# Home Truths – Maths Homework Ideas

I have mixed feelings about homework in primary school. As a teacher, setting, collecting, chasing up, marking and returning homework took up a lot of valuable time, and I wasn’t always sure it was entirely worth the time expended. However, most schools have a homework policy that stipulates setting at least one maths homework a week, so over the years I developed some ideas to make it as painless and productive as possible for me and the children.

**Using online games**

I’m always very keen for children to learn their number bonds and tables. The underlying conceptual understanding of these is vital, but at some stage sustained practice is needed. There are lots of online games that can help children to do this, not to mention apps that can be downloaded onto tablets and smart phones. Some schools buy into subscription sites like mathletics, but there are some very good free alternatives too like tutpup and sumdog. It’s possible to set up accounts on these sites as a teacher and track children’s progress so that if you set a homework of spending time on one of the sites, you can check it’s been done, or it may be sufficient to ask parents to sign a homework diary to confirm their child has done this. Of course, there will still be some children who don’t have ready access to the internet or access to tablets, but these days that’s often very few and it may be possible to accommodate these with a weekly homework club where they can use school devices, or give them an alternative homework.

**Adopt a Shape**

This was an idea I used when we were just about to embark on looking at 2D and 3D shapes. I gave each child a shape to ‘adopt’ – this gave me a chance to differentiate fairly easily by giving more familiar shapes to some of my less able children and challenging my higher ability children with less familiar shapes like icosahedrons. They were given the task of finding out as much as they could about the shape and presenting the information in any way they chose. I gave some suggested starting points, like finding the number of sides and corners etc. or finding the number of diagonals. The children really engaged with this idea and came up with some fantastic presentations, including 3D models in some cases. It made a fantastic starting point to our unit of work (not to mention filling up the working wall nicely!)

**Write a worksheet**

This was a task I used quite often when we’d spent some time looking at particular calculation methods. I would ask each child to write a worksheet for another child in their group. They had to include at least one worked example with an explanation of the ‘steps to success’. They also had to include some word problems and if possible give the worksheet a theme, possibly linked to our current class topic. Again, this was something the children usually responded well to. I would often give small prizes or stickers for the best ones and display these on the working wall and this appealed to the competitive streak in many children. Some would hand in beautifully illustrated sheets. Writing word problems to go with particular calculations really tests children’s understanding of that operation. A variation on this theme at the end of less calculation based units was to ask the children to make a poster to display their learning and be a learning resource for others. Again, this often produced some beautifully presented responses.

**Handling Data**

When beginning a unit of work on handling data, I would often start by recapping all the different ways the children already knew of presenting data. Depending on the age of the children, this might include tally charts, pictograms, bar charts, bar line graphs, line graphs, venn diagrams, carroll diagrams or pie charts. I might then ask them to collect as many examples as they could from newspapers, magazines or the internet and make a poster which they would annotate with explanations of what type of representation it was. For older children, I might also ask them to comment on whether that was a good representation and why that particular representation of the data had been used. This encouraged the children to notice how often data was presented in different ways in real life and start engaging with this.

Another data handling homework I would sometimes set in Years 5 or 6 was to give the children an opportunity to investigate something themselves. They were given a free choice of what to investigate and how they would collect the information. We spent some time discussing possibilities in class beforehand. They then had to collect the data and decide which was the best way of presenting the information. They also had to draw some conclusion from their data and lastly to reflect on their project and decide whether it was a true picture or whether their were factors which might have affected their results. This was a homework I set over 2 or 3 weeks, often over a half term holiday to give them time to plan and carry out their projects. I gave some helpful hints and prompt questions at the outset. This led to some really good work and some good discussion afterwards when the children shared their projects. One particularly memorable one was the boy who patiently recorded each visit to the toilet by each member of his family over a few days. Some definite trends emerged and the conclusions he drew were very entertaining!

**Using Skills**

Particularly when using measures, it can be good to set a homework which gets children using their newly learned skills in a practical context. So, for instance, homework could be to follow a recipe using metric units and record the result in some way (ideally be bringing in a sample of any particularly delicious results for the teacher to critique!) Or it might be to measure up a bedroom and plan an ideal lay out using furniture of given dimensions.

I hope this has given some new ideas to try. The beauty of many of these ideas is that they often take very little marking or can be used to stimulate discussion or as a learning resource in future lessons. They also tend to engage children much more than a traditional worksheet, and often get parents involved as well. Some can take a little planning to set – a bit more than photocopying a worksheet maybe, but I always make a point of keeping the prompt sheets etc and they can often be quickly adapted for a different age group or mathematical area.

# Read All About It – Using Story and Picture Books in Maths Lessons

This blog was my very first venture into blogging on the fabulous Primary English blog. I’m very grateful to them for publishing it last May which led to me thinking seriously about starting my own blog. Their site is well worth a visit and they also have some amazing pinterest boards on all sorts of themes.

Here is what I blogged back in May:

As a maths leader, I quite often have the privilege of doing planning trawls and looking at weekly and medium term planning from other teachers. I’m often very impressed by the thought and detail that goes into these. But there’s one section that seems very rarely to be given much thought. If your weekly or medium term planning format is anything like mine, there’s a small section headed ‘cross-curricular links’, and I hardly ever see it filled in, except perhaps with the suggestions given on the format itself, and these are nearly always Science based.

On the whole, we are very good these days at making cross-curricular links, particularly at bringing writing opportunities into a whole range of curriculum areas. At the start of units, topic webs are drawn up and connections made – but maths is often very difficult to fit in to these and so we agree that it’s probably best to teach this discretely.

I’d be the first to admit that it is often difficult to bring maths into our topic themes – although I do think it’s worth making the effort. It’s so important that children see the relevance of maths to their lives and the way that the skills they learn can be applied. However, one great way of linking maths to other curricular areas is by using story and picture books.

As I write, my daughter – in her first year of teaching – is spending a few days with us. Yesterday, she was starting to plan the maths for her Year 1 class for the Summer term and looking for activities in particular for time and money. She’d already planned to use Eric Carle’s ‘The Very Hungry Caterpillar’ as a starting point for learning and ordering the days of the week, and ‘What’s the Time, Mr Wolf’ by Colin Hawkins and ‘The Bad-Tempered Ladybird’ (another book by Eric Carle) for telling the time and sequencing the day. I was able to introduce her to the wonderful Mick Inkpen book ‘The Great Pet Sale’ and she then happily spent most of the rest of the afternoon having lots of fantastic ideas about how she could use this – her role play area for the start of term will be a pet shop with lots of opportunities for the children to practise paying for items, finding the correct money and giving change, but also stimulating lots of writing opportunities too – descriptions of their pets, instructions for looking after a pet, recounts of visits to a pet shop – like most teachers, given an engaging starting point, the possibilities she’ll find will be almost endless. She also found some fantastic resources to use on T.E.S. and some good labels for her pet shop on Twinkl as well as a reading of the book on Youtube.

I suspect KS1 teachers have always been quite good at using story and picture books in some of their maths work, but as a KS2 teacher I wasn’t so aware of good books with mathematical links until I was introduced to some by the Coventry Primary Maths team at subject leader training and also during my MaST training. A particular favourite is Anna Milbourne’s ‘How Big is a Million’ which tells the story of a young penguin eager to find out just what a million looks like. Big numbers tend to fascinate children of all ages and although younger children would love this book with its very simple story line, I’ve also used it very successfully with children in UKS2. Another is ‘The Rabbit Problem’ by Emily Gravett, again a very simple story attractively presented, but with some quite challenging maths to explore for older primary children. I’ve used this with UKS2 when we’ve been looking at number sequences to lead into looking at the Fibonacci sequence and algebra.

There are so many books that can be successfully used in maths, from simple counting books like the beautiful Anthony Browne book ‘One Gorilla’, through books about measures like Pamela Allen’s ‘Mr Archimedes’ Bath’, to books about working with very large numbers like ‘Anno’s Mysterious Multiplying Jar’ by Anno Masaichiro. For fans of the ‘Horrible History’ books, there is even a whole series of ‘Murderous Maths’ books written by Kjartan Poskitt.

I’m continually collecting new ideas for my Pinterest board and Coventry Primary English also have their own board of ideas.

# Level Playing Field – the Problem with Levels

As we move to the new primary maths curriculum, the old NC levels no longer apply but we are still waiting to find out what will replace them under the new assessment arrangements which have not yet been finalised.

I suspect many primary schools will continue to use the levels for the purposes of tracking children across the school or key stage. Whilst I agree that it’s important to track children’s progress in some way over time, over the last few years I have had increasing misgivings about the way the NC levels are used to do this. I feel there are several problems with this and I’d like to outline some of them here.

**How we assess**

QCA tests are commonly used to assess children at the end of a school year, and often at other points in the year as well. Others use other commercially published assessments. My problem with these is that in my experience, they are not reliable. As a maths leader, I got to know the year groups where we could expect rapid progress (according to the tests) and those where progress would be much slower and this often remained the same year on year, regardless of which teachers were in those year groups. As a class teacher, I got to know the tests that were likely to make my children look good and those that weren’t. I like to think that I bore this in mind in using my teacher judgement to moderate the results from the tests but see my later point about performance management.

To be fair, most schools don’t rely completely on test results and teacher judgement is used as well. The problem with this is that it takes a lot of experience to really know inside out what children ought to be able to do to achieve a particular level, let alone then knowing which sub-level to give. In theory, APP should have helped with this, but most systems are cumbersome to use and often wrongly used – just because I can find evidence in a child’s book that he or she has been adding 3 digit numbers, does not mean that they are secure in this.

**Who does the assessment**

In most cases, assessment is done by the class or group teacher. In theory, this is great. They are the person best placed to know what the child can really do, to be aware that a bad performance on a test is not typical, for example. They are in a position to see which aspects of maths children are secure on and which they need to revisit. However, in many cases, the progress of children in a teacher’s class or group contributes to their performance management targets, and now with performance related pay, the stakes are even higher. Added to this, in the current educational climate, is the ever present threat of capability procedures for those whose children’s progress dips. I do believe that most teachers try to act with integrity but the high stakes attached to progress but huge pressure on them to report optimistically. Unfortunately too, there are definitely teachers who knowingly play the system. In one school I worked in, a recently appointed class teacher discovered from his TA that the previous teacher had always gone over tests with the children just **before** they took them. The poor TA, herself fairly new, had assumed this was common practice!

**The precision to which we track**

When levels were first introduced, they were meant to give an overview of what should be expected of average children at certain stages. So the components of level 2 were those which an average 7 year old would be able to do. (Later these average expectations somehow became minimum expectations, but that’s a whole other blog!) However, this made tracking progress across key stages difficult because children would typically take 2 years to move up a whole level. So sub-levels were introduced and APS points. Many primary schools now use these APS points to track progress termly but levels were never intended to track progress at this level of precision. We simply can’t measure progress precisely in the way that we measure, say length precisely. There may be some justification for comparing the progress of different cohorts from the end of KS1 to the end of KS2 because at least here we are broadly speaking comparing progress with similar start and end points. But comparing how much progress one set of children have made in a single term of Year 2 against the progress another set of children have made in the same term in Year 3 is just not valid, in my opinion. When I was in Year 6, I knew that if children came up to me at the start of the year with a 3A, I had a fighting chance of getting them to level 5 by May, progress of at least 4 sub-levels. It would be very unusual for a Year 3 teacher to move a child at 1A at the start of the year to level 3 by the end of they year, and I would imagine it only happens very rarely. Yet, we make judgements about teachers based on comparing situations like this. From experience, I feel that level 2 is probably the level that takes the longest to move through. The jump from a 2C to a 3C in terms of conceptual understanding and skills is huge. Is it any wonder then that there is typically a dip in progress in Year 3 where the majority of children will be in the process of moving through level 2?

**Life after Levels**

I’m aware that I’m putting forward lots of problems about tracking progress using levels without really suggesting a solution. I’d suggest that any way of tracking progress term by term or even year by year is bound to be fraught with problems. Some have suggested that with the new curriculum we use a system similar to that currently used in Early Years, where children are judged to be Emerging, Expected or Exceeding the expected standards for each year group, but many of the problems outlined above would probably still apply. All I would urge is that any system of tracking progress using data is treated with great caution. The removal of the high stakes involved might also help teachers make more carefully considered judgements.

# New for Old – Introducing the new Primary Maths Curriculum

I’ve already blogged about some of my hopes and fears for the new curriculum here. In this blog, I want to think more particularly about introducing the curriculum to schools and suggest some useful resources.

It’s important to plan the change carefully and make sure teachers are well prepared. As the KS2 assessment arrangements don’t change until 2016, our current Years 3 and 4 will be the first to be assessed under the new curriculum at the end of KS2. The expectations for them in some areas will be higher and it may well be that schools choose to start teaching at least some of the new content this year so that there is less for these children to catch up in Years 5 and 6. This is particularly true in the areas of written calculations and fractions. Similarly in KS1, the tests and reporting arrangements will remain the same until 2016. This means that from September 2014, Years 2 and 6 should still continue to be taught using the current curriculum but all other year groups will need to move to the new curriculum.

Expectations for fluency with number facts and calculation methods will be raised and it may well be worth tackling this with some whole school initiatives. Some schools are choosing to give an extra 10-20 minutes each day to focus on this in particular, outside of the maths lesson, rather in the way that phonics is often taught discretely. For number bonds and tables, it would be well worth listing exactly which facts your school expects children to learn in each year group and sharing this with parents. It’s also worth tracking the facts that children know so that children who are falling behind in learning these can be given extra support. It would be good to discuss as a staff just what you all understand by ‘rapid recall’ of facts. You may find that some teachers feel children know their two times tables if they can chant the table, whereas others would expect them to be able to answer mixed 2 times tables questions, answering 20-30 or more in a minute. I have suggested some ideas and resources for teaching number facts and tables here.

The NCTM has a growing library of resources to support introducing the new curriculum. In particular, their Resource Tool could be a useful starting point. So far, only material for Years 5 and 6 have been added, but we are promised other year groups’ material before too long. For each year group, the content has been divided into several different strands. Selecting a particular strand and year group and choosing ‘Show Selection’ brings up the information below the tool. So for each of strand and year group, there is information on subject knowledge, connections (to content in other year groups, to other mathematical topics and to other subject areas), articles about good practice in teaching that strand, some suggested activities that could be used in teaching it, exemplification of the expectations and videos that support aspects of the strand.

The subject knowledge resources may be particularly useful for teachers in UKS2 where raised expectations may mean that they need a refresher in eg. calculating with fractions.

For more information about the new curriculum and some resources which might prove helpful when introducing it, my New Curriculum Pinterest board may be helpful. For subject leaders or senior leaders based in the Midlands, you may be interested in a course I am running next month on preparing for the new curriculum. I have lots of ideas and resources to share!

# Summing Up – Teaching Addition

Addition is perhaps the most straightforward of the four operations to understand, but that doesn’t necessarily mean it’s always easy to teach. I was speaking to a Year 5 teacher earlier this week who had planned to start this term by spending a couple of weeks revising the four operations with her (lower set) maths group. She’d planned only a couple of days on maths, but after two days still felt there was a lot the children weren’t understanding and decided to keep going for the rest of the week and possibly into next week too.

Having a good understanding of the progression of skills for addition can help when trying to ‘unpick’ why older primary children are having difficulty with it. Are they familiar with the vocabulary around it? Do they have good mental images of what is happening when they add? Are they being let down by a shaky grasp of basic number bonds which leads to mistakes in some steps of longer methods? Is there understanding of place value secure? Have they got a good conceptual understanding of the method they are using rather than trying to remember a ‘trick’ they were taught last term or last year?

Children’s early experiences of addition should be very practical and the idea should be introduced in a meaningful context? They need to understand addition both as combining two sets of objects and as adding more to an existing set. Early Years environments tend to be full of opportunities for them to do this. We have 4 red cars and 3 blue cars, how many cars altogether? Seth has 3 sweets and Tami gives him two more, how many does he have now? After lots of experience with concrete objects, children may be ready to move to using representations. So instead of using actual cars or sweets, cubes or counters might be used to represent them. Another step beyond this is to use pictorial representations, such as drawing circles or dots to represent objects. One very powerful representation for addition is the bar model (as above) which clearly shows two parts making one whole.

After lots of experience of combining and augmenting sets, children will begin to learn some of the number facts, beginning with those within ten. Working with tens frames, Numicon or Cuisenaire can all be helpful when doing this. Tens frames and Numicon particularly reinforce the idea of ten being two lots of five, helping children to build mental images of numbers. This program is useful for demonstrating the use of tens frames. Begin by adding on one more and then two more – if children are used to counting, this should come fairly easily. After a while, they will need to start learning the number bonds to 10 and within 10 – doubles can often be a good place to start with this. For some ideas about learning number bonds, one of my blog posts from last year has some ideas.

Before children start to add larger numbers together, they should be familiar with the idea of place value and have experienced making numbers with Dienes or other base ten equipment. As the totals they add go beyond ten, they can use the Dienes units to model this and start to exchange ten unit cubes for a tens rod. Later, children can start to add single digit numbers to 2-digit numbers using the Deines. It can be helpful to also model how to do this using hundred squares.

When adding 2 digit numbers, again it is helpful to start by using equipment so that children see the way that partitioning and recombining works in practice. This can later be recorded using lines and dots to represent the Dienes rods and cubes. The next step is to record the partitioning and recombining process, eg.

leading later to expanded column addition, eg.

and later still to more formal column addition.

The important thing is not to move children on until they are secure at any particular stage.

The same process can then be applied to increasingly large numbers so that by the time children get to the top end of primary they are able to add numbers with at least 4 digits. When children are familiar with decimal numbers and their place value, the same methods can be used to add decimals too.

# Order, Order – Reading, Writing and Ordering Numbers

Early in the term is a good time to go over the basics of reading and writing numbers and putting them in order.

Young children need plenty of practice in reading, writing and representing numbers, and this can usefully be part of a ‘Number of the Day’ activity like this one. It’s important that children start developing their number sense alongside this and representing numbers with practical equipment like Dienes, Numicon or ten frames or by drawing tally marks will help them to do this. The Gordons program ‘Dienes and Coins’ is useful for these representations and this site has some nice interactive ten frames. As children get older, they need to learn to understand much bigger numbers. Children are often fascinated by really large numbers, and once they get the hang of how the number system works, more able KS2 children will enjoy trying to read and write multi-digit numbers. This Wikipedia page lists the names up to centillions.

Number tracks and number lines can also be useful in helping children get a sense of the relative size and position of numbers. The Mathsframe site (which I love) has a really useful activity where children put numbers on number lines. There are lots of different levels at which to use this activity and the option of showing divisions on the line or not. Older children need to also get a sense of how decimal numbers work and the Decimal Number Line ITP is very useful for this. The programme allows us to ‘zoom in’ on a portion of the number line and expand it to look at what happens within that portion. Children in KS1 will also be starting to find numbers on hundred squares. One useful activity is for children to cut up a hundred square along the horizontal lines and then lay out the rows end to end to make a 0-99 (or 1-100) number line. This helps them to see the connection between the hundred square and number lines and shows them why we skip to the next row when counting on over a tens barrier. Putting together ‘jigsaw’ pieces of the hundred square can be useful for children in developing their understanding of how these work, and Nrich has a jigsaw activity which can be used either in its interactive version or in printed form.

Ordering numbers is also an important skill. When the NNS first came in, washing lines of numbers were standard in nearly every classroom and these are well worth using still. Having sets of number cards of different sizes means that these can be regularly changed. Children enjoy putting numbers in order on these or spotting numbers which have mysteriously been switched overnight. The Gordons ordering program uses this idea and again Mathsframe has some good ordering activities. Some of the levels on this are only available to subscribers but a subscription is good value in my opinion as there is a wealth of resources on this site.

Reading, writing and ordering numbers links well with work on place value and there are ideas for that at my blog from last year and there are other ideas for teaching number on my Number Pinterest board.

# Only Connect – The Importance of Making Connections in Medium Term Planning

Over the holidays, many teachers will be sitting down to make medium term plans for their maths lessons. This might be for the entire time or it might only be for a block of learning, perhaps two or three weeks, but I’d hope that they will be giving some thought as to what the learning will look like over the course of the whole term. They’ll be looking at assessment records or notes they’ve written on their weekly plans or elsewhere to see what the priorities are. They’ll be looking at the objectives for the year or for the next steps in learning and making sure there’ll be opportunities to visit these during the term. For Year 6 teachers, with the SATs in May drawing ever closer, there’ll probably be a particular urgency and focus on the gaps that need to be plugged before Easter.

Medium term planning is important in Maths. It has to be flexible. Even for a very experienced teacher, each class is different and some topics will end up not needing as long as we planned, whilst others will need longer or will need revisiting. Just like our weekly plans, our medium term plans should be working documents which regularly get annotated and highlighted throughout the term. However flexible it is though, it needs to be well thought through to ensure coverage of all the important topics and that will probably mean building in some contingency time, just in case several topics take longer than we imagined.

In recent years I have often been involved in monitoring planning in different schools – this is usually weekly planning rather than medium term planning, but usually I’ll be looking at several weeks at a time. Plans vary enormously in the amount of detail they give, and there are teachers whose plans give very little detail who manage to teach great lessons, and others who dot every i and cross every t but whose lessons are not so sparkling. By and large they are thoughtful and thorough and it’s clear that teachers are on the whole familiar with what their children already know and what they need to learn next. One thing that does concern me, however, is that over the last few years, I have increasingly seen a rather ‘scatter gun’ approach to planning: a lesson or two on one topic, another lesson or two on another topic and then perhaps a quick problem solving lesson on Friday. I believe there are two main reasons for this. The first reason is the way the renewed framework which was introduced in 2006 divides into blocks of learning meant to last for 2-3 weeks. In each block there is a whole plethora of possible material, and I don’t think it was ever the intention that anyone would try to teach all of this in such a short period of time, but there was such a lot there, that it was common for teachers to try to teach far too much far too quickly. The second reason I believe is the increasing pressure from Ofsted that so many schools are feeling now. I know there’s lots of debate about progress in lessons currently, but whatever the rights and wrongs of this, it has made many teachers feel they need to teach something new every lesson. It’s relatively easy to show progress within the lesson when you introduce something new – at the beginning of the lesson, most children know nothing about it, at the end they do. Whether they will remember anything about it next week, let alone tomorrow, if we don’t then revisit it, is much more open to question.

I really believe we need to slow things down. I’m not suggesting individual lessons should lack pace (although there’s possibly a debate to be had about that too), but that we should plan sustained periods of time where we focus on one topic or a few very closely related topics. Within that period of time, our children can certainly make progress within that topic, but each new step will be connected to a very recent one, and there will be time for new skills to be practised and consolidated.

As well as taking longer over topics, our medium term planning should be exploiting the natural links between different mathematical ideas and topics. So, for instance, it makes sense to teach finding fractions of amounts soon after work on division, so that children naturally see how the two things connect, and can further practise their division procedures with fractions problems. If you haven’t seen it before, take a look at the picture at the top of this blog and try to work out what comes next. Unless you see the connection between the symbols, it’s pretty hard to do (if you’re still struggling, imagine a mirror line drawn vertically through the middle of each one). Once you see the connection, it’s easy. Similarly, we can make things much more difficult than they need to be for our children if we don’t exploit the natural connections between different mathematical ideas.

So if you’re sitting down to do some medium term planning over the holidays, think about the connections you can make. Think about giving children time to really get to grips with a topic. If it’s possible, also think about the connections that can be made with other curricular areas. Would your technology topic give opportunities for weighing or measuring using different scales? Could your geography topic give opportunities for using negative numbers in context when comparing temperatures or comparing large numbers when looking at populations? Could the children show some of the information from their history topic using their newly acquired data handling skills? Don’t force it, try to make the contexts as real as possible, but teachers tend to have great imaginations so I’m sure you’ll find some creative connections.

# Higher, Faster, Harder? Supporting More Able Mathematical Learners

**Harder, Faster, Higher? – Supporting More Able Mathematical Learners**

The new curriculum, we are told, is a mastery curriculum. This means there is an expectation that instead of pushing our more able learners on to ever higher level curriculum content, the focus is much more on making sure all our children are secure with the core content for each year group. This leaves us with a challenge for our more able learners, but also with a great opportunity. With less pressure (we assume – the assessment procedures are not yet clear) to push these children through the levels, we have to think of different ways to challenge them – not so much higher and faster as broader and richer content. These are a few ideas about how we can support these children.

**Open ended questions**

Challenging more able children should not be primarily about moving them on to ‘harder’ questions with higher numbers. We want to extend their thinking by asking more open ended questions which challenge them to apply their knowledge in new ways. We also want to develop their reasoning skills by asking them to explain their reasoning. Using Bloom’s question stems can be helpful in planning this. Ask children to explain how to find the answer to a problem and decide which approaches would be best to use. Ask them to explain the rule for a growing pattern or to explain what would happen if … Get them to think of other ways of doing things and compare approaches to decide which is best. Challenge them to explain their reasoning so that a younger child could understand it.

**Mathematically rich activities**

Children need to learn to think mathematically and to apply their skills. The Nrich website provides lots of games, challenges and activities to encourage this. They aim for activities to be ‘low threshold, high ceiling’ ie. accessible to as many children as possible but with enough to challenge more able children. Their curriculum mapping documents are very useful in identifying activities which link to different curriculum areas.

**Investigations**

Investigations can help children to extend their mathematical thinking in a more open-ended way. Typically in an investigation, children are given a starting-point and some ideas of how to get started, but they won’t know what the answer will look like. They need to look for patterns and identify what is happening. The Maths Warriors site has a number of interesting investigations suitable for primary aged children.

**Challenges**

More able children often respond well to challenges. The ‘Mathematical Challenges for more able pupils’ have a number of challenges divided by age group. Another good source of challenges for KS2 are the Challenge cards on the Maths Warriors site.

**Problem Solving**

Whenever a new skills is taught and learned, make sure the children have the opportunity to practise their skills in a real context by applying them to solving problems. It can be particularly meaningful to give the problems a context from another curricular area. As well as regular opportunities to solve problems as part of their maths lessons, children often also respond well to the challenge of a ‘Problem of the Week’ which can be displayed in class for a set time. The Nrich site is a good source of suitable problems, some of which are available as posters. The Numeracy Strategy Logic Problems also have problems at a range of levels.

**Missing Number questions**

For calculation in particular, once a calculation process is learned (eg. column addition), presenting questions with missing digits can extend children’s thinking about the process they have been using.

**Other useful websites**

Mathpickle has some interesting videos and other activities.

Mathsticks has lots of useful resources. There are lots of great activities which are free to download, and some premium resources if you can stretch to a membership.

7puzzle posts a new puzzle every day. The site also categorises the archived puzzles into Easy, Medium and Hard etc.

My Pinterest board has lots of other ideas for investigations, puzzles and challenges.

# ‘Tis the Season – Christmas Maths Ideas

With Advent almost here, our children’s excitement levels rising even faster than our energy bills and shops turning on their Christmas playlists, there’s no getting away from the fact that Christmas is rapidly approaching. So I thought it would be timely to share some ideas for Christmas maths activities which might just exploit the children’s natural excitement and give some of our maths a topical context. I also recognise that it’s the time of year when the best laid plans go awry – overrunning Christmas production rehearsals, staff laid low by seasonal viruses and bad weather preventing outdoor activities can all mean that even the best prepared of teachers need to reach for a ‘pick up and run’ activity, so let’s make sure that these have some meaningful mathematical content.

**Good sources of Christmas maths activities**

For straightforward maths activities categorised into different topic areas try Math Drills Christmas Maths Worksheets; Kidzone has Christmas themed maths pages sorted by age group and Primary Resources Seasonal Activities include lots of maths ideas. For younger children, there are lots of ideas at Making Learning Fun. For a bit more challenge, Maths Salamanders have some Christmas themed challenges to help develop reasoning and problems solving skills. The same site has Christmas themed games and other activities including Christmas co-ordinate pictures. Mathwire has several seasonal investigations and other activities. I like the Mathsticks Christmas activities too. Some of these are free but Mathsticks also produce a whole booklet of Christmas activities each year for about £4 which are well worth investing in.

**Measurement**

Work on measures always lends itself to practical activities and Christmas offers a wealth of opportunities. Children can compare the lengths of stockings, parcels or candy canes or measure them using standard or non-standard measures. Christmas cooking brings opportunities for weighing, as does working out the postage costs for parcels. Play games where children have to estimate and measure time, perhaps timing how long different children will take to wrap different parcels. Capacity can be explored when making up drinks for the Christmas party or leaving glasses of milk for Santa’s reindeer. For younger children, this Kindergarten blog has some nice ideas.

**Data Handling **

It’s usually fairly straightforward to find uses for data handling skills. Make tally or bar charts to record favourite Christmas films or songs or food. Construct a Venn or Carroll diagram to show who likes sprouts, Christmas pudding, both or neither. Track the temperature on a cold day using a line graph. Investigate the types of programmes on television on Christmas day and record the results in a pie chart.

**Word Problems**

Lots of Christmas themed word problems can be found online including these and these. However, why not challenge children to make up their own word problems to match calculations that you give them and then they can use these to challenge each other. This makes a good quick homework activity at this time of year too.

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**Calendars and Countdowns**

Nrich have an online advent calendar each year with a different mathematical challenge behind each number. I’m sure this year’s will be available soon, but in the meantime, here is the 2012 version. For a different way of counting down to Christmas, this blog has instructions for making a calendar made from Santa’s beard which will get shorter each day as bits are chopped off. The instructions are in Italian but the picture is fairly self explanatory! If your children want to make calendars for 2014, this site has printable templates to make dodecahedron calendars from nets.

**Games**

Christmas is a good time to play games to practise and reinforce skills and there are lots available online like this Gingerbread Dice game, or this Santa’s Beard game. There are games for practising doubling or games for practising all four operations. For younger children these games are clear and attractive. Or for games that involve a little more strategy and problem solving try these. Gordons Christmas Maths has some nice interactive activities for younger children or if tablets are available, this Christmas themed dot-to-dot app might be useful.

**Puzzles**

As well as the investigations and challenges at Math Salamanders and Mathwire already mentioned, there are some Christmas themed puzzles here and here. Nrich also have several challenges with a Christmas theme. If the pace slows down a little at the end of term (and I recognise that this doesn’t happen as much as it used to in today’s pressurised classroom environment), it’s great to let children have a little more time to work on puzzles and challenges.

All these ideas (and several more) can be found on my new Christmas Maths pinterest board.

# Picture This – The Importance of Representation in Teaching Maths

Last week, I talked about the great importance of building conceptual understanding in teaching maths and how fluency should build on this understanding rather than be based on teaching procedures without understanding. One of the most powerful ways of doing this is by using concrete materials and representations and there are a wealth of these available to us. When I was in school (admittedly rather a long time ago now), the only concrete materials I can remember are some shells and counters we used to help us do ‘sums’. There was very little in the way of representation either – possibly shapes and fractions might be illustrated by diagrams, but otherwise little comes to mind. Admittedly, I did manage to learn maths despite this, but even with the benefit of a maths degree, I found that some mathematical concepts became much clearer when I started teaching them and discovered representations that would support me in this.

This week, I have been reading a very helpful book by Tandi Clausen-May. Teaching Mathematics Visually and Actively introduces a whole range of concrete and visual material to support teaching maths in different areas. Clausen-May argues that visual and practical approaches are vital in teaching children who may have struggled to learn maths in a more abstract way and the book is aimed mainly at teachers of these groups. However, I believe that these approaches are actually beneficial for children of all abilities. I want to be upfront and admit to being sent a copy of the book by the publishers for possible review, but I have no hesitation in recommending it. The book is divided into chapters for several different areas of maths and for each introduces some key ways of using visual and practical approaches. I am always keen to use this sort of approach in my own teaching, but I found here some useful reminders of approaches I was already familiar with, together with some that were new to me. As well as key representations and materials for each area, there are also practical ideas about how to use these in the classroom and suggestions for further reading. Information is also given about online tools and information, or in the case of concrete materials, guidance as to where these can be obtained. As a bonus, a CD is included with the book, on which can be found useful printable materials and powerpoints.

In schools today, lots of visual and active approaches to teaching mathematical ideas can often be seen in Early Years setting and in KS1, but much less in KS2 and beyond. Where representations and concrete materials are used it is often with less able children. Children can then become reluctant to use these because they see them as ‘babyish’. We need to use these approaches much more routinely, so that this sort of stigma is not be attached to them. Admittedly, some of the concrete materials will need to be bought, but arguably this is a much better use of our budget than buying text books or photocopying worksheets. Many can be fairly simply made or printed off and in many cases there are interactive versions available (although caution needs to be taken that these don’t completely replace the ‘hands on’ experience of manipulating objects which is so important in the early stages of learning a new concept).

I have started a pinterest board which includes some of my favourite concrete and representational resources and I hope to be adding to this regularly as I remember and come across others.