The student work below is provided to help prompt discussion and encourage reflection on alternative approaches. The images of students’ work on the warm-up were taken from the filmed lesson and the work on integrating \(\arcsin x\) was done as homework following that lesson. Please note that where work has been rewritten, the layout and all marks on the page have been reproduced as accurately as possible.

Warm-up

Group A

What have these students noticed about the graphs?

How could these ideas be used to work out the two areas?

Student B

What has this student calculated?

Why has the calculation been written down twice?

Group C

What could \(e^{\ln{3}}-e^{\ln{2}}\) refer to?

What explanation could link the lines of algebra?

Which region has area \(R-1\)?

Problem - integrating \(\arcsin x\)

Student A

How has this student used the relationship between the two graphs?

What explanation could link the lines of algebra?

How could this student start to generalise their approach?

Student B

How is the calculation to the right of the graphs related to the work below the graphs?

What explanation could link the lines of algebra?

How do the two decimal values support the student’s argument?

Student C

How has this student developed the ideas from the warm-up?

How might the values written by the limits in the printed integral have been obtained?