Category Archives: Maths ideas

I See Reasoning – UKS2

We all want to be able to build reasoning into daily maths lessons. For a time-pressured teacher, that can be easier said than done. I See Reasoning – UKS2 provides rich tasks to deepen learning across the maths curriculum. It’s my ‘go-to’ resource when preparing lessons.

Concepts in I See Reasoning – UKS2 are often shown visually. In the Which picture? questions children match questions to a correct visual representation:

Explain the mistakes questions draw attention to likely errors:

Questions encourage connections between related calculations:

Children are encouraged to find multiple solutions:

And there are a range of other question types besides:

I See Reasoning – UKS2 comes as a PDF file emailed direct to your inbox. You can then save the file in a location of your choice. You can view the file from an Etsy account if you have one (although you don’t have to make an account to receive the file by email). Circulation of the file is prohibited.

Screenshots can be taken to be used in presentations or printed for children’s work. There are 176 questions, all varied in form, with answers provided where necessary. I See Reasoning – UKS2 corresponds to US grades 4&5 and Australian year groups 5&6.

I believe that I See Reasoning – UKS2 can be used to supplement any scheme of work. I hope it helps to deepen the learning in your classroom; I also hope that it makes your life easier when planning at the end of a busy school day!

CLICK HERE TO BUY I SEE REASONING – UKS2

Training and Resources for Summer ’17

I set up I See Maths to help time-limited teachers create powerful learning experiences in maths, engaging children intellectually and emotionally. To that end, here’s what I’m offering this summer:

Training
I’m delighted to announce four new conference dates this summer: full conference details can be found here. Early Number Sense: Beyond Counting  will give a clear Nursery-Y2 vision for how children build a strong feel for number and learn to calculate using non-counting strategies. We will explore how mathematical play can be extended and how reasoning can be embedded. Reasoning and Depth in KS2 Maths will give an exciting and practical vision for deepening mathematical learning, including how images and resources can be used to build understanding.

If you are interested in this training, you may consider arranging a conference event at your school – all that is needed is a spare room. This is a very cost-effective and popular way of running training – for full details click on the top two links on this page.

Resources to Buy
I’m working hard on the I See Reasoning eBook range and hope to write the UKS2, LKS2 and KS1 versions this term (I may be dreaming!). This will give teachers a massive bank of questions and tasks that will open up discussions and encourage reasoning. I’m extremely excited about this project – this blog gives more detail.

The iPad app I See Calculation is also in the final stages of being built. It will show standard written methods for calculation one step at a time. A child could check their answer to a question with a calculator; with I See Calculation they will be able to check each step of their written calculation.

Free Resources
I’m intending to create a series of free ‘flipbook’ dot pattern games that will help children to visualise addition, subtraction and multiplication, opening up discussions about calculation strategies.

Full details about my INSET training and in-school support can be found by clicking the links. I’m a NCETM Charter Standard provider of CPD and, being a class teacher, still very au fait with the realities of teaching in the classroom.

I hope that, in some way, my work can help you in the daily challenge of delivering great maths lessons. Enjoy the summer term!

I See Reasoning – In Production!

I’m passionate about creating maths tasks that get children thinking in new ways and generate curiosity. I’ve spent many enjoyable hours dreaming up such tasks: open-ended prompts that promote discussion; images that build understanding; questions that get children exploring big mathematical ideas in depth.

This summer I’m releasing all of my favourite tasks in a series of eBooks called ‘I See Reasoning’ – there will be UKS2, LKS2 and KS1 versions. I believe these tasks will become a ‘go to’ resource for primary teachers as they plan lessons, giving a range of thought-provoking questions and prompts for each maths topic. This isn’t another bank of SATS-style questions – tasks are more visual, more extended and much more open-ended.

First released will be ‘I See Reasoning – UKS2’. For each topic expect:

Prompts that facilitate open discussion

Explain the mistakes (above left), less information (above right), rank by difficulty and ‘broken calculator’ are common structures.

‘Minimally different’ questions
Varying the structure of questions very slowly. All of a child’s working memory is focused on the mathematical concept being developed – a structure I suggest using early in a sequence of learning.

Tasks providing variation and deep exploration
A wide array of varied question structures and ideas. Think visual, open and extended, often making use of structures like ‘how many ways’ or ‘always, sometimes, never’ and a range of games using digit cards 0-9.

A place value activity using digit cards 0-9


Sorting quadrilaterals branching database task 

I’m aiming to release the eBooks every 4 weeks. They will be view-able from different devices, making them user-friendly. I hope they help save teachers’ time in preparing lessons, supplementing your current resources.

Alongside First Class Maths and Maths Outside the Box, I believe that the ‘I See Reasoning’ eBooks will help children to engage in mathematics intellectually and emotionally.

More updates to follow!

Designed to Thrill: Maths Outside The Box

There’s so much to applaud about the way primary maths education is changing. Equipment and images are being used to build understanding; open questions allow children to explore ‘big ideas’ in depth; fixed mindset views are being challenged and changed.

I want to see one more piece added to this jigsaw: children becoming more emotionally engaged in mathematics, the kind of mathematics that I love. Rich, diverse and intriguing tasks that fire the imagination, the kind that you don’t want to put down. That was the vision behind Maths Outside The Box.

The 15 Maths Outside The Box tasks will broaden children’s experience of maths and give them interesting, extended contexts in which to apply their skills. I trialled the resource with a group of high attaining Y4 children (we had so much fun); I also used the tasks with all but my most able Y6s. Challenge comes more from the application of logic than the difficulty of calculations, so tasks aren’t specifically designed for children in a particular year group.

There are four Number Challenge tasks: for example, in The Raffle Puzzle the challenge is to work out the five winning raffle ticket numbers by piecing together the information from the six clues:
raffle

One of the three Data Cruncher tasks is Can We Have a Dog? where a range of information and graphs are used to estimate the cost of owning different breeds of dog over the course of their lifetimes:
dog

The Mountain Pass is one of four mind-bending Logic Puzzle tasks: can you piece together the information to work out how the four walkers can all cross Gravely Gorge before sunset?
gorge

I love the Investigation tasks. The Human Ruler allows children to explore the relationship between different body parts and I will always remember trialling Marathon Pace: the children tried to replicate the exact running speed of Uncle Grant and Aunty Kirsty on the school field!
marathon

I’m extremely proud that my resources are published by Alan Peat ltd. I first attended one of Alan’s training sessions in 2006 and was absolutely blown away by the quality of his ideas. Alan and Julie also happen to be 24 carat gold as people too. They have given me unconditional support, are fiercely principled and are great company. Amy Doorbar also deserves great praise for her amazing graphic design on the resource.

I hope Maths Outside The Box inspires many: on sale here!

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: http://www.iseemaths.com/visual-supports/

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: https://itunes.apple.com/gb/app/i-see-addition-subtraction/id1097967938?mt=8

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 gareth.metcalfe@hotmail.co.uk

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:

ap-tweet

So there we have it: the best set of three Christmas song graphs (by teachers, children and any others) emailed to gareth.metcalfe@hotmail.co.uk 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?

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:
fullsizerender

The Dot Pattern feature allows the user to create repeated addition images. How do children calculate the total number of dots?
img_3415

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

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:
img_3411

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!