At the end of the Second World War, a number of different systems of measurement were in use throughout the world. In 1960, the 11th General Conference on Weights and Measures synthesised the results of a 12-year study and created a new system that was named the International System of Units, abbreviated SI from the French name, Le Système International d’Unités. The SI is the only system of measurement with an official status in nearly every country in the world, with some countries still using different measurement systems, such as the Imperial measurement system used in the UK.

Table 1 shows the units of measurements and some derived units for length, mass, and volume in the two systems:

Table 1. Units of measurements in different measurement systems.

Your child might be too young to learn all of these yet. However, your child will hear these measures being used all of the time in their daily lives. Showing your child how these are used in your everyday life and how they relate to each other (how many centimetres in a meter, how many millimetres in a foot) will help your child develop a full understanding of how and when we use these words. Moreover, you might want to create, with your child, visual resources to support their understanding of measurements in different systems and their relationships (Figure 1 and 2).

Figure 2

Figure 1 and Figure 2. Visual resources to support your child’s understanding of measurements.

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Mathematics is a term that is often used as if it is one thing. However, the Greek origin of the word actually refers to ‘learning or knowledge’ and includes a number of things, including quantity (numbers), algebra (structure), space (geometry) and analysis (change). As such there are a number of concepts that children need to learn.

When it comes to measurement there are two concepts that are often confused: volume and capacity. They are both properties of three-dimensional objects. Three dimensional objects can be a cube, a cone, a cylinder etc.

Volume is the space that a three-dimensional object occupies or contains. For example, the volume of a cube that is 3 cm by 3 cm by 3 cm is 27 cm³ (3 x 3 x 3 or 3³). As you can see in the drawing below it is the space that it occupies.

Capacity, on the other hand, is the property of a container and describes how much a container can hold. So, when we refer to a measuring jug or a glass/ beaker or mug and how much liquid it can hold, we should refer to the capacity of it.

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Have you ever thought about how children represent numbers in their head when they learn to count?

The dominant theory is that numbers are stored along a mental number line, with small numbers associated with the left-hand-side of space and large numbers associated with the right (for languages where one reads from left to right). Just like a tape measure.

When children are young and they learn numbers, the tape measure in their head is not yet very accurate and their idea of how numbers relate to each other might be incorrect. For example, whilst the distance (2) between number 1 and number 3 is the same as between numbers 7 and 9, when asked to place numbers on a blank number line, young children might place 1 and 3 more far away than 7 and 9 (Figure 1).

Figure 1. Line A shows the representation of a compressed number line, typical of young children.

Line B shows the representation of a developed number line.

The more children learn how numbers relate to each other, the more their number line will develop. It has been shown that children who have a firm mental number line are better at manipulating numbers (add and subtract numbers but also multiplicate and divide) and, as a result, they have better mathematical abilities.

For further reading see:

Siegler, R.S. & Booth, J.L. (2004), Development of Numerical Estimation in Young Children. Child Development, 75: 428-444.

http://www.cs.cmu.edu/afs/cs/Web/People/jlbooth/sieglerbooth-cd04.pdf

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