![alt text](/filestore/BlogImage/be9a10da-5ddb-46e6-9dd9-b99420b0f051/6201c90d-bc7f-4f4d-a456-8b670ac2f389TeacherDiaryblogphoto.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. ## 1st February 2019 Aim of the lesson: to deepen understanding of linear expressions using [Expand and Simplify Linear Expressions](https://www.lbq.org/Questions/UserQuestionSetPreview/Expand-and-Simplify-Linear-Expressions). Length of session: 38 mins 10 secs Number of students: 28 Number of answers: 376 Answers right first time: 62% ## Learning by Questions lesson overview I had planned the lesson to do [Expand the Product of Three or More Binomials](http://www.lbq.org/Questions/UserQuestionSetPreview/Expand-the-Product-of-Three-or-More-Binomials/) Question Set. I started the lesson at the board with: (3 - y)(4 - y)(5 - y) This was to show the pupils that the coefficient of y cubed can be negative - up until now we had just seen positive coefficients. Unfortunately, the Expand 3 Binomials Question Set* was not available online and, so I told the pupils that we could not use LbQ today. "You've promised us all week that we can do LbQ on Friday after the exams are out of the way." This was true, so I had to think quick. I found the Expand and Simplify Linear Expressions Question Set and clicked on ‘View’. The reasoning and problem solving questions looked great. I [adapted the question set](https://www.lbq.org/HelpVideos) and then ran it. This had saved the day. ### Teacher Intervention ![alt text](/filestore/BlogImage/be9a10da-5ddb-46e6-9dd9-b99420b0f051/04e0c7c1-5444-4ac3-b746-bad5e6fc5908Lesson12.JPG "Matrix 1") **Q2. Expand and simplify the following expressions and arrange in ascending order (smallest first).** ![alt text](/filestore/BlogImage/be9a10da-5ddb-46e6-9dd9-b99420b0f051/c855f724-11bc-4d23-b5be-fc463a7a3930Lesson12Question2.JPG "Q2") Pupil A was expanding 3(4x + 1) + 6x and was getting 18x + 6. She was adamant that she was correct and that the LbQ software was, "wrong." I said, "Do it again from scratch, another go." She did it again and said, "Oh, it's 18x + 3." Problem solved. **Q3. Zoe has made one mistake in her homework on expanding and simplifying expressions.** **What is the correct answer to the question she got wrong?** ![alt text](/filestore/BlogImage/be9a10da-5ddb-46e6-9dd9-b99420b0f051/9ee7e00b-b39c-4d0d-9e16-f79b1503931fLesson12Q3.JPG "Q3") Pupil B told me that Zoe had not made a mistake and that she had answered all 3 questions correctly. Whilst I worked them out myself, she said "Oh yeah!" 9 (4x+3) - 6(3x-2) is not 18x + 15. "You add the 12, not subtract it." Pupil B has spotted the mistake - the penny had dropped. **Q6. What is the area of the shape? Simplify your answer. ** ![alt text](/filestore/BlogImage/be9a10da-5ddb-46e6-9dd9-b99420b0f051/98bb8c0c-d002-4188-ba58-9e7d8020d8a1Lesson12Q6.JPG "Q6") This question produced some great mathematical discussions. Pupil C had split the compound shape into 2 rectangles (see slide), but thought that the height of the left hand rectangle was 5 cm instead of 5 + 7 = 12 cm. Pupil D, rather interestingly, correctly did the hard work and got the correct algebraic areas of the 2 rectangles, but then multiplied them together to calculate the total area instead of adding them. Some pupils had finished these 10 questions with 15 minutes of the lesson remaining, so I quickly searched for "expand" and then found [Factorise Expressions Using Brackets ](https://www.lbq.org/Questions/UserQuestionSetPreview/Factorise-Expressions-Using-Brackets)Question Set. Again, I adapted this for just the Reasoning and Problem solving questions and then ran these as a 2nd task. ![alt text](/filestore/BlogImage/be9a10da-5ddb-46e6-9dd9-b99420b0f051/5371ec0d-77cf-4fea-8f0d-3a51b7229308Lesson12matrix2.JPG "Matrix 2") Q1. Explain why the expression 3a(6a - 10) is not fully factorised. Pupil E said, "But sir, it is fully factorised." I said, “look inside the bracket - can you factorise the bracket any further?” She said, “Yes, you could take out a factor of 2.” I said, “Yes, you have answered your own question - it is not FULLY factorised.” She carried on. Mission accomplished. *This was Question Set was taken down for review and is now available again to be used with pupils.