| Teaching and learning Measurement | Measuring equipment used in schools | Activities | The language of measurement |

The measurement topics covered on this CD-ROM extend well into secondary school level. However both primary and secondary teachers need a firm grasp of these topics. Many secondary level concepts arise, if only in an informal sense, in primary school.

Teaching and Learning Measurement

Here is a framework for teaching and learning measurement from the early years.

 The PLACIFIER framework Play (structured exploration) Language Attribute awareness Comparisons Informal units Formal units Interrelationships Estimation Real applications

PLACIFIER is a useful reminder of the nature of activities for measurement teaching. It is not meant to be sequential. Not all aspects would be included in every lesson nor in the teaching of every concept. Some aspects only apply to the early years. At times you will cycle back and forth through various aspects. 'Language' and 'Real Applications' have a role at each stage of development.

Elaboration of the Framework

Children develop an awareness of the concepts of quantities (attributes), including under what conditions an attribute is conserved, through structured exploration. Structured exploration to develop an awareness of an attribute needs good choice of contrasts and similarities. Developing awareness of volume, for example, will require objects with the same volume, but differing on other attributes (e.g. height, shape, mass) and objects differing in volume but with the same height or length or mass or general shape.

Discussion during activities is crucial to introduce and then use the necessary vocabulary.

Attribute awareness is reinforced by comparing objects on one or more attributes, eg. length and/or mass, and the simultaneous development of associated language. Both direct and indirect comparison activities should be undertaken.

Most of the principles of measurement can be developed using non-standard units, including the fundamental principle that the number of units that matches the given property can be used, with the unit, as a valid description (measure) of that property. Another important principle that can be developed through nonstandard units is that if the unit is smaller, the number of units measuring a given object is greater.

Experience with comparison and nonstandard units can precede formal or standard (ie common) units. Once proficiency in measuring using the metric system is established, appropriate interrelationships between attributes can be investigated and used for calculations. For example, length is used to find the area of a rectangle.

The goal of all measurement is competent application of measurement concepts and principles in real-life situations. Measurement derives its sense from practicality so an emphasis on pen and pencil activities is inappropriate. Applications begin in the early primary years - they are not left until later.

Real-life measurement situations often involve estimation. The selection of appropriate measuring tools and units is an important aspect of estimation in practice.

Progress in developing measurement skills is dependent on the development of prerequisite number and computation skills.

 Using the PLACIFIER framework It is important that teachers understand how to use the PLACIFIER framework, if they choose to do so. Not every aspect is in every level. For example, a unit on Length at Year 3 level would not start with a "play" session to develop an "awareness" of the attribute of length, nor would the unit need to include the earliest direct "comparison" of two objects to find the longer/shorter. It would be expected that students in Year 3 understand the concept of length and that they have been engaged in lots of activities using concrete objects, such as, finding 3 objects that are the same length as the book and the block etc. At Year 3, measuring length could be the focus. Whilst some students might be measuring with nonstandard units (e.g. the line is four pencils long) the others will be using standard units, such as centimetres. These students would not be ready to work on calculation of area, so the "real applications" would not be using dimensions in an abstract way to calculate area. Instead, length measurements would be used to predict answers to real length problems: e.g. how much string do I need to hang up the decorations made by everyone in our class - will I be able to hang them all along the back wall?

(The PLACIFIER mnemonic was derived from one used by Lola Hill of Deakin University.)

Measuring equipment used in schools

There are numerous pieces of equipment which can be used in measurement activities in the primary school. We have listed some ideas below.

Early primary years

 Time clock faces, clock stamps, time lotto, digital and analogue clocks Money money stamps, play money, money lotto, money Length tapes, measuring sticks, trundle wheels, Cuisenaire rods, unifix Volume and capacity litre containers, everyday containers, MAB pieces Area tiles, coloured paper squares, MAB Mass balance, bathroom scales

Middle and upper primary years

 Time stop watch, tockers, egg timer, clock dominoes, clocks and watches Length depth gauge calliper, graduated calliper, tapes, metline - graduated line, rulers, trundle wheels Area area dominoes, tiles Volume volume dominoes, cubes, MAB pieces Capacity litre: cylinder containers 25 ml - 2 l, measures 1/3 - 1 cup Mass kitchen scales, balance - plastic, spring balances, metal weights, plastic weights Angles protractors - set, clinometer, protractor - large

Secondary years

Similar equipment as in upper primary and more precise equipment is used. Scientific instruments now often have a digital display.

Activities

Generally, activities can be sequenced from those where concrete materials are used in a direct way (early primary) to activities where a mixture of concrete materials and pictorial or other representations are used with indirect comparison using units of measure, both nonstandard and standard (middle primary). Activities finally move towards the abstract (later primary and secondary), e.g. given the dimensions of a cube, find the volume.

It needs to be noted that even at later primary and secondary levels, students will still be working with concrete materials at times.

 A cube of 1 m3 made in the classroom (Annie O-Mahoney kindly gave us permission to use this picture)

An emphasis in all activities at all levels would be on language, from the earliest levels, with 'bigger than', 'smaller than', to later levels with the more complex language of comparison, e.g. 'this is three times as long as.'

Examples of activities at the different levels, early (early primary), middle (middle primary) and late (late primary and secondary) could be:

Length

 Early: Cut a short and a long piece of ribbon. Middle: Measure the length of the two tables to find which is longer and by how much (using either nonstandard or standard units). Late: Find the total length of 4 pieces of ribbon which measure 42 cm, 1m 60cm, 0.75m and 1.4m.

Area

 Early: Cover a large sheet of paper with shapes, making sure there are no gaps. Middle: Use small tiles to cover 2 rectangular pieces of card. Which is larger? Late: The table measures 2m by 1.5m. What is the area?

Perimeter

 Early: Build a fence around the farm animals. Middle: Select a book from the library. Put unifix blocks around the edge. Remove the book. How many unifix did you use? Find something else with the same perimeter. Late: Draw as many rectangles as you can that have perimeters of 12cm.

Volume and Capacity

 Early: Fill a jug with water. Find 2 containers that will hold this water. Middle: How many cups of water will it take to fill the jug? the bottle? Which has the greater capacity/volume? Late: Use the dimensions of the square prism to find the volume in cubic centimetres.

Mass

 Early: Use pan balances to find materials to balance your shoe. Middle: Find 6 things that together weigh one kilogram. Late: Find the total mass of 4 packets of flour each weighing 1.5kg.

Time

 Early: Sequencing ­ draw pictures to show what you did on your excursion. Middle: Move the hands on the clock (small model for each student) to show the times listed. Late: How long do you spend in the car each day traveling to and from school if you leave home at 8.06 am and arrive at school at 8.31 am, then leave at 3.51 pm and arrive home at 4.28 PM?

Angles

 Early: Sort the shapes into groups according to the number of corners each has. Middle: Find all the shapes with right angles. Late: What is the angle on a clock made by a five minute interval?

Temperature

 Early: Sort the pictures into hot and cold foods and drink. Middle: Record a daily reading of the room temperature from the thermometer in the room. Late: From the weather chart, work out the average daily maximum temperature for September.

The language of measurement

When measuring we compare objects. Some examples of the comparative language we use are listed below:

 Comparative shorter/shortest longer/longest smaller/smallest larger/largest far/farther taller/tallest heavier/heaviest lighter/lightest quicker/quickest slower/slowest same size as equal to twice the size older/oldest most least difference between more than less than

We also use words and phrases to indicate location and proximity:

 up down above below next to beside as long as as wide as same length as close away distant