Teaching mental mathematics from level 5: Measures and mensuration in number

This resource addresses the importance of understanding measures and mensuration, and includes activities that you can use to help pupils comprehend the subjects.

Included are rich tasks designed to improve mathematical thinking skills in number. Use these teaching activities to help learners develop greater confidence with aspects of number associated with practical settings. You can design revision or intervention tasks for pupils who are struggling with the application of number in context, or develop mental mathematics images and mathematical talk by engaging pupils in paired or group work.

What this resource covers

This supports Teaching mental mathematics from level 5: Number. It describes teaching approaches that can be used to develop mental mathematics abilities beyond level 5.

The advice covers the aspects of number in the context of measures and mensuration that have been reported as difficult to teach and hard to learn. Areas covered include:

• estimation
• rounding and continuity
• conversion
• compound measure.

The importance of understanding measures and mensuration

Mensuration problems provide useful contexts in which to develop pupils’ understanding of accuracy, and provide a purpose for making decisions about appropriate levels of accuracy.

Working with measures and mensuration can provide an ideal context in which to develop pupils’ skills in using and applying new knowledge from different strands of mathematics. For example, as pupils make decisions about the measures in a problem, identifying and obtaining necessary information has real meaning.

It is important for pupils to understand that many measures are continuous and that mensuration often involves rounding to a suitable degree of accuracy. They need to appreciate that the degree of accuracy of a solution is linked to the degree of accuracy of the input measures.

With experience, and through discussion, pupils will begin to ask themselves questions such as:

• What are the units of the answer and how should it be rounded?
• What is the effect of the accuracy of the input data and interim calculations on my solution?

… and ultimately deal with error bounds by asking themselves:

• What is the effect of an error or rounding in a measurement? How big is the effect on the solution?
• How does this relate to the size of the solution? What is my percentage error?

It is particularly important when pupils are trying to model a real-life context through the use of mathematics that they are supported in making connections in their understanding of different forms of representation and that they are able to choose appropriate forms to help solve a problem.

Activities

The activities described in this resource build upon and develop activities suggested in Teaching mental mathematics from level 5: Number. They may be easily adapted to adjust the level of challenge and keep pupils at the edge of their thinking.

The suggested activities target some aspects which pupils continue to find difficult. They will support pupils’ thinking by, for example, encouraging them to recall the common conversions from one metric unit to another, to use consistent units in calculations, and to read scales carefully and not to assume that each division represents a multiple of 10.

The activities provide opportunities for pupils to refine their mental images by discussing and describing these different forms of diagrammatic, algebraic, numerical and graphical representation. For example, having a mental image of the number line or a place-value chart supports pupils’ understanding of the base-10 number system and so helps with the relationships between different units of metric measurements.

The ability to translate fluently between measure and number is an important stage in the problem-solving process. This process may begin with a problem involving measures, values of which need to be used as numbers in a calculation. The result of the calculation must then be translated back into the appropriate unit of measurement and checked against the context of the problem.