nrich problem solving cards

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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

South Australia

Department for education.

Nrich - a website with maths activities and games

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Resources to develop mathematical reasoning and problem solving. Nrich aims to enrich the mathematical experiences of all learners and embeds rich mathematical tasks into everyday classroom practice.

Structure and features

Activities and games can be explored independently or together with families.

The website covers topic such as:

• measurement
• problem solving

The 'Thinking Mathematically' sections provide additional educational activities.

Links and files

Teacher notes.

The resources are grouped into levels. Level 1 aligns with early years, while level 4 aligns with lower secondary. Teachers can use the search functionality to find tasks that match the topic that they are teaching.

The tasks are not mapped to the Australian Curriculum but align well with the mathematical concepts.

Page last updated: 12 Oct 2022

learningathome [at] sa.gov.au

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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

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14 November 2023

NRICH are launching an exciting new FREE initiative for schools this autumn.

Part of the University of Cambridge, the NRICH project is launching a new programme to support the teaching of problem-solving in schools. NRICH is inviting schools to sign up to the new Problem-solving Schools charter and become a recognised NRICH Problem-solving School!

High-quality problem solving resources and dedicated teacher CPD will also be shared with schools in the new year.

Schools can  find out more and register for free:  nrich.maths.org   

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As a trainee, I have benefited massively from joining ATM. Their resources are developed by experienced members of the mathematics community, and you'll find a variety of adaptable activities/books to enrich your development as a mathematics teacher. I'd certainly recommend a classroom support pack or Thinkers to start with.  Ross Swindells

The ATM has been my spiritual and pedagogical home regarding how I understand children learn mathematics and, therefore, how I might teach mathematics. I am proud to be associated with the ATM and take every opportunity, through my work and writing to encourage others to join. Mike Ollerton

ATM membership has shaped my career and outlook not just on mathematics teaching but on learning and teaching generally. From the outset, ATM has supported me and challenged me in equal measure, and continues to do so. From the journal to the amazing annual conference I have felt part of a professional group who listens as well as articulates its views. It has made me who I am. Thank you ATM! Helen Williams

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Number and Place Value Challenge Cards - Year 6

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

6 July 2023

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FREE KS2 Maths Teaching Resource: Number and Place Value Challenge Cards - Year 6

These FREE challenge cards have been designed to consolidate pupils understanding of the curriculum objectives of the Year 6 maths programme of study - Number - number and place value.

Related Resources:

https://www.tes.com/teaching-resource/number-and-place-value-year-6-12150637 https://www.tes.com/teaching-resource/numbers-to-ten-million-year-6-12150570 https://www.tes.com/teaching-resource/comparing-and-ordering-numbers-year-6-12150707 https://www.tes.com/teaching-resource/rounding-numbers-year-6-12150713 https://www.tes.com/teaching-resource/understanding-negative-numbers-year-6-12150716

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Great for end of unit consolidation.

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Thanks for your 5-star review and kind words. Please check out my website - www.Teacher-of-Primary.com - for lots more primary teaching resources. Use promo code PRIM25 and get 25% off.

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Really brings the learning of place value together. Thank you!

Thanks so much for your 5-star review and kind words - I really do appreciate it. Please check out my website - www.Teacher-of-Primary.co.uk - for thousands more primary teaching resources. If you use the promo code PRIM25 you'll get 25% off too! Have a great day.

Well produced very handy thanks

Thanks so much for your review - I really do appreciate it. Please check out my website - www.Teacher-of-Primary.co.uk - for thousands of Maths, English and Science teaching resources for KS1 and KS2. If you use the promo code PRIM25 you'll get 25% off too! Have a great day.

VERY USEFUL

Thanks so much for your review - I really do appreciate it. Please check out my website - www.Teacher-of-Primary.co.uk - for thousands of Maths, English and Science teaching resources for KS1 and KS2.<br /> <br /> If you use the promo code PRIM25 you'll get 25% off too!<br /> <br /> Have a great day.

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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
• 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

What's the Problem with Problem Solving?

What's the Problem with Problem Solving?   Age 5 to 11

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Same Length Trains   Age 5 to 7 Challenge Level

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How Would We Count?   Age 5 to 11 Challenge Level

Build it Up   Age 7 to 11 Challenge Level

Zios and Zepts   Age 7 to 11 Challenge Level

Teddy Town   Age 5 to 11 Challenge Level

Tea Cups   Age 7 to 14 Challenge Level

• The Problem with Problem Solving at Stage 1
• The Problem with Problem Solving at Stage 2