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Problem-solving Maths Investigations for Year 1

Nick Barwick

Hamilton provide an extensive suite of problem-solving maths investigations for Year 1 to facilitate mathematical confidence, investigative inquiry and the development of maths meta skills in 'low floor – high ceiling' activities for all.

Explore all our in-depth problem solving investigations for Year 1 .

Use problem-solving investigations within every unit to encourage children to develop and exercise their ability to reason mathematically and think creatively.

Investigations provide challenges that offer opportunities for the development of the key mathematical skills while deepening conceptual understanding. They are designed to be accessible in different ways to all children. An added bonus is the substantial amount of extra calculation practice they often incorporate! The problems are designed to help children identify patterns, to explore lines of thinking and to reason and communicate about properties of numbers, shapes and measures.

Hamilton provide a mix of our own specially commissioned investigations, that include guidance for teachers together with a child-friendly sheet to guide your pupils through the investigation, as well as links to investigations on other highly regarded websites.

I am very grateful for Hamilton Trust resources, particularly the maths investigations. Julia, teacher in Wiltshire

You can find Hamilton's investigations for Year 1:

Do read our extensive range of advice for more information about the investigations and for tips on how to use them effectively.

Hamilton’s problem-solving investigations are 'low floor, high ceiling' activities that give all children opportunities to develop mastery and mathematical meta-skills. Explore a set for a whole year group.

Hamilton’s Problem-solving Investigations provide school-wide solutions to the challenges of building investigative skills from Early Years to Year 6.

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Fun Maths Activities and Investigations for KS1 and KS2 in Primary School

Anantha Anilkumar

Anantha Anilkumar

Over the years, we’ve created lots of different fun maths activities and investigations to add to the primary teachers creative toolbox. Some of these maths activities our tutors use in our online maths interventions, others we share here as part of our continual support for KS1 and KS2 teachers working in UK classrooms. 

The purpose of these maths activities, especially the event-based ones is three-fold:

1. To support you the teacher with problem solving and reasoning questions (with answers of course where relevant) and save you writing your own. 

2. To give children the opportunity to see more everyday maths in context, and experiences of how maths reasoning really matters in the real world. 

3. To add some variety and relevance to the maths lesson slides, questions and worksheets, you may be doing with your class every day. We love what the White Rose maths hub resources provide in terms of weekly planning, but sometimes we may be looking for some more exciting and fun maths activities, whether for year 1 or year 6. 

Topical Maths Activities For The Term

Topical Maths Activities For The Term

Maths investigations linked to key calendar dates this term, designed to develop reasoning and problem solving in your pupils

Some of you may question the  place that fun has in a child’s education , and whether fun maths lessons will achieve the long term goal of retention and retrieval. While we’ve all had a class who require an upbeat tempo of fun games as part of their learning process, some children will find this a distraction if important new teaching is introduced through a game. You will know your pupils best in this context. 

The majority of maths activities and investigations shared below use a fun concept or relevant idea to develop children’s fluency, reasoning and problem solving skills in the pursuit of learning maths.

Follow the links to find out more about the kind of maths activities and maths investigations we’ve got available to you. 

Fun maths activities KS2 (with some KS1 in there too)

Fun outdoor maths activities  13 flexible and fun activities to do outside, many of which can be adapted for early years to Year 6; most of these involved some kind of physical activity as well as treasure hunts for angles, ways to incorporate data handling and measurement into the school fair, and using maths skills to make mathematical connections to nature. 

Fun back to school maths activities  teaching ideas to help you get back in the groove of maths lessons after a long summer break. These are maths activities the whole class can get involved in, some practising quick mental maths skills, others involving more complex reasoning, plus the odd card game maths activity as well.  

Fun end of term maths activities : We all know that by the end of the summer term the atmosphere in class tends to get a bit overexcitable. Here are some ideas to harness that excitement into some fun and lively maths investigations that recap children’s knowledge from across their year’s work from 2d shapes to averages and algebra.

Fun maths games for kids at home : This might almost be our favourite collection – one to hand out to parents; it includes home made board games, fun ways to practise times tables and lost of fun games that help children with their maths skills and require only a pencil, a piece of paper and a pack of playing cards to get going. Essential for anyone undertaking any kind of home learning with their children. 

We’ve also now extended our maths games collections to include KS1 maths games , KS2 maths games , and even KS3 maths games .

Fun maths lessons for KS2 : a collection of our favourite fun maths lessons, suitable for Year 3 to Year 6 (ideal for after SATs) which include human bar charts, sharing 3D shapes, and planning the teacher’s next holiday! 

Fun maths starters KS2 : 15 of the best maths starters to help you introduce a new topic, consolidate previous work, or just to use as part of a maths meeting with your class, improving their mental maths – includes a printable version to use in school. 

Fun SATs revision games : Even 11-year-olds need a break sometimes, so we asked some fantastic teachers on Twitter what their favourite top tips for keeping SATs revision fun were, and here’s your answer – loads of great ideas in here for anyone  teaching Year 6 . 

Fun maths club activities : Provided you’re armed with some creative, open ended, and ideally practical maths club activities to give children, maths clubs are not nearly as hard to set up and run as you might first imagine. The benefits are manifold; this article has all you need to get started including several really fun group games specially designed for primary school maths clubs.

Fun maths investigations for topical events

KS2 maths problems solving investigations: For many years now Third Space has been creating maths investigations for Year 6 only originally that we’ve now adapted to be suitable across KS2. In the main these tend to be open ended maths investigations, focused around key events in the primary school calendar; some of these are also slightly shorter activities but they all require pupils to do extensive problem solving and reasoning based around events in everyday life. Here are some favourite KS2 maths problems solving investigations from each term

Autumn Term maths investigations year 6:  Bonfire Night maths activities  and Christmas Maths activities

Spring Term maths investigations year 6:   Pancake Day Maths activities ,  World Book Day Maths activities  and Easter Maths Activities

Summer term maths investigations year 6: Football Maths activities and World Cup Maths activities

Mixed ability maths investigations

We know most of you now teach  mixed ability maths  classes so something we’re often asked for is year 6 maths activities with a low threshold and a high ceiling. Take a look at these  open ended maths investigations for Year 6  and the rest of Key Stage 2. You’ll also be able to download one of our favourite free teaching resources – 8 low threshold high ceiling activities including the famous fox chicken grain puzzle. 

We’ve also collected the  best KS2 maths challenges  here for any of your pupils who are working at  greater depth in KS2 maths  and need further extension in your maths lessons. 

Holiday maths

We all know about the summer brain drain and how easily children forget what we’ve taught them but it can be difficult to know what to do about it. These  summer holiday maths activities  were created with parents in mind, you can also use these KS1 and KS2 holiday maths packs to give your pupils lots of fun maths challenges to do over the holidays. 

National Curriculum maths activities for KS1 and KS2

The final way we’ve organised our KS2 maths activities for you is by national curriculum topic. We’ll continue to add to this section so bookmark this page and check back if it’s useful. Get started:

Do you have pupils who need extra support in maths? Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons and maths interventions designed to plug gaps and boost progress. Since 2013 we’ve helped over 130,000 primary and secondary school pupils become more confident, able mathematicians. Learn more or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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FREE KS2 maths SATs practice papers

Get ready for SATs with this set of 6 maths SATs practice papers designed to help your Year 6 pupils improve test skills and build confidence.

Includes: - 2 arithmetic and 4 reasoning papers that follow the National Curriculum Assessments. - Mark schemes to diagnose and assess where your pupils need extra support.

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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.

ks1 maths problem solving investigations

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.

ks1 maths problem solving investigations

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.

ks1 maths problem solving investigations

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.

ks1 maths problem solving investigations

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.

ks1 maths problem solving investigations

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

ks1 maths problem solving investigations

Problem Solving 2

Reasoning about numbers, with challenges and simplifications.

Quality Assured Category: Mathematics Publisher: Department for Education

KS1 problem solving investigations Maths

KS1 problem solving investigations Maths

Pencil Playground's Shop

We provide a wide range of high quality primary resources to enhance learning opportunities and save teacher's time! They have been trialled in school before publishing to test how effective they are. We are delighted with the results and hope you will be too!

Last updated

24 July 2022

Resources included (3)

KS1 Building problem solving investigation

KS1 Building problem solving investigation

Easter Eggs Problem Solving Investigation

Easter Eggs Problem Solving Investigation

KS1 Maths investigation Truffula Trees

KS1 Maths investigation Truffula Trees

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