![alt text](/filestore/BlogImage/246b2a1a-1233-4012-b564-3ca03d6a766c/ae90da41-6ef5-4bfa-ba16-6883e6ca297dTeacherDiaryblogphoto.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 10.1: This is a class of 32 very high ability pupils who mainly want to learn mathematics and reach their full potential. They have enjoyed several LBQ lessons and are waiting in anticipation for the completion of the year 10 syllabus. They enjoy LbQ’s ability to provoke mathematical conversation and have found the problem solving questions quite a challenge. Their average current estimated grade for the end of year 11 would be grades 7 and 8. ### 28th February 2019 Aim of the lesson: revise finding the gradient and y intercept using [Find the Gradient and y Intercept of a Line from the Equation](https://www.lbq.org/Questions/UserQuestionSetPreview/Find-the-Gradient-and-Y-Intercept-of-a-Line-from-its-Equation). Length of session: 25 mins 24 secs Number of students: 31 Number of answers: 854 Answers right first time: 74% Learning by Questions lesson overview I started the lesson with discussion based work to find the gradient (m) and the y intercept (c) for the following lines: 1)    y = 8x - 60 2) y = 30 - 2x 3)  y -2x =  -17 4) 2y = 13x + 8 5)   3y - 4x + 1  = 0 The pupils were fine with 1, 2, and 3 - they could recall this knowledge from year 9. However, 4 and 5 proved problematic for a significant proportion of the class. This formed the basis for my examples which were recorded in the book. We then ran the LbQ question set. The first 20 questions were fine for all pupils, then the fun began. ### Teacher Intervention ![alt text](/filestore/BlogImage/246b2a1a-1233-4012-b564-3ca03d6a766c/25176aad-b147-4858-a031-c817c0b7ec22Lesson11.JPG "Matrix") Q21. Which line passes through the origin? I asked Pupil A what the coordinates of the origin were. He said, "0,0." I asked him to substitute these into each equation and then check whether the equation balanced. He understood this. We then discussed what crossing the y axis at y = 0 actually meant. He then realised that the y intercept must be zero. Q22. Leo says that the following lines are parallel: y - 3x = 1and 2y = 6x + 5 Is Leo correct? Explain your answer. Pupil B and C were working together on this question. They told me that there was a "glitch" in the system and that the software was not displaying the graph. I read the question and smiled. There wasn't supposed to be a graph! I asked them both, "What is it that makes two parallel lines to actually be parallel to each other? One replied, "they have the same gradient." She smiled and then remarked, "Oh, we don't need a graph!"   The penny had dropped. Q27. A straight line has a gradient of 3 and passes through the point (2, 7). What is the equation of the line in the form y = mx +c? Many pupils were stuck on this question. I asked them, how should all equations start? They said,  "y =" I asked them, "What is the gradient"? They said 3. I said, “So what can we write now?” Pupil D said   "y=3x" I asked them, “what do we now need to find out?” They said "the y intercept" I wrote on the board. ![alt text](/filestore/BlogImage/246b2a1a-1233-4012-b564-3ca03d6a766c/1533b5c2-a752-4a72-9481-8176e2e2a816Lesson11Ad-hoc.jpg "Ad-hoc") Unfortunately this was not enough, and they needed a little more help. I asked them, “What does (2, 7) actually mean if you had to explain it to your Mum?” Pupil E said, "When x = 2,  y = 7." I was ecstatic, "Yes!  So substitute these values in." A few pupils were able to get it from here, but still a large number required further help. I wrote on the board ‘7 = 6 + c’ They all shouted,  "plus one!" They all got it now. This was a great lesson and good progress was made by all pupils. On the way out, Pupil F said, "It's great that Sir. You can work at your own pace, but it's still a competition."