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.
Last week’s #mathscpdchat focused on what we could do to support less mathematically able children. It’s an important issue for teachers. Poor numeracy skills put children at a definite disadvantage in life as outlined by National Numeracy here.
In my experience of teaching less able children, I have often found that one of the main problems is that they have been moved onto abstract methods and thinking too quickly, before they have really got a strong sense of number and good mental images to support their understanding. Pressure to prepare children for assessments contributes to this, but we need to be aware that if we move children on too quickly, we are often trying to build understanding on very shaky foundations and sooner or later the cracks will show.
In last Tuesday’s discussion, we agreed that building up basic number sense was essential. Ideally, this starts to happen in Early Years Settings and KS1 with lots of use of concrete apparatus and representation, but in KS2 and beyond, the use of manipulatives and images remains an important tool in building up understanding. The CRA approach to building understanding is a good one to bear in mind. We start with Concrete apparatus, move to Representation when children are more confident and finally to Abstract when children have a firm grasp of what is happening, linking each step to the previous one.
I’ve found ten frames and Numicon particularly useful for helping children to build their number sense, but Cuisenaire, multilink and Base ten equipment can all be helpful too. Another way of building this is by regular use of dot talks in the lower years of primary and number talks at higher levels. In dot talks, children are presented with a pattern of dots and asked to work on their own to calculate how many dots there are in all. Then the class or group discuss the different ways they worked this out. This helps children to see different ways of breaking up numbers. Number talks work similarly. Children are given a calculation and initially work on their own to solve it. Then the class discusses the different approaches. Again this helps children see that there can be multiple approaches to the same problem and that no one way is the ‘right’ way. They may also start to see connections between the different approaches.
@School-LN reminded us of the importance of making connections, and suggested an interesting way of helping children to do this. Children are given sets of numbers, shapes or bar charts, for instance, and asked to sort them into groups and then explain their choices. For less able children, maths can seem to be a lot of disconnected facts and procedures that they have to learn, but if we can help them to make connections, they start to realise that there is much less to learn than they feared. @PGCE_Maths suggested the report ‘Deep Learning in Mathematics’ which is well worth reading and argues the case for focusing on connections and relationships in maths rather than technical procedures.
@Janettww had some experience of using 3 act maths lessons, where students devise their own questions before attempting the maths and has found it very motivating for students at all levels of ability. This seems to be something that could really promote mathematical thinking.
@bm332 also raised the important issue of classroom climate. Many students really lack confidence and it’s important that they feel able to speak up when they don’t know or don’t understand something; @Maths4ukplc also pointed out that mistakes need to be valued as learning opportunities.
So altogether, lots of food for thought and lots of good ideas. The complete record of the discussion can be found on the NCETM site here and I’ve also put together a pinterest board which includes some of the resources mentioned together with some other ideas.
Have you ever had the experience of looking for a household object, knowing you’ve seen it somewhere but unable to remember where, then finding it in a place that you walk past several times a day? If things are there long enough and we don’t make use of them, they become ‘wallpaper’ and we often stop noticing them altogether.
Unfortunately classroom displays can suffer from the same fate. We can spend hours in the Summer holidays putting up impressive displays, but if we don’t ever refer to them, sooner or later our children will stop noticing they’re there, let alone making use of them. This is where working walls should come into their own. The idea of a working wall is that it should be full of things that will support children’s learning and help them to learn more independently. They should be constantly changing to match our current topic. I appreciate this can be difficult to achieve in the life of a busy teacher and so my top tips for saving time would be:
- Keep things simple – there’s no need for triple mounting and laminating (unless it’s a resource you will use again and again), as long as it’s legible and clear.
- Keep everything – devise a system for filing away your resources so you can dig them out next time you teach this topic. I usually keep things in folders labelled by topic.
- Make use of printable resources – lots are available from sites like Teacher’s Pet and Communication4All.
- Get the children to help – independent or homework tasks could include making posters about your current topic, showing how to use a method or illustrating some new vocabulary.
What should be included on a working wall? This might vary according to the age of your children, but might include:
- Vocabulary related to your current topic (the very useful Cheney Agility Toolkit has this editable word wall which you could use)
- Relevant models and images
- Worked examples of methods – these can be screen shots from your whiteboard or photocopies of children’s work
- Problems and challenges – make these interactive if possible, perhaps by children responding on sticky notes (Nrich have some good posters that could be used for this)
- Number lines or washing lines related to your current learning (eg. lines counting in hundreds or in decimals or in multiples of 2)
- Examples of children’s work (What A Good One Looks Like)
- Real life examples of your current topic (again this is a good task to give for homework – ask children to look for eg. examples of circles, or bar charts or timetables and bring them in)
- Photos of children working on practical tasks
- Practical resources that children can use (eg. mirrors, hundred squares, number lines etc.)
- Success criteria
Whatever you include, make sure you refer to it often and wherever possible refer children to it when they need help.