Our teacher diary follows one maths teacher's journey using LbQ. Duncan Whittaker at [St Christopher’s Church of England High School](http://www.st-christophers.org///) gives us a snapshot of its application and its impact in these regular updates. ### ![alt text](/filestore/BlogImage/f8ec82cb-3c55-4469-ac7b-bfa70edd8a55/58a17718-a6a3-4bb9-948a-c5ede219badfDuncanPicEdit.png "Duncan") 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. ## 10th January 2019 Aim of the lesson: consolidate students ability to divide mixed numbers by mixed numbers using [Divide a Fraction by a Fraction](http://www.lbq.org/Questions/UserQuestionSetPreview/Divide-a-Fraction-by-a-Fraction/). Length of session: 31:53 Number of students: 28 Number of answers: 803 Answers right first time: 69.9% ## Learning by Questions lesson overview Last lesson, we divided mixed numbers by mixed numbers using traditional teaching methods, but I saw that the Divide a Fraction by a Fraction Question Set required a mastery grasp of the topic, which looked perfect for this class of pupils. It certainly was. ## Teacher intervention ![alt text](/filestore/BlogImage/480d0c94-82e5-4c2d-a12b-8c4092e48e81/a03f3499-ade0-4dca-9e53-1dc469a877bcLesson310012019.jpg "Lesson Matrix") ### Q3. How many fifths in seven-tenths? Several pupils were inputting 3.5, but the question asked for a mixed number fraction - a valuable lesson in reading the question! ### Q15. How many feet are in ¾ of a metre? Same issue as with Q3 - pupils were typing in 5/2 but the question asked for a mixed number fraction and not an improper fraction. ###Q17. 3/8 divided by ? = 33/40 Pupil A asked for help. I asked her 3 x what = 33 ? She said 11. I then asked 8 x what = 40? She said 5. She knew she had to "flip" this fraction due to the divide sign. ###Q26. The area of a wall is 12 ⅚ square metres. If the height of the wall is 2 ¾ metres, what is the length? A brilliantly written question. Pupil A initially asked me about it, and I drew on the board a similar rectangle but with area = 12 and width = 2. She said the length would have to be = 6. I said, correct, but how have you got the 6 using the 12 and the 2? She understood and continued. At the very end of the lesson, when most other pupils had got to the Problem Solving stage, I paused the session and put Q26 up and asked them all to discuss the method for this. After 30 seconds of discussion, Pupil B said "you have to use the inverse method to find the missing length." I thought this was a great use of literacy. ###Q27. ? x 5/12 = 3/8 Pupil A then asked me about this. I related Q27 to Q26. I said which part of this question is the "area". She said 3/8. I then said which part of this question is the width? She said 5/12. **Summary This was one of the best question sets I have done in the past few months - I really enjoyed it and felt as though the pupils really mastered it. I have never seen a better resource on dividing fractions.** The next instalment of Teacher Diary with Duncan Whittaker is coming soon. In the meantime, if you would like to try out Learning by Questions in your classroom, open your free account and take advantage of all our Question Sets for free.