Formal Units for Measuring: 2.25

• Indicator of Progress
• Teaching Strategies

Supporting materials

• Related Progression Points
• Developmental Overview of Measurement Attributes (PDF - 30Kb)

 

Indicator of Progress

At this level students appreciate the need for uniform, standard units when measuring (i.e. units of constant size with the unit’s magnitude known to all users). Success depends on students being able to use correctly and accurately the appropriate measuring instruments for the unit. Students choose the appropriate unit for the attribute of interest (e.g. grams for mass), and, in an appropriate range of situations, are able to choose the unit of best magnitude (e.g. metres rather than centimetres for the width of a room).

Before achieving this, students may have difficulty using measuring instruments correctly, because they do not fully understand the necessary procedures to achieve accurate measurements. They may choose a less effective instrument for measuring, such as a 1m ruler for measuring the width of a book.

There are three phases for teaching measurement – in terms of the measurement phases, this indicator is about ‘learning to measure’, with a focus on the use of measuring instruments.

Illustration 1: Difficulties with ‘zeroing’ measuring instruments

‘Zeroing’ is a common difficulty that students experience with many measuring devices. For example, students may be unable to use a ruler to measure length to the nearest centimetre, because they do not align the 0 of the ruler with one end of the object to be measured. This problem is exacerbated by the fact that 0 is often not right at the end of the ruler.

Other examples of this difficulty:

• Students may operate a trundle wheel in such a way that they count 1 before the wheel actually completes a full revolution.
• Students may not understand that scales for measuring mass should be ‘zeroed’ before use.

 

Illustration 2: Accurate use of a ruler for measuring lengths longer than the ruler

Students with a good understanding of measurement and ruler use are able to handle accurately a single ruler to measure lengths that are longer than the ruler. They understand the importance of carefully marking the end-point of the current measured length, and also of aligning the zero of the newly moved ruler with the mark. Success in this task also depends on facility with addition.

 

Illustration 3: Links to the Mathematics Online Interview

Examples of the types of tasks that would be illustrative of successful use of formal units and measuring instruments aligned from the Mathematics Online Interview:

• Question 47 – Using the Ruler
• Question 48 – Tearing the Streamer
• Question 52 – Using formal units (Mass)
• Question 53 – Using kitchen scales