.com/teaching-resource/-12163597 – Negative Numbers https://www.tes.com/teaching-resource/-12163601 – Addition and Subtraction Word Problems https://www.tes.com/teaching-resource/-12163606 – Short Multiplication https://www.tes.com/teaching-resource/-12163614 – Square and Cubed Numbers https://www.tes.com/teaching-resource/-12163616 – Short Division

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Not quite what you were looking for? Search by keyword to find the right resource:

Or search by topic

Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Developing positive attitudes
• Cross-curricular contexts
• Physical and digital manipulatives

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

For younger learners

• Early Years Foundation Stage

The Problem-Solving Schools' Charter

The NRICH team has developed this Charter to help you reflect on how you currently promote mathematical problem-solving in your school

Values and ethos

We have a shared belief that:

• Mathematical ability is not fixed: everyone can learn and make progress
• Problem-solving often involves taking wrong turns and making mistakes: every learner has the right to struggle and the right to enjoy success
• Everyone should have the opportunity to develop the skills and attitudes necessary to become confident problem-solvers
• Problem-solving can motivate learners to learn new mathematics, apply previous learning and make mathematical connections

Leadership and professional development

In our setting:

• Our staff promote positive attitudes towards problem-solving
• Time is set aside to discuss problem-solving in our meetings
• Our displays, newsletters, website, and social media content celebrate problem-solving for all
• Our monitoring system ensures that priority is given to problem-solving and mathematical thinking
• We engage with printed, online and face-to-face professional development opportunities offered by subject organisations

Curriculum, pedagogy and assessment

We are committed to:

• Regularly embedding non-standard problem-solving opportunities in our maths curriculum for all
• Ensuring that problems, and classroom support, offer opportunities for all to experience both struggle and success
• Allocating time to developing key problem-solving skills and positive attitudes
• Including non-standard problems in our internal/formative assessments
• Liaising with other subjects so that meaningful cross-curricular links can be made

Classroom culture

• Create a safe environment in which learners explore, take risks, and appreciate the value of learning from their mistakes
• Celebrate multiple approaches to solving problems and discuss the merits of the different strategies offered
• Provide frequent opportunities for individual and collaborative problem-solving, where learners are given both thinking time, and opportunities to share ideas and insights
• Celebrate the mathematical thinking of every learner

Problem-solving beyond the classroom/school

We encourage:

• Learners to engage with school Maths Club(s) and high quality maths books, ideally stocked by the school library
• Learners to take advantage of printed, online and off-site mathematical enrichment opportunities
• Parents and carers to engage with problem-solving through family homeworks and in-school events, while recognising that not every adult has had a positive experience of maths
• Our learners to appreciate, and learn more about, the achievements of a diverse range of mathematicians

Become a Problem-Solving School

Or search by topic

Number and algebra

• The Number System and Place Value
• Calculations and Numerical Methods
• Fractions, Decimals, Percentages, Ratio and Proportion
• Properties of Numbers
• Patterns, Sequences and Structure
• Algebraic expressions, equations and formulae
• Coordinates, Functions and Graphs

Geometry and measure

• Angles, Polygons, and Geometrical Proof
• 3D Geometry, Shape and Space
• Measuring and calculating with units
• Transformations and constructions
• Pythagoras and Trigonometry
• Vectors and Matrices

Probability and statistics

• Handling, Processing and Representing Data
• Probability

Working mathematically

• Thinking mathematically
• Mathematical mindsets
• Cross-curricular contexts
• Physical and digital manipulatives

For younger learners

• Early Years Foundation Stage

Advanced mathematics

• Decision Mathematics and Combinatorics
• Advanced Probability and Statistics

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