As a new term begins, one of the topics we tend to cover early in term is Place Value. An understanding of this is central to understanding our number system and underpins most written calculation methods, so it’s something that is well worth spending time on. In my experience, there are two approaches that really help to build children’s understanding of place value: using concrete apparatus and representations; and regular use of counting in a structured way.
Concrete apparatus and Representation
Base ten equipment, such as Dienes, is commonly found in KS1 classrooms and I would love to see it more widely used in KS2 too. Working with this helps children to visualise the tens and ones (and later the hundreds and thousands) they are working with and see how they relate to each other. The Gordons ‘Dienes and Coins’ program has lots of ways of using Base ten equipment virtually too. This program also gives similar activities with coins, and coins are another good way of exploring place value with children – giving it a context which they may already be familiar with. Don’t forget too that fingers usually come in handy sets of ten and for whole class work, building numbers using several children holding up all their fingers as tens and one child holding up as many fingers as needed for ones can be a good way of building two-digit numbers together. When children have had some experience of exploring place value with concrete apparatus, place value arrow cards can be very useful in relating this to written numbers. The Gordons ‘Place Value Chart’ program links these to place value charts which again can be helpful in moving understanding on.
Regular use of counting in a structured way really helps to build children’s understanding of the way the number system works. Again, it’s something that tends to happen a lot in KS1 classrooms but perhaps not so much in KS2. Counting supports so many different areas of maths, but to build place value understanding, it’s particularly important to get children counting in steps of 1 and 10, and later in steps of 100, 1 000 etc or in decimal steps of 0.1, 0.01 etc. Make sure that you count up as well as down and as confidence grows, you choose lots of different starting points, particularly focusing on counting which involves crossing the tens or hundreds boundary (or whatever boundary is appropriate to the stage you’re at). With younger children, make sure you don’t stop at 100 when counting in ones. It’s amazing how many children, even in early KS2, I’ve heard count … 107, 108, 109, 200! When children are confident in counting in tens or ones, mixing the two can be an extra challenge. One activity I’ve used with different age groups is to give children a starting number and get them to watch me crossing the front of the classroom. When I take a small step forward, they count up in ones, when I take a stride, they count up in tens; and similarly for stepping backwards. This can of course be adapted for different step sizes. When children are working with decimals, the ‘Decimal Number Line’ ITP can be very useful in helping them see the way that decimal numbers fit together. It gives a number line counting in ones, tens or hundreds and then allows the user to ‘magnify’ one small step to see what happens within this step. This can then be repeated to make the steps even smaller. Using a counting stick can help children visualise the steps they’re counting. Having number lines around the classroom counting in different steps can be helpful, as can ‘washing lines’ of numbers where children can order the numbers or spot numbers that are missing.
Moving Understanding On
Once children have an understanding of our number system, they are often fascinated by really large numbers and enjoy writing these in digits and then ‘translating’ this into words or vice versa. Nrich have some place value related challenges for KS1 and some for KS2.
There are more ideas for teaching place value on my pinterest board.