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 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!

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,

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

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

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

LIVE Maths During UK Covid-19 School Closures

In the event of UK school closures, I’m planning to run daily live maths lessons via YouTube aimed at all KS2 children and provide guidance for maths games to play with younger children. In this blog I’ve explained what I’ve planned so far but I’m after your help and ideas! All the content will be free.

Live Lessons
If schools do close, I want to keep alive the sense of community that comes from engaging in learning maths together – of having a shared experience. I also wanted to help families keep a sense of routine by sharing lessons at the same time every day. Whilst I plan to record lessons and upload them onto my YouTube channel (which I created this afternoon), I hope as many people as possible watch the lessons live to enjoy that shared experience. I also want to really engage children in rich, thought-provoking challenges and be an uplifting presence!

Soon, I’m going to create a short YouTube video to introduce myself to children/parents and explain all about the videos. At a guess, each live lesson will be 20 minutes long. They will build understanding of the mathematics in small steps, they will be interactive and they will all introduce a rich task for the children to complete independently. Further guidance (and answers) will be shared on my website for children to self-assess their work. Provisionally, the lesson aimed at Y3-4 may air at 9:15am and the Y5-6 lesson at 10:00am. This is all subject to change and to your suggestions!

I thought teachers might suggest ways for children to collaborate with each other during the tasks. It would be great to get some live comments/examples of work coming through from teachers during the lessons too, to poke fun at some of us teachers! Also, if you know any famous people we could rope in…

If I stay healthy and people keep watching, my pledge is to keep this going every school day (not including the Easter hols) for the duration of UK school closures.

Tell me how to improve my plan. What I can do to help share this content with children/parents? To engage children? And PLEASE, share with me your favourite maths tasks for me to use in the lessons!

I’m also going to make a short series of videos showing a range of games that parents can play at home with younger children, including personal favourites like my Connect 4 games. Again, please send through ideas of games and activities that I could include in these videos.

When I have finalised tech side of streaming/recording the lessons, and listened to your ideas, I will either update this blog or launch a page on my website that will host everything. I look forward to hearing as many ideas as possible from you all. And please tell people in your school and share with your friends. I hope, in some small ways, it helps at this time.

My very best wishes to you all. Keep well,


A favourite multiplication investigation

Here’s a multiplication investigation that I used with a mixed-age Y5/6 class. Before the task we recapped on the grid method (it will become apparent why the grid method was used). Then, the main task was introduced:

Immediately, the children positioned 8 in one of the tens columns and 0 in one of the ones columns. Some children tried 85 x 40, but then we established that the larger digits (8 and 5) need to be placed in the tens columns and the smaller digits (4 and 0) in the ones columns. But where, then, should the digits 4 and 0 be positioned? Which gives the larger product: 84 x 50 or 80 x 54? Will these two calculations give the same answer? This was explored:

We compared these two calculations and asked ‘What’s the same? What’s different?’ The grid method helps to show that multiplying the tens values gives 4000 in both calculations. However, the TO x O parts of the calculation are different. We saw that 80 x 54 gives the largest product. One child even said ‘The short method for multiplying is quicker, but the grid method is better for showing what’s the same and what’s different.’ I show the children an area model to help them to understand the difference between 84 x 50 and 80 x 54:

In the image above, we see the TO x TO part of the calculation. We ask the children to visualise how each image will be changed when the TO x O part of the calculation is also shown (see below):

Of the two calculations, 80 x 54 gives the larger product because we are multiplying a larger tens value by the 4. I also commented that the pair of numbers that are relatively closer together gave the larger product. Then we look at the examples below, comparing pairs of numbers with the same sum that are multiplied:

We see that the pairs of numbers which are closer together have the greater product.

I have run a very similar investigation using a TOxO calculation. Here’s an opening prompt:

And it led into the I See Problem-Solving investigation below. It’s one of the free sample tasks that can be found here:

If you have a go at these investigations or something similar, I’d love to hear about how you get on!

I See Problem-Solving – UKS2 and I See Problem-Solving – LKS2 give a huge bank of rich tasks. There are Worked Examples and Support, Explain and Extend features that help to deepen children’s understanding.

Information can be found here about INSET/Twilight training on developing reasoning and problem-solving. Bookings are currently being taken from late February onwards. For very cost-effective training, you may consider hosting a training event, or running example lessons in your school. 

I See Problem-Solving – LKS2: Support and Challenge

I’m delighted to have released I See Problem-Solving – LKS2. It’s a resource that I’ve lived and breathed in the classroom over the last 10 months! The aim is to help all children to access rich problem-solving tasks, whilst ensuring that all children are challenged and engaged. It is the practical outworking of the research on solving problems from this EEF report (see point 3). 

I See Problem-Solving – LKS2 is comprised of 54 tasks. Each task gives various challenges: the Build prompt introduces the key themes and concepts, before the main Task is presented. Then, there is a Support prompt to help children access the task. The Explain and Extend challenges give rich opportunities for extended exploration.  Here’s an example task, starting from the Build prompt:

This introduces some of the key language that the children will need to understand before they access the main task. Here is the Task:

Children might choose 1, 2 and 3; they could work with 21, 22 and 23. Either way, we can all explore this idea and visual representations can be used to help. If children are need help, they can look at the Support prompt:

The Worked Example shows the solution to the main task step-by-step. The Worked Example can be viewed as a PowerPoint or as a PDF:

To deepen the challenge, the Explain and Extend prompts provide related challenges:

Not all the tasks follow this exact format. Sometimes there are Practise questions:

And there are always questions that extend the challenge:

Information about the resource, plus a link to the Etsy page to buy the resource, is found on the I See Problem-Solving – LKS2 page. There are 5 free example tasks to use too. It costs £24.98 and is available as a digital download of the PDF file. I hope you find this resource super-helpful for engaging children in meaningful problem-solving. It’s certainly given me many great classroom moments already!


Place Value: Seeing the Relative Size of Numbers

In place value, children learn about the value of each digit in a number (e.g. that the 5 in 153 represents 5 tens) – the Deepening Understanding in Column Value blog gives some ideas for extending thinking in these lessons. However, to give children a more complete understanding it’s important that they can also reason about the relative size of numbers. In this blog I will explore how I’ve used a blank number line to develop this form of understanding and look at the wealth of opportunities for reasoning that it can provide.

Consider this task. Children are given a long number line with 0 and 100 at either end and are asked to position 31, 39 and 84 accurately on the number line. Children are challenged to think about whether the lengths between the numbers are appropriately sized.

I have found that children are generally able to order numbers, but that the common mistake is to make the spaces between numbers too similar. In this example, I may ask children to compare the distance between 31 & 39 with the distance between 0 & 31 (which is almost four times longer) and the distance between 84 & 100 (which is exactly twice as long).

In a similar task, children have positioned 4, 7 and 9 on a 0-10 number line. It’s common for children to position 4 by counting four small ‘steps’ on from zero (placing 4 far too close to zero) rather than thinking about the position of 4 relative to the half-way point of the line. Similarly, 7 and 9 are often positioned by counting back from 10, leaving an overly large gap between 4 and 7. With careful modelling, and by looking at the number lines in the classroom, children learn to reason spatially with greater precision.

I’ve included two such tasks in I See Problem-Solving – LKS2 (click on the link for sample tasks), which is due to be released on 29th September. Here’s one of the pages from the Worked Example:

And here is the extension prompt for the task. There’s so much additive and multiplicative reasoning that go into estimating the value of the missing numbers:

I would love to hear about any practical examples of how you are outworked these ideas in the classroom. The blog Deepening Understanding of Column Value gives some more ideas for how to deepen the challenge in place value. Have a great term!

For information about NCETM-accredited training by Gareth Metcalfe, please visit – bookings are being taken from Spring term 2020 onwards.

Deepening Understanding of Column Value

When learning about place value, an emphasis is placed on the column value of each digit. For example, the value of the digit 7 in 273 is 70. In this blog I will look at two ways to extend this understanding of place value. In the blog Seeing the Relative Size of Numbers I explain another important building block in children’s knowledge of number.

A child is asked to show 32 using dienes blocks. They get three tens and two ones. I ask the child to show me 32 in another way. Do they recognise that they can use 32 ones? Given two tens, I ask ‘How many more ones make 32? We see that 32 is also two tens and twelve ones.

This basic idea is the foundation for many place value investigations. For example, the I See Reasoning – Y5 question ‘How many ways can 0.42 be made using 0.1 and 0.01 coins?’ One of the I See Problem-Solving – LKS2 tasks also explores this idea: it’s one of the free sample tasks which can be downloaded from this page. The ‘build’ task introduces the idea of making 230 in different ways:

The main task presents this challenge:

There are ‘support’ and ‘explain’ tasks. Here’s the ‘extend’ prompt:

Of course, 423 can be made with four 100s, two 10s and three 1s. It can be made with 423 ones. There are so many combinations beyond that to be explored.

Another of my favourite types of investigations are ‘sum of the digits’ tasks – this blog gives an example from I See Problem-Solving – UKS2. Here’s how you can introduce a sum of the digits question. To start off with, present this question from I See Reasoning – Y6, but with part of the instruction covered up:

The correct answer is 102 and 98. Then the sum of the digits element of the question can be uncovered:

Children have to find ways to increase the digit sum for the 3-digit number without increasing its size too much (e.g. increasing the ones value), and how the sum of the digits for the 2-digit number can be reduced without making the number significantly smaller. Should the 9 be used in the ones column for the 3-digit number or the tens column for the 2-digit number? It’s one of my favourite tasks!

The blog Deepening Understanding of Column Value gives more ideas for how to develop children’s understanding of large quantities. I would love to hear from you if you use any of these ideas or questions in your classroom. I hope you enjoy getting to know your new class!

For information about NCETM-accredited training by Gareth Metcalfe, please visit – bookings are being taken from Spring term 2021 onwards. Online training is available this term.

Guest Post: Supporting maths at home can help tackle maths anxiety

This is a guest post by Jill Cornish, Editorial Director, Primary Maths, Oxford University Press

Maths anxiety is a huge issue across the UK from early childhood into adulthood. National Numeracy have found that across the UK four in five adults have a low level of numeracy and individuals earn less when they are less numerate .

Everyone involved in influencing education has a role to play in tackling maths anxiety, from teachers and families at home to media and government. Maths anxiety can be contagious. Parents and carers who aren’t confident with maths themselves often inadvertently pass on these feelings to their own children, creating a cycle of negativity around maths.

As part of Oxford University Press’s Positive About Numbers campaign, we recently ran a series of teacher-led hackathons with primary schools across the country. These were designed to give teachers a safe space to share their experiences of maths anxiety in the classroom and start to pool ideas about practical ways to reduce it.

Amongst other issues, bringing together this wealth of professional insight highlighted the importance of taking a holistic approach to tackling maths anxiety across the classroom and at home. While many teachers are aware of the challenges and potential impact of maths anxiety, parents and carers may not have the background or resources to help their children overcome this barrier to learning. This is why collaboration between school and home is so crucial.

It’s important not to add more pressure or overwhelm families who may already feel nervous about maths. The hackathons identified many light-touch ways teachers can support families to be confident about helping children develop a positive maths attitude. It could be as simple as signposting trusted resources for learning at home, or encouraging families to introduce gameified elements of maths, for example through puzzles and quizzes. Small changes at home can make a big difference to young learners’ attitude to maths over time.

Teachers who took part in the hackathons also highlighted the importance for children of making meaningful links between maths and everyday life. Cooking with the family at home or keeping score in games can engage young children with maths in a way that really brings it to life.

One of the main challenges for teachers is that maths anxiety is not always easy to spot. It can be displayed in many different ways depending on the child and these presentations are not always obviously linked with maths anxiety. Some children may openly copy or make up answers, some may be unusually quiet, other may act up and be disruptive in the classroom. This challenge is even greater for parents and carers who don’t see their children in a structured learning setting. This makes open communication between school and home even more important.

To support teachers and families we’ve pulled together helpful tips and advice from the Positive About Numbers hackathons and combined them into a toolkit with easy-to-use learning resources for the classroom and home. The toolkit has lots of practical ways for teachers to start to address maths anxiety in their lessons, alongside ideas to engage parents and carers with their children’s maths development at home too.

Working together, we really can inspire children to be positive about numbers from an early age.

Please see more details on #Positiveaboutnumbers here, and download a free toolkit with some great ideas for teachers that brings together tips and learnings from the teachers who contributed to the Positive About Numbers hackathon events.

[1] Data sources: Skills for Life 2011PIAAC 2014; National Numeracy YouGov Survey 2014

‘Early Number Sense: Helping at Home’ video series – your thoughts!

I passionately believe in the Early Number Sense Helping at Homeimportance of children’s early maths experiences. My training and resources are designed to help children become fluent with small quantities, develop counting skills and learn to reason mathematically.

In my work supporting schools, teachers often comment on how great it would be to show parents how they can best support their children in maths at home. Parents might, for example, teach their children to count to 100. However, skills which are more predictive of children’s long-term success, like the ability to subitize small quantities, have not been developed. This is where I can help.

Over the 2019 summer holiday, I plan to make four YouTube videos to show parents how they can best support their children’s early mathematical development. This series of videos will be called Early Number Sense: Helping at Home. Each video will be approximately 2 minutes long, explaining key principles and giving lots of practical ideas for exploring maths at home. The video titles are Developing Counting Skills, Recognising Quantities, Maths Around Us and Playing With Maths. They will be available on my soon-to-be-established YouTube channel and compiled on a new page at

I want these free videos to be as good as possible and reach as many parents as possible; for that I am seeking your help. Firstly, please pass this information on to your headteacher or EYFS leader. Also, I would be so grateful if you would FILL IN THIS SHORT QUESTIONNAIRE to tell me what I can do to make the videos as effective and user-friendly as possible. All ideas are welcome!

I have recently been running an innovation project with NCETM Maths Hub NW3 – the work group participants suggested that they would use the videos in their ‘meet the parents’ events in September and share the videos on their school websites. I will explain how this can be done once the videos have been created.

I can’t wait to get your thoughts and ideas about this project. Again, please feed your thoughts through to me via this short questionnaire.

Many thanks and have a great summer – Gareth

Click here for information about arranging Early Number Sense training at your school.