Shape Puzzles in Y2: small numbers, deep challenge

I’m busy writing I See Problem-Solving – Y2, a resource that I’m super-excited about. It will provide sequences of related questions, tasks and open-ended challenges so children can understand and then explore different problem-solving tasks. I will explain the philosophy behind the resource in a series of future blog posts.

For now, have a look at this sequence of tasks, how it builds children’s understanding of additive reasoning and lays the foundation for algebraic thinking.

Part A: Children are introduced to the idea that a shape represents a number.

Part B and C: Children find the value of each shape. They look for lines made using the same shape. Otherwise, they workout how the sum of a line increases when one more shape is added. Notice the top right example: an extra star is added but the sum for the row does not change. This shows that the star is worth zero!

Part D and E: They apply these principles to find the value of the shapes in these grids, where the sum of each column and row is given.

Part F: Then children can make their own examples.

This blog explains how these ideas can be extended using the I See Reasoning resources in KS2. If you want to trial I See Problem-Solving – Y2 as it is being written, click here to join the I See Maths mailing list

For more information about Gareth Metcalfe’s INSET and twilight maths training click here or for CPD sessions about using the I See Reasoning eBooks. My passion and expertise is in developing children’s ability to reason mathematically and building children as mathematical problem-solvers.

Shape Puzzles in KS2: exploring additive reasoning, laying foundations for algebra

I love using shape puzzles to explore some of the principles of algebraic thinking. The examples in this blog post are from I See Reasoning – Y4 (there are shape puzzles in all the KS2 I See Reasoning eBooks) and I often use these questions with older children too. I’ve found children love completing these questions and love creating their own puzzles!

Step 1: These questions help to uncover the key strategies for working out the value of the shapes.

Left example: the second line has one more circle than the first line and its total is 5 more. Therefore one circle = 5.
Right example: a rectangle is 2 more than a diamond. The child answering this question extended the pattern to show that three diamonds have a sum of 12 and therefore one diamond = 4.

Step 2: We complete shape puzzles using the thought processes from step 1. There are prompts (which can be used or can be hidden) to suggest possible starting points.

Step 3: Children complete different puzzles, explaining their starting points.

Step 4: Time for children to design their own puzzles! I specify two things: there can’t be any rows/columns that are made using only one shape; and the designer of the puzzle must be able to explain a possible starting point.

This webpage, designed by the brilliant Jonathan Hall, enables you to automatically generate these puzzles. And this blog explains how I’ve introduced shape puzzles to children in Y2. A fantastic way to explore some of the big ideas of algebra!

For more information about Gareth Metcalfe’s INSET and twilight maths training click here or for CPD sessions about using the I See Reasoning eBooks. My passion and expertise is in developing children’s ability to reason mathematically and building children as mathematical problem-solvers.

Click here to join the I See Maths mailing list and receive the latest new resources to trial.

Mathematical Reasoning Routines

We all have a very limited attention: as you might be aware, children can’t think about many different things at once! So establishing routines that promote mathematical reasoning – routines that children become familiar with – will allow children’s attention to be focused on the key learning in the lesson. Thinking about these routines in advance can therefore be very important.

And so much better if these routines are consistent throughout the school. In Thinking Deeply About Primary Mathematics by Kieran Mackle, I loved Matt Swain’s routine for how children hold up their whiteboards. The children always hold their whiteboards to their chests; the teacher tells the children to put their boards down one table at a time. When children are familiar with routines like this, their attention isn’t wandering to ‘will Mr Swain see my answer?’ but is held on the content of the lesson.

Here are four routines that I think support learning in a primary maths classroom:

Pair work: short independent thinking slots
In pair work, I often ask children to start by working on a task individually before discussing with their partner. This promotes different methods/thought processes and lessens the risk of one partner becoming too dominant in a conversation. The length of time that I would expect children to work independently will increase as they get older, but it’s something I try to establish with all children. In most contexts, I’d have periods of silence when working independently – children find it more difficult to block out background noise than adults. I have found that these short periods of individual thinking make children value their collaboration time more.

Re-state the views of others
In group or whole class discussions, I generally try to spend longer drawing out the detailed thinking of a child or a small number of children. It’s important, though, that all children are actively thinking about what is being discussed. As a result, I routinely ask children to re-state the opinion of the person that has been speaking. This helps children to follow a conversation rather than just thinking about what they would like to say or to give their opinion. It also opens children up to different ways of thinking or different methods.

Doubt at the point of answer
I want children to focus on the process of their thinking and encourage them to reason. I don’t want children overly focused on whether answers are right or wrong. As a result, I tend to react with indifference when children give an answer. This gives children a reason to explain their thinking and it shows them that the thing I value is their thought process. Also, where a child has answered some questions and has made a few mistakes (but doesn’t hold a clear misconception) I often tell them how many questions they have got correctly/incorrect and ask them to find their mistakes. This gives the child more thinking to do than when the questions are marked and they simply correct their mistakes.

Consistency in question types
I like to have a consistent bank of question types, using common headings, throughout the maths curriculum. These common question types are woven throughout my I See Reasoning eBooks (this blog explains some of the Y3 & Y4 techniques and this blog explains about some of the Y5 & Y6 techniques). So when building understanding, children are used to being given an Explain the Mistakes task; they know that they will be asked to explain links between questions when answering Small Difference Questions and they have become used to working systematically when given a How Many Ways? challenge. By establishing these norms, we can focus more of the children’s attention to the maths content of the task, rather than having to explain how to approach each new technique. I hope the eBooks are super-useful for this!

In the upcoming weeks, I will write a series of blogs explaining about some of my reasoning techniques in more detail. I will also keep sharing new resources for people to trial for those people signed up to my mailing list.

Also, please share your favourite school or classroom routines, however big or small. How do they create a positive learning culture? How do they help to direct children’s limited attention in a productive way? I’d love to pick up and share new ideas!

Join the Discussion: How Expert Teachers will Rebuild Mathematical Understanding

It’s session 2 of the free Heartbeat of Education series this Thursday (11th March, 6pm-7pm) and it’s going to be a really significant one: how, as Primary teachers, can we ensure that children continue to thrive as mathematicians? And how should our maths lessons be different in this new season?

I believe that this is a time of great opportunity. It gives us the chance to reflect on children’s experience of mathematics and think about the skills and attributes that we truly value and want to build within our mathematicians. What can we do, as teachers, to lay the groundwork for children to have long-term success in mathematics? And how is this more than just helping children to ‘catch up’ on end-of-year targets? We will discuss what should be prioritised and how our teaching might be different in the upcoming weeks and months.

Register here to join the discussion live and to receive the recording of the session. I will be joined by award-winning Infant teacher Toby Tyler, leading teacher and teacher trainer Alison Hogben and the outstanding maths specialist Vicki Giffard. I want our discussion to explore YOUR questions. Here are some of the things that people have asked so far:
How do schools go about getting the balance right between focusing on the ‘Ready to Progress’ criteria as well as fully covering the National Curriculum?
How much weight should be given for retrieval practice if there are clear gaps in learning?
How should I differentiate now there are such gaps between children’s knowledge/experience in maths?

I’d love you to join in and please spread the word. Also, add your questions to the debate. Either post them on social media or email me at iseemaths@hotmail.com. I’m looking forward to a lively, thought-provoking and important debate!

Heartbeat of Education Webinar Series

I’m delighted to announce the launch of the Heartbeat of Education Webinar Series. In these free webinar sessions, held fortnightly on Thursdays at 6-7pm via Zoom, I will host discussions between a panel of experts on some of the most pressing issues in Primary education.

There’s a specific agenda for each session and the four panellists will hold discussions that that will be relevant for teachers, school leaders and parents alike.

I can’t wait to introduce you to the panellists: they are people I have been challenged and inspired by in my 15 years in Primary education. Whilst we are being joined by top authors and esteemed professors, panellists also include some of the UNSUNG HERO teachers, headteachers and home-school mothers that I have learnt so much from. They are wonderful people, the kind of people who you want by your side in the middle of a challenge! And they all bring very different skills and experiences.

More than anything, we want to interact with YOU. We want to understand your challenges, respond to your needs and engage in a personal, practical way. We want our exchanges to be honest and meaningful. You are very welcome to join the sessions and observe in the background. But you are invited to become an active partner as we work through these issues. That’s why I’m so excited about this format!

Click on the links below to register for the free sessions:
Heartbeat of Education: Leading Emotionally Healthy Schools and Homes in a Pandemic, Thursday 25th February, 6pm-7pm
In this webinar, a panel of leading thinkers, school leaders and parents talk about how we can best support the emotional wellbeing of the children and staff in our care. We will have a 360 degree look at the different challenges that children have faced during the pandemic and how, as educators, we can respond in 2021. With author, educational researcher and leader Emma Turner, headteacher of two schools Mandy Jones and inspirational home-school mother of six children Katy Nyman.

Heartbeat of Education: How Expert Teachers Will Rebuild Mathematical Understanding, Thursday 11th March, 6pm-7pm
In this webinar we will consider how primary teachers can best rebuild children’s mathematical understanding when schools reopen to lay the foundations for long-term success. We will discuss how lesson design, planning and teaching pedagogy may be different post-lockdown as well as a range of other issues including subject leadership, accountability systems and differentiation. I’m delighted to be joined by Y6 teacher and STEM professional development leader Alison Hogben, expert maths consultant Vicki Giffard and Infant School leader and award-winning teacher Toby Tyler.

Heartbeat of Education: Building Children as Mathematical Problem-Solvers, Thursday 25th March, 6pm-7pm
In this webinar we will explore how we can enable all children to flourish as mathematical problem-solvers. We will consider the challenges children face in learning to problem-solve and how, as teachers, we can help to deconstruct and build these crucial skills. The panellists will share their various experiences in building mathematical problem-solving skills and developing problem-solving in other contexts. We will try to offer some light on how schools can support all children to become skilful, resilient, logical thinkers! With London SW maths hub lead and teacher Kate Mole, former school advisor and Deputy Headteacher teaching in Y1/2 James Jones and teacher of 38 years, teaching Headteacher of 23 years, former maths consultant and current Camden maths leader Kate Frood OBE.

Heartbeat of Education: Adapting School Life Post-Lockdown, Thursday 22nd April, 6pm-7pm
In this webinar we discuss how school life can best meet the needs of children post-lockdown. We will consider the different challenges, both academically and personally, that children have experienced and how we can respond to meet the needs of every individual. We are joined by Professor in Child Mental Health Jess Deighton, the phenomenal Salford-based Headteacher Jane Garner and Dr Lynne Bianchi who is the Director of the Science & Engineering Education Research and Innovation Hub (SEERIH) at The University of Manchester who specialises in primary science and engineering education.

Please sign up, join in and please spread the word by telling your friends and sharing this post on any relevant pages. Thanks, Gareth

If you are unable to attend live, a recording of each session will be shared with people registered for the session only. This recording will be available for 4 days after the event. Details of how to access the recording will be shared via a Zoom email the day after the event.

I See Reasoning for Y3 and Y4: the big vision for deepening mathematical thinking!

I’m delighted to have released the eBooks I See Reasoning Y3 and I See Reasoning Y4. They are breakthrough resources for building conceptual understanding; for helping children to notice patterns and relationships; and for deepening challenges. They are comprehensive and user-friendly.

Free Sample: I See Reasoning Y3 Division and Multiplication and Division

Free Sample: I See Reasoning Y4 Division and Multiplication and Division

These eBooks are a big upgrade on I See Reasoning – LKS2. First of all, between them there are 872 questions in the two eBooks, compared to the 240 tasks in the original eBook, I See Reasoning – LKS2. In each section of the new eBooks, mathematical concepts are shown using different images and representations:

Common misconceptions are highlighted and addressed:

Then there are a range of questions for highlighting patterns, generating discussion and digging deeper. Can children see the relationships between the Small Difference Questions? And find all answers to How Many Ways tasks?

Each eBook costs £24.98 and only one copy is needed per school. I believe that this represents amazing value – hopefully it means that my resources can impact many children. In-depth online or in-person CPD on embedding reasoning within sequences of lessons can also be arranged. To receive updates on all future events and to receive free resources, join the I See Maths mailing list community. Also, here are the links for I See Reasoning Y5 and I See Reasoning Y6.

I hope the eBooks will inspire many children to enjoy deep, rich mathematical experiences and that they will give you many great classroom moments!

Why I See Reasoning – Y5 and Y6 is new and unique!

I’m delighted to have  released the eBooks I See Reasoning – Y5 and I See Reasoning – Y6. They are an exciting development from anything I’ve done before and will enrich all children’s mathematical thinking. Here’s what makes them unique:

Detailed breakdown of small steps
For children to understand the individual parts of mathematical processes, I’ve introduced lots of new questions for breaking down learning into small pieces, focusing children’s thinking on specific points. For example, Next Step questions get children to analyse specific parts within calculations and Part-Complete Examples support children as they first learn to use methods. As ever, a range of misconceptions are addressed with Explain the Mistakes examples.

Opening up patterns and developing flexible thinking
There are lots of sequences of Small Difference Questions which highlight key mathematical relationships and give children surprises. For example, when children realise that different questions give the same answer, we can explore why. There are so many other patterns to uncover! There’s also a massive range of tasks that promote flexible thinking and using different strategies:

Explores big mathematical ideas (including word questions!) and allows children to create
Each topic is explored from a wide range of different angles. We look at different contexts for rounding; algebraic ideas are explored through shape puzzles; concepts are interleaved as children calculate angles between the hands of a clock at different times. There are ‘numberless’ word questions, where children explore different question structures without numbers, tasks where children are invited to create their own questions or extend sequences and How Many Ways? tasks to open up investigations!

Comprehensive
I See Reasoning – Y5 has 362 tasks and I See Reasoning – Y6 has 396 tasks, compared to the 176 tasks of the predecessor, I See Reasoning – UKS2. The tasks cover every area of the curriculum and they incorporate the ideas from the latest DfE Mathematical Guidance. And answers are given for every question!

The eBooks cost £24.98 each and only one copy of each eBook is needed per school. I believe this represents amazing value!

Click here to order I See Reasoning – Y5 and click here to order I See Reasoning – Y6.

I hope I See Reasoning makes a huge impact on your teaching and helps all children to think mathematically. Please spread the word!

My very best wishes to everyone for the new term,
Gareth

Online Training: the present and the future

From next week, I will run my first online training sessions for teachers  – it will be great connecting with educators again! Initially there are four different training events, each with 10am and 7:30pm sessions, so everyone can join in. I’m really excited to explore the opportunities that online CPD can provide.

Sessions will be 90 minutes long, with perhaps 60-70 minutes of content and 20-30 minutes of Q&A and discussion to unpick the themes of the training. This will give us time to explore key ideas in depth whilst leaving participants with a manageable number of take-aways. Future sessions will then develop these themes further. I hope that teams of people join in so they can work alongside their colleagues to implement the ideas.

I’ve already run five parent sessions on Zoom: I’m slowly learning to navigate the technology! So far, everything that can be shown at a training event can also be shown online. And with the ongoing chat and Q&A features, people have been able to interact well and ask questions as we go.

I’m particularly looking forward to the ongoing dialogue that will be created with myself and between participants both during and after. With people joining in from diverse settings, including teachers from overseas, we will learn a lot from each other! As the online training develops, I intend to run a wider variety of sessions and to build future training around the areas that people want to explore further. Sessions can be targeted to specific year groups, topics or aspects of teaching. Online training brings cost and time efficiencies. A recording can be viewed by participants afterwards too.

This form of training is new to me. I’d love to get your ideas on how I can expand or improve my online CPD offering (email iseemaths@hotmail.com). This could be about the logistics of accessing sessions, thoughts on the content of training or anything else. At what time would you like sessions to run? What would your dream course title be? And how can we ensure that the impact continues long after the sessions? I would absolutely welcome your feedback. I will plan my training sessions for May soon.

I also regularly send out resources for teachers to trial to people on my mailing list so that I can get teachers’ feedback on my products as they are being written. At the moment I’m writing three new resources. I’m planning to run some free sessions in May where I’ll show some of these resources and ask for people to say what they like and what they would add/change. I’d love to get as many people joining in with these sessions as possible. The more viewpoints I can get the better!

I can’t wait to get started. Hopefully you’ll join me!
Gareth

Click here to book and for full details about April online training.

Home Learning Lessons: plans for the summer

It’s been a wonderful start to the home learning project, the vision for which is described in this short video. During the school closures, I want children to experience rich, emotionally engaging maths learning. I also wanted them to feel as if they are part of a vibrant, real community of children.

Each day, I post a video lesson for Y3/4 children (all Y3/4 lessons here), and a separate video lesson for Y5/6 children (all Y5/6 lessons here). Each video explores a big mathematical idea in small steps and a range of independent tasks are set for children to complete. Everything is free. In the first six weeks, the videos have had 335k views!

Here’s the outline plan for the rest of the school year. I will continue making the videos for the duration of the UK school closures (however long that lasts):
18th – 22nd May: Measures: Money and Time
1st June – 5th June: Data Handing
8th June – 19th June: Fractions
22nd June – 3rd July: Flexible Calculation
6th July – 17th July: Mathematical Puzzles

It’s been thrilling to hear how much the children have loved the lessons and how it’s helped time-pressured parents too:

I want as many teachers and parents to find out about this project as possible. Tell friends, share with colleagues! Lessons can be uploaded onto school websites; many schools retweet my evening tweets each day from their Twitter feeds. Also, if you like the videos it really helps if you give them a thumbs up on YouTube! Here’s the first Y3/4 lesson and here’s the first Y5/6 lesson – they will give a taste of what the lessons are like!

I have also compiled maths games to play with KS1 and KS2 children and I have been running a series of online training sessions for teachers.

I hope you are all keeping well,
Gareth

The Plan: Primary Maths Lessons During School Closures

Here’s the plan for the online maths lessons that I will run over the period of the Covid-19 school closures. I hope it will help many children to engage in rich, thought-provoking maths learning during this time. I hope they will be uplifting too!

Every weekday at 9am, two new lesson will be posted on this page via YouTube: one aimed at children in Y3&4 and another for Y5&6. Each video will help children to build the skills needed for the main task. Then children will complete the main task – a challenge or short series of questions – working individually or with adult support. These tasks can also be downloaded from this page by clicking the relevant links. Answers will be provided! The first videos/tasks will be uploaded on Monday 23rd March.

Underneath each video is a short description of the key calculation skills for each lesson. Children may benefit from practising these skills before watching!

A series of games that can be played with children aged 5-8 will also be shared. The first of these videos will be published here on Tuesday 24th March and I plan to release two of these videos per week. I’ve got some great, easy-to-use games to show.

An introductory video has been put together to explain the project – please share this with children and parents. The videos will run until 3rd April (my health permitting), then there will be a two-week break over Easter. I will share a range of games that can be played during that period. Then, all being well, the daily videos will recommence for the duration of the school closures.

I am hoping to be able to run these lessons as ‘live lessons’ soon. I’ve not quite got the technology or expertise for that yet! But watch this space, I’m working on it – I’d love to introduce this and make the lessons more interactive and real.

How you can help
I also want to make the lessons engaging and personal. I’d love to end each video with a message, a joke or a thought from a range of teachers, parents or people from the community. Let’s make the videos feel like ours – help the children feel loved by the wonderful teaching community. Please email, tweet or FB message me with your personal message! And keep sending ideas for maths challenges to include. Spread the word far and wide…

Best wishes
Gareth

I’m looking into ways that I could deliver free, 45-minute tutorials for parents to show how they could use some of my maths resources at home. If you might be interested, email iseemaths@hotmail.com

I am also exploring possible ways to deliver maths training sessions online to Primary teachers during school closures. Email iseemaths@hotmail.com for more information.