To illustrate this talk move, we are going to ask you to work through a geometry task yourself and then think about examples of how other teachers worked on the task, with a focus on naming. The task is taken from Geometry Sparks, written by Dietmar Küchemann and published by the Association of Teachers of Mathematics.

Try to complete this first task visually to begin with, without writing or drawing anything. When you find yourself wanting to write something down or draw something, try to notice both what you want to write or draw, and why you need to write and draw this.

There are lots of different ways of approaching this task.

Here are the verbal descriptions of how two teachers completed the task. Try to follow their descriptions to work out how they found the value of angle LaTeX: a . Try to notice where you found something unclear or difficult to follow without writing or drawing something.

Lorna's description of how she worked on this first task.

Paula's description of how she worked on this first task.

These two teachers draw on different mathematical properties and relationships, as well as different ways of visualising the relationships between the different lines and angles.

You may have found that you worked on the task in a different way. Students may also work on this task in many different ways, and it can be difficult to follow their reasoning, particularly when it is different from our own way of working on the task.

As you listened to Lorna's and Paula's descriptions of how they worked on the task, you may have found it easier to identify which line segment or angle they were talking about at some points than at others. Using names and labels often makes it easier to be more precise, but there are choices about what we name or label as well as how we might label or name features of a diagram. In this task, the colours of the lines give us a way to talk about the pairs of parallel lines as a pair (the brown lines or the purple lines), but the relationship between them is sometimes left unsaid. Contrast "the brown lines" with "the brown parallel lines". Similarly, "the 40 degree angle" can act as a name for the angle but also tells us something about that angle, its size.

What names for angles, vertices and line segments were used?

How were relationships between line segments, angles and/or vertices labelled?

Choosing when and how to name or label can influence both how students work on a task and what mathematical features are important and in focus. For example, deliberately and explicitly labelling the angles in a diagram enables the students to write down the relationships they notice, but also do this in a consistent way so that later on in the task the relationships can be discussed using the same labels.

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