### Measuring Length - the importance of units

In a previous post I discussed how to introduce the idea of measuring length to young children. The post explored the use of non-standard units (such as Lego bricks), with a particular focus on how and why we need to measure things. In this post I continue with non-standard units, this time demonstrating the importance of unit choice when measuring length. I will evaluate important points to consider when introducing the idea of units, and give some practical, discovery-based task ideas to help provide a deep understanding.

Units may, at first thought, seem like a dull topic that deserves a mere mention when learning about other aspects of measuring. However, units are vitally important and, unfortunately, all too many learners continue to neglect and misuse units throughout their school careers. Units come up again and again in maths, science and other subjects and failing to understand the importance of being consistent and specific with units can lead to great difficulties.

There are four key points to consider when introducing units, and they are listed below. They may seem obvious, or reiterations of the same point, but remember that we are teaching this to young children who, up until now, have had no concept of using units to measure the length of objects. We must help them to discover the usefulness of units and the link between how large each unit is and the number of units required for measuring.

1.     It is important to be specific about units
2.     The number of units you need to measure an object depends on the size of the unit itself
3.     If you build/draw something that is a certain number of units, the size will depend on what unit you are using
4.     Some units may be preferable to other units when measuring a specific object.

The Importance of being Specific about Units

We could just tell children that units are important and that you must be specific. Some might even believe you - but they won’t all remember. However, if you get children to discover the importance for themselves, they are much more likely to digest just how important units are and will therefore remember and understand units throughout their school career.

A nice practical example of this is to get children building. Perhaps with Lego bricks, or maybe using cardboard (though more difficult to measure at this stage). Divide the children into two teams and get them working on different parts of the same project. Maybe one team can build the walls of a house, while the other team builds a roof. However, they are not allowed to look at what each other is building until they are done. Tell them that the house should be "3 by 3" in size, and let them decide for themselves what "3" means with a little help from you to make sure that they interpret it differently (e.g. one team could use 3 hands, the other could use 3 large Lego bricks).

When they are done, try putting the roof on the house and you will find that it won’t fit (because you have secretly made sure that it won’t). Talk to the children about why it doesn’t fit and how each team interpreted the “3” to mean different things. Have a discussion about how it would have worked if both teams had been using the same ‘unit’ to measure the "3". You could then get them to complete each other’s houses using the correct units.

Doing a practical example like this is fantastic for getting children to really appreciate why we bother measuring things and why we have units. It also really highlights the importance of making sure that you are specific about units.

Check out the start of our video – a space ship goes bang because one child used small Lego bricks whilst the other used large Lego bricks to measure an important part. This leads into a successful lesson on appreciating the difference between different units.

Different units give different results

Again, this may seem obvious, but research ('Children's Understanding of Mathematics: 11-16' ) has shown that many students (including those of secondary school age) do not fully understand the fact that the number of "units long" an object is depends on the unit that you are using to do the measuring. Instead the child focuses on the number and 'completely ignores the unit used to measure'. This is an important aspect of measuring length and grasping the concept at a young age can make future length conversions easier when considering standard units. It will also aid with the ability to estimate lengths and to check whether or not answers are sensible.

To help children discover and understand this concept, there are many simple and practical tasks to employ. One example is to give the child a few piles of different objects. For example, you could give them a pile of paperclips, a pile of multilink cubes and a pile of lolly sticks. Then give them something to measure with each of the different units – maybe the length of their hand from their wrist to the tip of their middle finger. Get them to record the results in a table. You may have to help them with this, encouraging them to line the measuring units up properly and helping them to understand the table. It would help if you have already done some work on how to measure things using non-standard units. Once the child has finished measuring their hand, you can ask them to measure more objects with each of the units, recording their results in the table. Below is an example table.

 Object Paperclips Multilink Cubes Lolly sticks Hand 6 8 2 Foot 12 16 4 Pencil 15 20 5

After the child has measured three or four objects, talk about what they noticed. Encourage them to think about how many of each of the units they needed each time and the fact that they always needed more paperclips than lolly sticks. Ask them to think about why this was so, and lead them towards thinking about the fact that if the measuring unit is larger, you won’t need so many of them.

This task gives children a really good, practical sense of the fact that different sized units will give a different answer for an object that is the same length. This will help to reinforce the fact that units are important.

As an extension, you can ask the child to answer some comparison questions and do some estimation. For example, questions such as "I have a pen that is 12 paperclips long, how long is it using lolly sticks?" leads children to think about the fact that 12 paperclips will always be the same as 4 lolly sticks - it does not follow that the pen will be 12 lolly sticks long because it is 12 paper clips long. You could also ask them questions such as "daddy’s foot is 30 paperclips long, can you guess how many multilink cubes this would be?". This is a hard question and strongly links to ratio - something that is probably beyond the current level of children being introduced to non-standard units. However, children are often surprising in their logic and practical reasoning skills if allowed to investigate. They will probably be able to make a good guess, and may even be able to come up with the correct answer, especially if allowed to use paperclips and lolly sticks to work it out.

Using the same number of units that are different sizes will produce different results

This strongly links to the previous point, but it is not always obvious to young children. However, it is a relatively easy concept for children to grasp, especially if allowed some practical experience. You could simply give children different units to measure with (paperclips, multilink cubes, lolly sticks) and ask them to make play-dough caterpillars that are five units long using each of the units. Once they have made their three caterpillars, ask them to compare the lengths. Encourage them to think about why they are all different, even though they used three units each time.

You can then ask them to make the longest possible caterpillar that is only four units long. This will encourage them to think about the fact that the biggest unit they have will produce the longest caterpillar. Then ask the child to make the shortest caterpillar possible using six units. Again, this encourages the child to think about the possible lengths of caterpillars in terms of the length of the measuring units themselves.

Some units are preferable to others

If you ask the child to measure something that is quite long using a relatively small unit of measurement (maybe the length of the room using their hands) you can encourage them to think about how it requires a lot of hands and takes a long time. At this point, you can have a discussion about whether it would be easier to use something else to measure with instead and encourage them to choose another unit of measure. Hopefully they will choose a larger measuring device, such as a stride or a long stick.

Equally you could use a relatively large unit to measure something small and talk about how it isn't very useful - if you wanted to equate the length of two short objects but both were about half a stride long, it is not easy to compare. However, if you know that one is four hands long and the other is five hands long you have information that is much more useful and comparable.

It is also worth discussing with children why some units might be preferable to others if you are describing the length of an object. For example "if you tell someone over the phone that your new toy car is 5 hands long, why will that not be useful?" Encourage the child to think about the fact that the size of their hand is unique and different to the size of the other person's hand. The person on the other end of the phone can therefore not measure the length of the car, as they have nothing the size of the child's hand to measure with. You could link this in to a cultural theme by using a 2p coin to measure something and discussing why that would not be useful to someone in India. This will highlight the fact that it is more useful to use a unit of measurement that is readily available to everybody and is a nice lead into introducing standard units.

Sometimes it is preferable to use one type of measuring unit over another; the above tasks 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 unit to measure the length of a larger unit, and then ask the child how many smaller units they would need to measure something that is two of the larger units 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 and ratio.

As children progress through school, they will be asked to complete lots of problem solving questions in maths and other subjects. These often involve some form of measurements. If kids can gain a deep and intuitive understanding of measurement and units at a young age, they will more easily be able to appreciate the importance of units when solving these problems. The process of learning units should be fun and investigative, allowing them to discover for themselves why units are so important. Up to this point children will have some understanding of the physical act of measuring. A thorough exploration of units in the classroom can demonstrate how they can measure things in a way that is more useful to themselves and to others that they may share their measurements with.

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