There are many ways of demonstrating to students that measurement and number concepts are connected. Some examples are listed below.
- A linear scale is a number line and is divided into groups of equal size – constructing or interpreting a scale involves skip counting.
- Like counting, metric measures are based on groups of 10, providing a real-world model of base-10 numeration. Every time students use a ruler, they see an example of a unit (centimetre) divided into 10 parts. Money (a measure of value) is also based on groups of 10.
- Measurement can help students to recognise that a group of items can be a whole (for example, 100 centimetres is 1 metre), and at the same time a whole is made up of many parts (for example, 1 m represents 100 cm or 1000 mm). This parallels the concept of unitising in number.
- Measuring temperature provides an authentic context for starting to explore negative numbers.
- Learning how to read an analogue clock can reinforce students’ understanding of “whole” and “fraction”.
- Measurement can help students recognise that a whole is the sum of parts, which is the basis of all part–whole thinking.
- Calculating area and volume provides a reason to use multiplication. Like arrays, calculations of area are based on groups of equal size.
- A measurement is always only an approximation of a quantity (dependent on the accuracy of the measuring tool and the context). For example, when describing a person’s height, we measure to the nearest centimetre, when measuring a field, we use the nearest metre. This introduces students to the concepts of rounding and fitness for purpose.
- Measurement tasks often involve estimation (requiring students to calculate using known facts and/or relationships).
Numbers must come from situations that involve counting or situations that involve measurement. Using numbers derived from measurement ups the level of challenge for students at the same time as it develops and reinforces their understanding of number concepts.
- Counting usually involves small quantities, limiting the size of numbers students work with; measurement typically involves much larger numbers.
- Counted data usually involves just whole numbers and simple fractions; measured data is continuous, requiring the use of fractions and decimals.
As they come across large numbers and continuous quantities, students find they must move beyond counting strategies. There is evidence that delaying this transition may not help number understanding.
It has been suggested by Sophian (2007) that in many education systems there is an overemphasis on counting. Sophian argues that the focus on discrete quantity (i.e. “how many?”) draws attention away from continuous quantity (i.e. “how much?”) and could help to explain the difficulties that students worldwide experience with fractional quantity, which requires co-ordination of both “how many?” (e.g. the numerator) and “how much?” (e.g. the denominator). The NDP data analysis shows that students in the early years of school are using counting strategies for longer than is desirable, according to the expectations conveyed in the curriculum and the national standards (Ministry of Education, 2007, 2009) … The strong emphasis on counting in the NDP may send students the wrong message, resulting in some students being reluctant to move away from counting at any stage because of its proven reliability for solving problems with small numbers.
Young-Loveridge, 2010, page 30
Counting is done by observation – it requires no device (though devices can be used to speed things up for big operations like counting banknotes in banks or votes in elections). Whatever is being counted ($10 notes, people, cars, seats, books, and so on) is automatically the unit.
Measurement always involves a suitable measuring device and unit. The device (and unit) could be, for example: a ruler or tape (centimetre, millimetre, square metre, and so on), thermometer (degree Celsius), clock (hour, minute, second), scales (kilogram, gram, milligram), measuring jug (millilitre), barometer (kilopascal), protractor (degree), or multimeter (amp, milliamp, and so on). Informal devices and units are also sometimes used for measurement, for example: bucket (bucketful), hand (handful), stride (pace).