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.
‘Explore MTBoS’ is a series of challenges put together by a group of experienced maths education bloggers to help those of us with less experience to find our way around the world of maths blogging. I’ve found it a useful way of finding other people who blog about maths teaching and have already encountered lots of new tools to explore and ideas to reflect on. This week’s challenge was to engage with some collaborative sites and although I was already familiar with some of these, many were completely new to me and well worth exploring. I’m sure I’ll be coming back to them.
One that really caught my attention was ‘Estimation 180’. This is a site put together by Andrew Stadel who teaches middle school maths. He has posted hundreds of estimation challenge pictures which could be used as starter activities to lessons. There is a handout that can be used to keep track of estimations over a period of time. Students are encouraged to give an estimate that is too high, one that is too low and then their best estimate. Importantly they are also asked to explain their reasoning, based on contextual clues or pre-existing knowledge. There are lots of ways of using the challenges. Students can submit estimates online and explore the answers that others have submitted and their reasoning. They could fill in the handout each day and keep a record of their estimates. Or the challenges could just be posted up by the teacher at the start of each lesson. The challenges are varied – estimating heights and weights, number of objects, ages etc. and often build from day to day so that the answer to the previous day’s challenge can inform today’s estimate. Key to using this effectively would be giving students the opportunity to explain and share their reasoning. Sharing strategies and approaches could make a valuable contribution to building number sense. I like the fact that many of the challenges involve measures as I often find children find estimating these particularly difficult.
The site is a very useful resource because estimation can be a tricky skill to teach. Give children a typical sheet with pictures of objects and ask them to estimate and then count, and all but the most compliant will probably sneakily count first then make their estimate very close to the actual count (and the reasons why they are so reluctant to risk a wrong answer will probably make a whole new blog some time soon). I’ve found the Primary Strategies Estimation Spreadsheet (shown above) useful as it can be used on an IWB, and the stars can be shown and quickly hidden before the children have a chance to count them. It can be downloaded here. Another interesting looking site is the ‘Guess It’ game on the Problem Site. This gives children a series of estimation challenges by showing dots of different sizes and colours. There is a timer which can be used to adjust the number of seconds the dots are shown for.
I also like the idea of having an Estimation Station in the classroom, a transparent container that is regularly filled with small objects. Children then estimate how many objects are in the container and strategies are taught and compared. Looking at the price of the Amazon one though, I think I could probably come up with a cheaper alternative!
Some of the resources I have mentioned in this blog, can be found on my Number Pinterest board
I’ve just completed the excellent open access ‘How to Learn Math’ course led by Jo Boaler (author of ‘The Elephant in the Classroom’). There were lots of ideas to think about on the course and lots that I’ll want to revisit and mull over in the coming days and weeks. For a more detailed overview of the course, Pam O’Brien has written a helpful summary.
One of the big ideas is that children learn maths best by exploring real problems with a context rather than learning and practising routines. This, I’ll admit is a challenge. I really warm to the idea of exploring maths in context and feel that embedding maths in cross-curricular work is something we’re not at all good at as teachers. I also love the idea of children exploring problems and challenges for their own sake rather than as opportunities to use and apply their mathematical skills. However, there is a more ‘old school’ part of me that feels that it’s important for children to acquire fluency in calculation skills and fairly rapid recall of number bonds and tables facts. Boaler points out that these skills are not what real maths is about and I agree with her there, and I’m sure there are examples of real mathematicians who struggled with basic arithmetic. However, I do feel that having these facts and skills at their fingertips is for most mathematicians, part of their ‘toolkit’ of mental resources. That’s not to say that other attributes aren’t even more important – confidence, perseverance and curiosity all spring immediately to mind. In the real world of education too, both the current and the new curriculum require these skills and I have no doubt that children will continue to be tested on them for the foreseeable future, so as teachers we need to think about how we can help children acquire them.
What I’m not saying here, is that these facts and skills should be taught in isolation. Boaler is keen that children build up a conceptual understanding of number and mathematical skills and I would absolutely agree with her on this. There is little point in children acquiring rapid recall of number bonds and tables if they have little or no idea of what it means to add or to multiply. Before learning any number facts, children need to be building up a good ‘number sense’, a feel for numbers and how they can be manipulated. For a child without this understanding, ‘3 + 2 = 5’ is a fact to be learned in isolation. Whereas for a children with good number sense, they may visualise a group of 3 combining with a group of 2 to make a group of 5; they may use their knowledge of doubles facts to work out that the total will be one less than 6 or one more than 4; or they may be able to use this fact to derive lots of other related facts: 5 – 2 = 3 or 30 + 20 = 50.
Building up number sense needs to be an ongoing process throughout primary education, and probably well beyond. We can help children to do this in lots of ways but one of the key ones is by giving children lots of opportunity to explore the way numbers work using concrete apparatus and helpful representations before plunging into the more abstract world of numbers in isolation. This might be by using dedicated mathematical equipment: counters, Dienes, Numicon, multilink, ten frames etc. Or it might be by using the opportunities that occur every day: counting the steps as we walk upstairs, working out how many cakes will be left if we each eat one, combining our pennies to see what we can buy at the sweet shop etc. This brings us back to exploring real problems with a context. It would be great if this was happening naturally at home for all our children long before they ever got to school, and for many I’m sure it is. Creating opportunities in school for this to happen is something that I suspect EYFS teachers are already very aware of, but perhaps it’s something for the rest of us to be challenged by as we plan our classroom environments and cross-curricular work.