Digging Deeper into … Length (all classes)
Category : Uncategorized
Initial exploration of Length
Initial experiences of length in the infant classes should occur through exploration, discussion, and use of appropriate vocabulary eg long/short, tall/short, wide/narrow, longer, shorter, wider than etc. The children should also be enabled to sort, compare and order objects according to length or height.
The Aistear Play suggestions in the Operation Maths TRBs for Junior and Senior Infants (see example above) provide very useful ideas that can be used as the basis for purposeful exploration and discussion, for example, in the case of the garden centre-themed suggestions above:
- What plant/tree is taller/shorter?
- What gardening tool is longer/shorter?
- What plant pot/row of plants is wider/narrower?
Concrete-based exploration should follow and initial questions and discussion, to include direct comparison of the length of two objects, labelling them as long/short and/or longer than/shorter than etc. This can then progress to incorporate a direct comparison of the length of three or more objects, to now also include the labels longest/shortest. It is important at this stage that the children realise that if A is shorter than B and B is shorter than C, then, without further direct comparisons, we know that A is shorter than C, that A is the shortest of all three and C is the longest. This is a very important concept for the children to grasp.
Non-standard and standard units
Children in senior infants should begin to estimate and measure length using non-standard units of measure, such as lollipop sticks, straws, pencils etc. Non-standard units are specifically chosen, as opposed to the standard measures of metres and centimetres, as most objects that the children will choose to measure will be longer than 10cm, therefore outside the number limit of senior infants. Furthermore, the metre is almost too big a unit for them to work with at this stage, since the heights of many children in senior infants would be less than this. It’s difficult to develop a sense of a metre when it’s bigger than yourself! Whereas lollipops, straws etc are not too big nor too small for their hands and easier to work with. The children could also use a whole ruler as a non-standard unit in itself e.g. “the table is three rulers long”.
When the children have had some experiences measuring they should then be afforded the opportunity to choose which instrument is most appropriate to measure the length/height of various items. In this way, they start developing the notion that while many approaches can be taken, some are more efficient than others, and the most efficient approach will also depend on the target object being measured. This is the same as the Operation Maths approach to operations throughout the classes; there can be many approaches and some are more efficient than others, depending on the numbers/operations involved. The aim is for the children to become accurate, efficient and flexible thinkers.
Children in first and second classes should also be afforded the opportunity to explore non-standard units of length prior to being introduced to the standard units. Historical non-standard units can be introduced also eg spans, digits, cubits, strides etc. Work using these measures will not only encourage the children to appreciate the need for standard units, but once they are introduced to the metre (first class) and the centimetre (second class) they should also try to identify which non-standard units are closest to the standard units, eg the child’s stride or arm span is often close to a metre and their digit is close to a centimetre (quick investigation for second class: the width of which of your fingers is closest to a centimetre?). Connecting these standard units of measure back to the children themselves helps them identify with the measure and helps them internalise a sense of its size.
Estimating & measuring
The children should always be encouraged to estimate before measuring. And rather than estimating the length of A, B, C and D before measuring A, B, C and D, it would be better if the children estimated the length of A and then measured the length of A, estimated the length of B and then measured the length of B and so on. Thus, they can reflect on the reasonableness of their original estimate each time and use this to refine their next estimate so that it might be more accurate. As mentioned previously, the child’s ability to connect standard units of length to themselves, not only helps them internalise a sense of length, but to also use this sense to produce more accurate estimates.
While the children begin using cm rulers in second class to measure length, they can still struggle to measure objects accurately in both this class and higher classes. Videos, such as the one below can be a useful way to demonstrate this skill to the whole class.
When children are performing tasks that require them to measure longer lengths (eg of the blackboard, the length of the room etc) using rulers or metre sticks, remind them to make sure that there are no gaps between their measuring instruments, that they keep them in a straight line and that they do not overlap. It can also be useful, if available, to use two metre sticks/rulers together so that once the second one is placed at the end of the first, the first ruler can then be moved to the end of the second ruler and so on.
Renaming units of length
From third class on, the children will be expected to rename units of length appropriate to their class level. While changing 136 cm to 1m 36cm or 1.36m will typically be done correctly, converting figures which require zero as a placeholder (eg 1m 5cm, 2.4m ) are quite often problematic and can reveal an underlying gap in understanding, that is not revealed by the more obvious measures. In these cases, the children should be encouraged to return to the concrete and pictorial experiences as a way of checking the reasonableness of their answers, eg:
- “2.4m equals 240cm because 1m is 100cm (point to an actual metre stick) and then 2m is 200 cm and .4 is nearly .5 which is half of a metre which is almost 50 cm”
- “1m 5cm…well 1m is 100cm and then there’s 5cm more so it’s 100 plus 5, which is 105cm.
T-charts, one of the three key visual strategies for problem-solving used throughout Operation Maths, can be very useful when renaming units of length, as can be seen below.
Perimeter and area
In Operation Maths, perimeter is deliberately taught separately from area; these topics are better taught independently because children can often confuse the concepts and processes of measuring area and perimeter.
Rather than introducing perimeter via a formula, it is critical initially that the children understand perimeter as the distance around the edge of a 2D shape and that they should actually measure around various 2D shapes as a way to identify the perimeter. Then, as they begin to look for more efficient ways to do this, they should be encouraged to discover and explain how they might calculate the perimeter of various types of shapes.
Scale drawing is introduced in sixth class. Encourage the children to experiment with drawing rooms, houses or gardens to scale. This may be integrated with map reading or making maps in geography.
T-charts, once again, can be very useful when exploring scale. For example, see how a t-chart can be used to help answer the question, below:
When the children are making scale drawings themselves, or when they are solving problems such as those above, it can be useful to use a t-chart to set out some benchmarks measures for reference:
A fun way to extend scale drawings, and to integrate maths with visual arts, is to do scale drawings of a simple cartoon or line drawing, with the finished scale being larger than the original eg 1:4. This slideplayer presentation could be used for inspiration.