PEDAGOGY

# On closer inspection

![alt text](/filestore/BlogImage/09b80d64-6b76-497b-8476-8785a5d6be09/1167ab2a-84bb-4659-8b1e-ddad21ea7ef2TeacherDiaryblogimage2.jpg "Duncan")
Our teacher diary follows one maths teacher's journey using LbQ. Duncan Whittaker at St Christopher’s Church of England High School gives us a snapshot of its application and its impact in these regular updates.
Class 9.1 - this group of pupils all work at a fast pace and often the challenge is to ensure they reach their full potential at all times. They love Learning by Questions and often compete with each other as they climb the matrix. The average estimated class grade for the end of year 11 is grade 8.
### 3rd May 2019
Aim of the lesson: to develop an understanding of calculating the area of a triangular prism and introduce how to calculate the area of a cylinder using [Calculate the Surface Area of Prisms, Including Cylinders](https://www.lbq.org/search/mathematics/measurement/area-and-perimeter/calculate-the-surface-area-of-prisms-including-cylinders?keywords=prisms).
Length of session: 34 mins 28 secs
Number of students: 30
Number of answers: 580
Answers right first time: 79%
### Learning by Questions lesson overview
As the pupils entered the room, I had an old GCSE question on the board that I found on the Maths Genie website. They had to calculate the surface area of a triangular prism. They could do that with no problem, so we progressed quickly onto cylinders. They told me that they had never done this before so I asked them to discuss what the net of a cylinder looked like. They quickly grasped that it was a rectangle and 2 circles and so I drew an example using Active Inspire. One pupil said that we needed to calculate the circumference of the circle. I said, "but aren't we calculating the area of the circle?" He said, "yes, we are, but to get the area of the rectangle you need the circumference of the circle because this is the width of the rectangle." I was very impressed with this explanation and so I gave him a credit on Synergy.
I could have adapted this lesson and started at the Fluency or even the Problem Solving Questions but I decided to run it from the very start and we seemed to be doing well for time. The mathematical conversations during the Understanding questions were phenomenal - there was clearly a lot of learning taking place and pupils were explaining to others how they had arrived at their answer - very natural and very pleasing.
### Teacher intervention
![alt text](/filestore/BlogImage/09b80d64-6b76-497b-8476-8785a5d6be09/7ba20839-a8ea-4dd6-93cc-4ce10f724388Lesson15.JPG "Matrix")
**Q14. The surface area of the trapezium is ___ cm².**
![alt text](/filestore/BlogImage/09b80d64-6b76-497b-8476-8785a5d6be09/d7f0be7b-9d9a-452f-b97c-8c282dbfb301Question14.JPG "Question 14")
Question 14 (trapezoidal prism) provided the first major difficulty. Pupil 20, who had recently been at the UK Maths Challenge, asked, "I know that the formula to calculate the area of a trapezium is (a+b)/2 x h, but what are a and b?”
I paused the session and asked the class this question. One pupil said "the top and bottom side?"
I said, "in this example then yes, but not in all examples of trapeziums. Who can tell me what a and b are for ALL trapeziums?" Several pupils had a go, but nobody could tell me that a and b were the parallel sides. I drew on Active Inspire a trapezium where the vertical sides were the parallel sides and then the penny dropped. " a and b are the parallel sides, sir" said pupil 3. They had all learnt something. I pulled up a MyMaths demonstration of a trapezium being a rectangle and explained to them that the (a+b)/2 part of the formula was simply "finding the mean average of the 2 parallel sides." This had been a great whole class conversation.
**Q16. The surface area of the hexagonal prism is___ cm².**
![alt text](/filestore/BlogImage/09b80d64-6b76-497b-8476-8785a5d6be09/5ad1042c-30bd-4c6f-a35d-481c5e5b4e80Question16.JPG "Question 16")
Pupil 20 then said she was stuck on question 16 and that LbQ was marking it wrong incorrectly! On closer inspection, we realised that she had given the area of the 2 shaded sides as 60 cm² and 20 cm² instead of 40 cm² and 20 cm².
**Q24. What is the surface area of the cuboid in terms of a, b, and c?**
![alt text](/filestore/BlogImage/09b80d64-6b76-497b-8476-8785a5d6be09/c8151a77-aa6f-4a24-a7df-1bbe3d13decfQuestion24.JPG "Question 24")
Pupil 29 asked to get the surface area when the dimensions were algebraic expressions. I showed her how to find the area of one pair of identical sides (2ac) and then she was able to calculate the remaining sides. Another pupil said that they had done this and that it had been marked as incorrect. I explained that "simplify your answer" involved factorising the answer.
This had been a very successful lesson with LbQ; the pupils clearly enjoyed their learning and learnt plenty. As a follow up, I will adapt the lesson and run only the problem solving questions as they did not get this far.