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.
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.