Help! Long Multiplication

So it turns out that I’m not 100% sure how to do long multiplication. I really should be, you probably are. Please help.

I want to make a resource that will support children doing long multiplication so but first I want to make sure I’ve got my method straight. Here’s the issue: when you are multiplying by the tens value in a 2-digit number, where are you supposed to position the digit being carried? Here, I’ve done 80×3=240 and have put down 40. Where should the 2 hundreds go?


A shows where the 2 hundreds will be added to (but it could make the calculation messy). B shows the 2 above the hundreds column, the column that it will be added to (but two places along from the 3 we’ve just multiplied by). puts the 2 above the next number to be multiplied, but in the same column as the 4 tens.

The example on the national curriculum (below) somewhat ducks the issue in that there are no carries from the 20, and the examples in the mark scheme for the 2016 SATS don’t show the position of carried digits.

I inferred from this it’s up to schools to decide which way is best. Is there a ‘right’ way? What do you do? I’d love to know. Just to repeat, this isn’t me trying to make a point, rather I’m in the process of designing a resource that will model this calculation process, but I want to do it right. I’d love to know what you think, or from any ‘higher power’ if they can give a definitive stance.

All input welcome!


Calculation Flipbooks

I’m really excited to release my first range of Calculation Flipbooks – an initiative designed to support children in KS2 becoming fluent in written multiplication and division calculation.

Each flipbook shows a written calculation modelled step-by-step, with visuals or links to other methods shown to support an understanding of the calculation process.

This short video shows the calculation flipbooks being used:

Calculation Flipbooks from I See Maths on Vimeo.

These flipbooks can be downloaded and used by children so they have a ‘live model’ which they can view on a tablet device, for example to view methods or to check their own calculations. They can also be shared with parents to show standard methods of calculation in KS2.

The 16 flipbooks are free to download from this page:

And why no addition and subtraction examples? Simple! The place value feature on iPad app I See Addition and Subtraction models vertical methods for addition and subtraction step-by-step. It’s available on the App Store here:

If you use the calculation flipbooks in your classroom I would love to hear from you: specifically, is there anything about their design (big or small) that can be improved? I’d be delighted to get your thoughts and ideas. Send me an email at

I hope they help your children to become fluent in carrying out written calculations!

A Christmas Competition

I was given a book called ‘Venn That Tune’ by my sister-in-law a few Christmases ago. The idea is that you identify the song title by looking at the graph:
vttAfter all, who doesn’t love a good Venn diagram?  Well, yesterday I was emailed these three Venn That Tune’s for Christmas songs:

venn-christmas-1 venn-christmas-2 venn-christmas-3

Answers at the bottom!

Then the main man Alan Peat saw the graphs and had a great idea:


So there we have it: the best set of three Christmas song graphs (by teachers, children and any others) emailed to or tweeted to @gareth_metcalfe wins a free app. We will share as many entries as possible. Should be fun – join in!

Happy Xmas, War Is Over; I Wish It Could Be Christmas Every Day; Do They Know it’s Christmas Time At All?

Enrichment in mathematics

In the early 20th century, psychologist Lewis Terman carried out a now-famous research project: he aimed to prove that by knowing a person’s IQ at an early age, you are able to accurately predict his or her life success. Using a series of intelligence tests, he identified an elite group of 1,470 children to study. Terman believed that it was these children (and others of extraordinary IQ) that ‘we must look for production of leaders who advance science, art, government, education and social welfare generally.’

Terman carefully monitored the progress of the ‘Termites’ over a period of 35 years to ascertain their life success. The results surprised many, including Terman himself. The group thrived in many ways, most notably being healthier, taller and more socially adept than the average American. However, their achievements were far from remarkable. In fact, a later study concluded that a random sample of people, given the same socio-economic status, would have achieved just as well. Terman himself reluctantly concluded that ‘intellect and achievement are far from perfectly correlated.’

Later studies went on to explore this idea more thoroughly, as explained in Malcolm Gladwell’s book Outliers. Generally speaking, people who achieve great professional success have an above average IQ: usually 115 or above. However, beyond this ‘intelligence threshold’, a person’s success is determined far more powerfully by other skills and attributes rather than the full extent of their IQ. Gladwell argued that it is hard to be highly successful without above average intelligence; however, beyond the intelligence threshold success is determined by other factors, for example the character and inter-personal skills of the individual.

Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content.
National Curriculum, Maths

This led me to think about the nature of the ‘rich and sophisticated problems’ that we should be providing. In order to equip children for long-term success, tasks should help children to develop personal and social skills as well as subject-specific expertise. Easier said than done for a busy and pressurised teacher!

That’s what I’m going to dedicate my working life towards: creating learning experiences in maths that engage children intellectually and emotionally; tasks create curiosity and lead to collaboration. I hope that this characterises First Class Maths, Maths Outside the Box and The Maths Apprenticeship.

I’m convinced that, if the system allows, these are the kinds of learning experiences that we as teachers want to provide for our children.

Personal Skills

I See Multiplication and Division

I See Multiplication and Division, the follow-up to I See Addition and Subtraction,  allows teachers to make a range of visual representations, allowing children to see the underlying structure of these calculations.

I got the idea for I See Multiplication and Division whilst watching an NCETM demonstration lesson. In the lesson, a year 3 class were writing multiplication number sentences based on different repeated addition images. My immediate thought was ‘how can a teacher create these visual representations?’ For many, probably by spending an age on Publisher or PowerPoint. So the concept for the I See apps was born: making it easier to create visual representations.

Here’s what you can expect from I See Multiplication and DivisionThe Singapore Bar section allows you to create proportionately sized bar models for both operations. Enter the number of bars, the size of each bar and for division the remainder:
Making Singapore Bar

Then the image is created. The calculation shown can be rearranged and the numbers displayed can be hidden as appropriate:

The Dot Pattern feature allows the user to create repeated addition images. How do children calculate the total number of dots?

UxUxU calculations can also be made visual: again, how many dots, and how did you work it out?

Multiplication can be shown as an area model, with the sections appropriately sized:
Area Model

And arrays can be created and adapted in a range of ways. For example, columns and rows can be re-coloured, for example showing 6×12 as double 6×6:

My hope is that I See Multiplication and Division can deepen learning for children and make lesson preparation easier for teachers. It will be available for iPad in the first week in October.

Again, huge credit to Alan Peat ltd for running with the idea and Doug Stitcher for his extraordinary effort coding the app. You are legends!

Plans for maths, 2016-2017

This is a great time to be involved in maths education: there’s a collective movement towards developing deep, conceptual and varied learning experiences; teachers are being proactive in promoting positive attitudes towards maths; maths hubs are growing in their influence.

I’m excited to play my part in this movement. Put simply, I spend hours thinking about and trialling ways to get children involved in maths tasks that are collaborative, open and (wherever possible) visual. I want children to become engrossed in maths; to experience its agonies and thrills, engaging emotionally as well as intellectually.

Here’s what you can expect from me in 2016-2017:

I can’t wait to release Maths Outside the Box, the natural follow-up to First Class Maths. The 15 tasks (logic puzzles, multi-dimensional tasks and investigations) will give children challenging, quirky contexts in which to apply their learning. The perfect way to end a unit of work – it’s been SO much fun writing and trialling.

I See Multiplication and Division for iPad is also coming soon. It allows teachers to create a range of visual images to represent calculations, including proportionally sized bar models, area models, dot patterns and arrays. It’s the natural follow-on to ‘I See Addition and Subtraction’.

I hope to write a range of open, visual questions that allow children to explore maths ideas in depth. Questions a bit like this:

I’m also planning on sharing lots of free resources, including (time permitting) videos for improving the quality of parent interaction in maths. Watch this space.

It’s a privilege being able to visit schools to share this passion. Here is the information about my training.

Conference events are scheduled for Manchester and Dudley with a KS2 focus. Expect future dates for bith KS2 and EYFS/KS1 training in the Spring and Summer terms. I am also soon to announce a 2-day training event in London (mid-November) and my first half-day TA training event in South Manchester.

I’m totally committed to my 2 days teaching my amazing Y1 class this year: I hope they can learn as much from me as I will from them. I’m always happy to promote the good work of other people & look for ways to collaborate, so be in touch.

I’ve got more plans than time, and more ambition than realism, but hopefully in one way or another I can play my part in enriching primary maths. I will also keep posting as many bits as possible on my social media feeds in the distant hope that it will inspire someone somewhere.

Have a great 2016-2017 school year!

Telling parents about The Celebrating Maths Project

I’m delighted to announce that The Celebrating Maths Project has been launched! This blog explains a few ways in which teachers can share the project with parents.

Put the page on the school website
1. Copy the following address:

2. Go into the menu on your school website. Select ‘Custom Links’ and paste the above address. Add the title that you want to display on your site. Click ‘Add to Menu’.
Web page

3. Position the link where you want it to appear on your website.

Send out the letter to parents
I’ve written a letter explaining the aims of the project. It’s posted on the page with all the tasks. It can be printed and sent to parents.
Letter pic

RT tweets from @gareth_metcalfe from school accounts
I have sent out a range of tweets about the project designed to by retweeted from school accounts.

I hope the project helps you to engage parents in the maths learning process!