PEDAGOGY

# What are you actually finding?

![alt text](/filestore/BlogImage/ad9a6ea3-c862-408c-8b52-854f506f3b23/531d8d4e-7179-4c27-b1c1-835e8ba2ebcfTeacherDiaryblogphoto.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.
### 5th February 2019
Aim of the lesson: [Find Gradients of Straight Lines](https://www.lbq.org/Questions/UserQuestionSetPreview/Find-Gradients-of-Straight-Lines).
Length of session: 18 mins 57 secs
Number of students: 32
Number of answers: 639
Answers right first time: 76%
### Learning by Questions lesson overview
I had a student teacher present in the classroom. He is training to a maths teacher in a behavioural unit. I was keen to show him Learning by Questions and asked him to focus on the pupil engagement and the mathematical discussion that the platform invokes.
### Teacher Intervention
![alt text](/filestore/BlogImage/ad9a6ea3-c862-408c-8b52-854f506f3b23/37215f0c-e91c-4c98-b612-4b6ef4d667d2Lesson10.JPG "Matrix")
**
Q5. What is the change in y-coordinates from point E to point F?**
Many pupils were entering 9 for the change in y values, but in fact the correct answer was -9. This produced a whole class discussion about the change in values being positive or negative.
**Q17. A ladder is placed against a wall to reach a window 4 metres above ground. The bottom of the ladder is placed 0.5 metres from the wall.**
What is the gradient of the slope of the ladder?
Pupil A asked, "How do you know if a question is asking for the gradient or whether it is a Pythagoras' Theorem question?"
I said, “This is a very good question.” I asked, “What can you use Pythagoras' Theorem for? What are you actually finding?"
She said, "Missing lengths of right-angled triangles."
And I said, “Yes, and how does this differ from the gradient?”
"Well, the gradient is the steepness," she replied.
I said, “Exactly, you do the gradient triangle stuff when the question asks for the gradient, and you do Pythagoras for missing lengths.”
**Q25. Tori says you can’t calculate the gradient of the line shown in the diagram. Is Tori correct? Explain your answer.**
This was the highlight of the lesson. Question 25 was a belter. Brilliant conversations were being had about this and the student teacher was really enjoying LbQ.
Most pupils were saying that Tori was wrong because you can get the gradient of a vertical line - it is simply 0.
I asked the class, "What was the formula we learnt and discussed at the start of the lesson?"
They all said, "Change in y values divided by change in x values."
I said “What is the change in y’s?”
They said, “It can be any number - depends on where you start and finish.” They were correct about this. We decided to go for 18.
I asked, “What is the change in x values?”
They said, “Zero.”
I said, “What is the change in y values divided by the change in x values?”
They said “18 divided by 0 equals 0, so Tori is wrong!”
I asked them to type in 18 divided by zero on a calculator. They said, “Why? It’s zero?”
I said, “Just do it!”
They all did 18 divided by zero and they all shouted out, "Error!"
I said, “Why is this?”
They all looked confused as they still thought that 18 divided by zero was zero.
I explained that you cannot divide by zero; they all said, "aaah."
So I asked, “Is Tori correct or incorrect?”
They said, “Tori is correct.”
I said, “Yes she is, why?”
They all paused, and eventually Pupil B said, “If the change in x values is zero, then you cannot calculate the gradient.” I was delighted with this. What a fantastic whole class conversation. The student teacher was very impressed!