The clips below are from a lesson using a modified version of Trig tables and may help you prepare to use the resource or reflect on classroom practice.

Here is the version of the task the students were working on. This is a Fluency exercise which can be tackled in many ways, depending on what students already know. Before watching the clips, spend a few minutes thinking about how students might tackle this task.

In the table below, \(0\leq \theta \leq 2\pi\) and the missing function is either \(\sin \theta\), \(\cos \theta\) or \(\tan \theta.\)

Some of the row and column headings are missing. Without using a calculator, try to work out what they could be and complete the table. A function does not appear twice in the same table.

If you think you know what a missing function or value is, make sure you check that it works for all the entries in its row and column!

\(\theta= \ldots\) \(\theta= \ldots\) \(\theta= \ldots\)
\(-1\) \(\dfrac{\sqrt{3}}{2}\) \(\dfrac{1}{2}\)
\(\tan \theta\) undefined \(\sqrt{3}\)
\(\cos \theta\) \(-\dfrac{\sqrt{3}}{2}\)

You can find a pdf version of the modified resource here.

These students kindly agreed to let us film them sharing their initial thoughts as they worked on this task. Our aim in selecting these classroom video clips is to offer an opportunity to see the different ways mathematical thinking is revealed, as it plays out, rather than as a final and polished piece of work.

After viewing each clip

  • Spend a minute replaying the clip in your mind. Try to reconstruct significant parts of the episode. If watching with a colleague, compare your accounts of what you saw — watch the clip again if necessary to reach agreement.

  • Consider the prompts relating to student thinking and the teacher’s role.

  • Try to relate these episodes to your own classroom experience.

What does each clip reveal about these students’ understanding of trigonometric functions?

As a teacher, what choices might you make in a similar situation in your own classroom?

Teacher intentions

Students’ thoughts

The students in this lesson were asked to work on the task before they had been taught all the content required. Here they first share their thoughts about this particular task, and then more general thoughts about working in this way.

As a teacher, what are the different ways you could use rich tasks with your students?

We are very grateful to these students and their teachers for allowing us to film them working on Trig tables and the subsequent discussion.

We are grateful to Julian Marshall for directing the filming, selecting and editing some video clips and for his guidance on the use of classroom video.