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.
‘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