### Why teach measurement?

- Measurement tools and skills have a variety of uses in everyday life. The ability to use measuring tools, rulers, thermometers, scales, and to estimate with these tools are necessary skills that enable us to quantify the world around us. They can tell us how tall we are, how hot we are, how much we drink, how heavy we are and how far it is from here to there. Basic measures of distance and time allow us to calculate speed and acceleration and ultimately tell us how fast we need to project a rocket to allow it reach the Moon, and how populations change and grow.
- Measurement is important in providing links between strands of mathematics. For example, it provides a rich and meaningful context for the use of number skills and of spatial concepts.
- Measurement also provides links between mathematics and other school subjects. Measuring skills, especially estimating, have an important place in many games and sports. In addition to being required in many science investigations they also play a part in some artistic and musical experiences.

### Overview of the measurement process

An analysis of the process of measuring suggests that there are five successive stages. Students learn to measure by first becoming aware of the physical attributes of objects and therefore perceiving what is to be measured. When students have perceived a property to be measured they then compare object by matching, without the use of other tools of measurement. This comparison leads to the need for a measurement unit. Initially the unit may be chosen by the student from everyday objects. The use of informal or non-standard measuring units leads to the need for standard units for better precision and unambiguous communication.

This sequence is quite general and can apply to the measurement of any attribute. In fact, we believe that one of the broad aims of teaching about measurement is to help students develop an overall picture for coping with any measurement situation.

#### Learning Sequence for Measurement

- Identifying the attribute

The first step in the measuring process is understanding that objects have attributes that can be measured. Initial experiences are needed to develop awareness of the attribute and to introduce the necessary language, for example, big, heavy, tall, empty. The students need lots of opportunities to manipulate the attribute being explored and to discuss these experiences with others. Considerable time may have to be spent on these experiences to allow the student to become aware of what can be done to an object without changing the quantity of the attribute that is being investigated (this is often described as

*conservation*of measure) . For example, does the length of the pencil change when it is moved? Does the volume of water change when it is poured into a different container? - Comparing and Ordering

When students are aware of the attribute being investigated they should be given opportunities to compare different objects. Adults realise that to say something is "long" does not have a lot of meaning. "Longer than what?" is a usual response. Students need also to discover that they cannot make themselves clearly understood unless a descriptive term compares two or more objects. For example, "My pencil is longer than yours."

Activities for comparing two objects lead to activities for ordering or seriating 3 or more objects.

Comparison activities are a measurement process in their own right in that adults often measure in real life without using units. Direct or indirect comparisons often provide the information that is required. For example, using your own height to check if there is space for the fridge.

- Non-standard units

Some form of unit needs to be used if a question such as "How much longer is your pencil than mine?" is asked. Non-standard units are ordinary objects which are used because they are known to students and are readily available, for example, paces for length, books for area and cups for volume. Students should be provided with many opportunities to measure using these kinds of non-standard units. Non-standard units introduce the students to the use of units to provide numbers that describe a measure outcome, for example, the desk is

**4**handspans across. Non-standard units introduce most of the principles associated with measurement:Measures are expressed by counting the total number of units used.

During a measurement activity, the unit must not change.

Units of measure are not absolute but are chosen for appropriateness. For example, the length of the room could be measured by handspans but a pace is more appropriate.

Prior to introducing standard units, students need to realise that non-standard units tend to be personal and are not the most suitable for communication. For example, my hands are smaller than yours, so telling me to measure a piece of cloth three hands wide may not be useful.

- Standard units

Standard units have been created to allow consistency and communication of measures. The standard units used in New Zealand are the metric units.

Appropriate learning experiences are needed to allow students to become familiar with the quantity involved in each unit, the correct language for naming each unit and the conventions for writing measured amounts using approved symbols. Students then need much practical experience in using measuring, using measuring devices, in making estimation of quantities in real-world situation and in mastering equivalence between units.

- Applications

When students are comfortable and efficient in measuring and estimating using appropriate standard units, learning experiences can be directed towards applications of measurement and to the use of measurement formulae. For example, simple measurement formulae may be developed and used to generalise methods for calculating areas, volumes and perimeters.

With a couple of exceptions (time and angles) the units used in NZ schools are those of the International System of Units (SI units) which is a comprehensive and practical system of units of measurement of all physical quantities for technical, scientific and general use.

SI Units used in school measurement

Length | metre (m) |

Area | square metre (m^{2}) |

Volume | cubic metre (m^{3}) |

Mass | gram (g) |

Time | second (s) |

Non SI units

Time | minute (min) hour (h) |

Angle | degree of plane angle (^{O}) |

Temperature | degree Celsius (^{O}C) |

For more information on the progression of mathematical learning in the Measurement strand you may want to try the Measurement Curriculum Exemplar. Note that while the progressions shown in the exemplars are still valid, their links to curriculum levels and AOs relate to MiNZC (1992) rather than to NZC (2007).