### Introduction to Measuring Length

I got quite excited about writing this post. Measuring length is a very practical mathematical topic, and so the potential for fun, hands-on maths is endless. I started with the title 'introducing measure' but soon realised that there was too much content for one post. This post, therefore, contains an introduction to measuring length using non-standard units. Posts will soon follow for understanding the importance of units, introducing the standard unit, measuring area, measuring perimeter and an introduction to capacity.

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So much more than using a ruler

Discovering how to measure the length of something for the first time is so much more than learning to use a ruler. In fact, I would strongly suggest not introducing children to a ruler until they are completely comfortable measuring the length and height of objects using a non-standard unit that they are familiar with (such as hand prints, Lego bricks etc.). With no other understanding, using a ruler is a rather abstract, non-intuitive activity - it does not explain measuring length but is just a way of standardising it. Prior to being introduced to standard measure, children should be given the opportunity to investigate and discover the following:

• the language that can be used to describe length
• why we need to measure length
• lots of different methods (or objects) can be used for measuring the length of something
• some methods are better than others for measuring certain things
• if we are talking about the length of something, we need to make sure that we are all measuring using the same thing
If children develop an understanding of the above points, they will really understand why they are measuring length and how to do it. They will then be able to understand the need for a standard unit, and it will be a natural step to introduce the ruler as a useful tool to achieve their new found goal.

Links to other areas of maths

Whenever teaching a topic, I am always looking for other areas of maths to link it to - the more children see ideas in different contexts, the more they will understand and be able to apply them. Learning to measure objects helps children to develop their spacial awareness and can also link to many other topics. For example:
• guessing the length before measuring can help a child's ability and confidence to estimate - an important skill in many areas of maths, including answer-checking.
• when measuring with objects such as Lego bricks, children will be practising their counting and it will help their understanding of cardinal numbers.
• comparing the length of different objects can help children to practise and understand adding and subtracting in a different context to what they are used to. (e.g. how many bricks longer is it? how many more bricks did we use?).
• by comparing different units of measurement, children will develop their multiplying and dividing skills in a practical context. For example, five Lego bricks might be the same length as one hand so if an object is two hands long, how many Lego bricks would it be?
• using a ruler can be linked to tenths and decimals. It can also be compared to number lines and placing such numbers on the number line.
• children can develop their problem solving skills and mathematical reasoning by investigating, ordering, explaining and describing the length of groups of objects.

Tasks for helping kids get to grips with measuring length

The tasks in this post are designed to get children familiar and comfortable comparing the lengths/heights of different objects using non-standard units of measurement. They are very hands-on tasks and, as well as being great for introducing the idea of measuring in primary school, can also be used with much younger children to initiate some practical understanding of measuring things.

Use the correct language to compare/order the length of different objects
Developing mathematical language is vitally important. It enables students to express their ideas and improves their mathematical reasoning. It also enhances their ability to interpret practical questions.

A very simple and effective task is to make (or get the children to make) play dough caterpillars. Alternatively, any set of familiar objects that are long, thin and vary in length (such as colouring pencils or twigs) can be used. Simply ask the children to compare them. They will inevitably start comparing the length and, if they do not automatically do it, they can be encouraged to use the correct language: long, longer, longest, shortest, equal length, etc.

Introduce the need for a unit of measure
There are many ways to encourage children to 'see' the need for a unit of measure - essentially it is about the requirement to be more specific than "it is longer". A very fun and engaging task is to ask the child to pick a caterpillar without showing you and then describe it to you so that you can make one the same.

Ask the child to compare your caterpillars and describe the similarities and differences, again encouraging the use of correct language. The child will soon realise that your caterpillars might both be the same colour, both be long and thin, but that they are not both the same length. Now is the time to ask the child why they are not and how you could make sure that they are next time. This will lead on to a discussion about using the original caterpillar (to compare the length to) when making the new caterpillar. If the child can grasp this idea, then they understand the fundamentals of measuring, as all we really do when measuring something is compare its length to something else (such as a cm). This type of task can be reinforced constantly during many different activities. For example:
• when drawing a house, make sure the two sides are the same length
• if making a butterfly, you want the antennae to be the same length so use the first to measure the second
• when making a football pitch, make sure the goalposts are the same distance apart
Once the child is confident with comparing the length to one unit, move them on to using more than one. Perhaps ask the child to make a caterpillar that is as long as two of the original caterpillars.

Start measuring and comparing objects using a non-standard unit

Introduce the task in a similar way to the previous caterpillar task, but this time using Lego brick towers. Ask the child to compare and describe the towers and order them from smallest to biggest. This time, you can encourage the child to be more specific about the lengths/heights of the towers. Ask the child how many bricks tall a tower is and how many bricks taller another tower is.

Once the child is used to describing the length of the towers, ask them to describe to you how long a pencil (for example) is. The child might not initially jump on the idea of using the Lego bricks to measure it, but a little encouragement should soon see them able to compare the lengths of different pencils using units of Lego bricks. It is now time to send the child on a mission to tell you how long different objects are - their toys, kitchen items, stationary, furniture... anything that you can find! Ask the children lots of questions encouraging them to describe and compare. For example: how much longer is it? would you be able to fit that pencil in that pencil case? which chair is taller? how many more Lego bricks will you need to grow to be as tall as daddy? guess (and then check) how long the rug is? The possibilities really are endless and this is where the questioning can be used to link in to problem solving, estimating, addition and subtraction, cardinal numbers...

Introduce another unit of measure
If you ask the child to measure something that is quite long (daddy's height maybe), you can encourage them to think about how it requires a lot of bricks or takes a long time. At this point, you can have a discussion about whether it would be easier to use something else instead and introduce them to another unit of measure. At this point, I like to use baby Duplo bricks. It strongly links in to what they have already been doing, so you can focus purely on why it is better to use the bigger bricks.

Sometimes it is preferable to use one type of measuring unit over another; the above task should emphasise this to children and therefore help them to be able to extrapolate the same concept to standard units in the future. The task can also lead to really interesting and intuitive activities that require the child to multiply and divide. For example, you can use the smaller bricks to measure the length of a larger brick, and then ask the child how many small bricks they would need to measure a pencil that is two large bricks long. The children can guess and then check. This helps to reinforce their ability to measure length and also gives them a visual understanding of multiplication.

Encourage the child to be specific about units
As well as understanding why and how to measure length and why different measuring units are useful in different situations, it is important for children to understand the need to be specific about what units they are using. I have struggled to get older children to see the importance of putting units with answers, so embedding it at this age can really aid their mathematical (and scientific) progress in the future.

The following is a lovely, simple task that can really help the children to realise why they must state their units. Ask the child to make a play dough caterpillar that is four Lego bricks long. When they are done, compare it to yours (which will be much longer, as you have used the larger Lego bricks). Discuss with the child why you ended up with different length caterpillars, and how you could have made sure that they would be the same. This will encourage the child to always state what they are using to measure it - a very good habit to get into at a young age.

Compare wiggly/diagonal lengths
It is a common misconception amongst children that you simply compare lengths by measuring from start to finish. Although this works in many cases, if the objects are wiggly or at a diagonal, it does not work. For example, many children would think that the blue and yellow lines are the same length, as they both start and finish at the same point. Help children to overcome this misconception by asking them to guess which one is longer from pictures and then getting them to use string or play dough to compare the actual lengths. Highlight the very important fact that the objects must both be straight and at the same angle to compare.

I believe that it is really important for kids to develop a deep and intuitive understanding of how to measure and compare the length of different objects. Children should have lots of opportunity to investigate and practise measuring using non-standard units that they are familiar with and can easily count before introducing them to a ruler. Now children have got used to measuring the length of objects, see how to enforce the importance of units and unit choice when measuring.