Trigonometry is the basis of the book’s subject. I begin with length and angle, and then generalise to coordinates. This requires the important idea of a directed angle, which enables us to relate the sine and cosine of an angle to coordinates in any given orientation of a set of axes. I discuss the details of inverting the sine/cosine/tangent functions, and introduce a new function name to replace the inappropriate name “atan2” that often appears in the literature. The chapter ends with examples of calculating bearing and elevation.

Measurement is an aspect of the mathematics curriculum that has wide usage in everyday life. A basic level of knowledge, skills and confidence in measurement is very much part of being numerate. An analysis of the measuring process suggests that children learn to measure first by becoming aware of the physical attributes of objects and how they compare with other objects. Estimation is a significant aspect of measurement and should be seen as an integral part of the measurement process. The ability to estimate is enhanced when students have strong spatial awareness and are able to visualise and represent measurement situations in their heads. Students therefore need to be given plenty of opportunities to engage in measurement activities that focus on developing a sound understanding of the attribute being measured, along with the act of measuring.