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.
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.
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.
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.
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.
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.
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.
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.
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.
Young children are often fascinated by comparing and ordering the sizes of things. Perhaps it appeals to their innate sense of justice to determine whose apple is bigger and their equally well developed competitiveness to see who is taller. Early Years teachers build on this by providing lots of opportunities to compare and order things and begin to use non-standard measures to quantify. How many grapes balance an apple? How many cubes high is the toy garage? How many cups of tea can be poured from the teapot? At this stage, it’s important too to give children lots of opportunity to experience and use the language associated with comparison: more, less, fewer, higher, lower, taller, shorter, heavier, lighter etc. I’ve put together a few ideas for activities which support developing comparison language and you can download the document from the link at the bottom of this post.
As children move on in their understanding of measures, we move to using standard units of measure. Children often struggle with estimating length, mass or capacity using standard units and they need lots of practical opportunities to measure familiar things using these units. Wherever possible, opportunities should be found outside of the maths lesson for these activities, perhaps as part of topic work, for instance, to give them a meaningful context. Children can weigh out ingredients for their chocolate snack in technology or find the capacity of a liquid before an evaporation experiment in science, or measure how far they can jump in P.E. Another activity that can support children in becoming more familiar with units of measure is to give regular opportunities for estimating, and use these as opportunities to develop the skill of working out an unknown measure by comparing it with a known one. Estimation 180 is a great source of visuals to support this (I blogged about this site here.)
Another common difficulty for children is remembering just how many grams in a kilogram, centimetres in a metre, millilitres in a litre etc. One activity that can support this is by including counting in measures in daily counting activities, alongside counting in whole numbers, decimals and fractions etc. So, for instance, when children are counting in hundreds, also count in steps of 100 grams. I find a counting stick useful for this. Develop skills progressively. So for instance, you might count up first of all from 0 to 1 kg in steps of 100g, moving backwards and forwards along the counting stick. As children become more familiar with this, use different starting points so that they become familiar with what happens after 1 kg. At this point you have a choice of ways to count: 1100g, 1kg and 100g, 1.1 kg or 11/10 kg, and I’d suggest you use all of these ways alongside each other so that children start to also understand the equivalence of these. Doing this will also help enormously when children begin to convert units of measure.
Children often find reading scales challenging too. Again, there is no substitute for practical experience, and if you are able to have analogue scales, measuring jugs, tape measures etc. continually available in your classroom, this can be helpful in making it easier to pick up on opportunities for measurement that arise in other subject areas – a trip to hunt through the maths cupboard will probably make you less likely to do this! The Measuring Scales ITP and Measuring Cylinder ITP can also both be helpful for focused opportunities to practise measuring scales skills. Again, counting can also be useful in supporting reading scales. Most scales are in intervals of 1, 2, 5, 10, 20, 50, 100, 200, 1000 etc. so regular opportunities to practise counting in these steps will help children to use these skills when reading scales.
One of the main problems with children working with measures, I suspect, is that we move far too quickly to working with abstract measures or with diagrams rather than working practically. I’ve been guilty of this myself – practical work involves finding equipment, it can be messy (particularly when working on capacity). But practical work can also be lots of fun and really help children connect their learning to real life situations, so I’d encourage you to do as much as possible.
There are other ideas and resources for teaching measures on my Measures Pinterest board.
My blog this week is not specifically mathematical. Instead, I’d like to share some of the tools I’ve found useful in the classroom. We probably all have our favourites and these are mine. I’d love to hear other people’s favourites too.
My favourite timer is the Classtools countdown timer. This allows you to choose from a great selection of tunes (including the Dr Who theme and the Mission Impossible theme) and timers from 30 seconds up to over 7 minutes. There’s also the option to upload your own tune in MP3 format. Children are often very motivated to tidy up, move to groups, line up in order etc. before the music stops. A large countdown can be displayed on your IWB which adds to the sense of urgency.
My class last year loved this behaviour management system. You can upload your class names fairly quickly and each child will be given an avatar. Later, you can give them the option of choosing a different avatar. Then you can use the system to award both positive and negative points to children or groups of children. You can choose the categories you can award or deduct points for, so for instance you could award points for helping others or good team work, or deduct them for failing to do homework or shouting out. The system keeps track of how many points each child has earned. There is also the option to allow parents access to the site so they can track their child’s behaviour.
Word cloud generators create attractive word clouds from text you input. They can be useful for creating a visual of key words for different topics. Two good ones are Wordle and Tagxedo. Primary English wrote a great blog about different ways to use word clouds in the classroom. For merging together photos or other pictures with a collage effect, Autocollage works very well. Or for displaying pictures on a big scale Block Posters will create large size pictures which you can print off in pieces to put together.
Random Name Generators
Again I like the Classtools version. In this version, you can copy in the names from your class and it acts like a fruit machine and picks one randomly. Class Dojo also has a random name picker option. Of course, there’s always the low-tech standby version of names on lolly sticks too. I’ve also used these in starter activities by eg. listing ways to improve a sentence and then using it to choose one at a time.
There are a number of tools that can be used to create slideshows from your own photos fairly easily, perhaps for a presentation in assembly or an end of topic celebration of learning. I’ve quite often used the Microsoft Live Movie Maker, but Animoto and Photo Peach are also well worth exploring. Some of these have their own bank of music that you can use to accompany the presentations and there is usually the option of importing your own too. One of the best ones I made was a simple but very effective idea for a leaving assembly. I took photos of classes and groups of children, teachers and other staff, governers etc. all waving and then made a slideshow accompanied by Andrea Bocelli’s ‘Time to Say Goodbye’. Although suitable music can usually be bought from itunes fairly cheaply, Youtube have also recently launched a free library of tunes that can be used in this way. You can search these by their mood, genre or duration which could be useful.
Padlet is probably the best known of these. You can quickly create a virtual pinboard and share the link. This can be used, for instance, at the start of a topic to find out what the children already know about it, or for creating a bank of questions to explore. It could also be used for sharing word problems created by children or responses to a challenge. One of my classes used it to share memories at the end of our year together.
There are so many online tools that can be used to enhance our lessons. All of these are very easy to use (believe me, I’m no ICT expert!). I come across new ideas all the time, so I’ve created a Pinterest board which I’m sure I’ll keep adding too. All the ideas I’ve shared on here are on it, together with a few more.