![alt text](/filestore/BlogImage/80e3ddfa-3276-47e9-87cb-2211583bcffe/687bffc7-f449-4298-8297-7e207c14374bTeacherDiaryblogphoto.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. ### 20th March 2019 Aim of the lesson: to practice skills in multiplying and dividing standard form numbers by standard form numbers using [Interpret and Compare Numbers in Standard Form](https://www.lbq.org/search/mathematics/properties-of-number/powers-and-roots/interpret-and-compare-numbers-in-standard-form?keywords=standard%20form). Length of session: 52 mins 37 secs Number of students: 29 Number of answers: 888 Answers right first time: 75% ### Learning by Questions lesson overview During the previous two lessons, we had multiplied and divided standard form numbers by standard form numbers.I saw the Learning by Questions lesson as an opportunity to practice these skills and answer some more challenging questions. ### Teacher intervention ![alt text](/filestore/BlogImage/80e3ddfa-3276-47e9-87cb-2211583bcffe/2b11ce38-0b1e-48ce-919b-9e78c83aa920Lesson14.JPG "Matrix") **Q13. Sort these numbers by size, from smallest to largest.** ![alt text](/filestore/BlogImage/80e3ddfa-3276-47e9-87cb-2211583bcffe/e58ebdd4-3d95-4ae4-801e-32f7a8ee4a41Lesson14Q13.JPG "Question 13") This seemed to bring quite a lot of silly mistakes from pupils. Pupil A said that 1 x10 ^3 was 100 instead of 1000 and Pupil B said that 3 x10^2 was 30 instead of 300. Eventually, there enough struggling with this question that I decided to pause the session and talk about their ordinary number equivalents, reinforcing that anything to the power of zero = 1. 5.87 x 10^ 0   = 5.87 x 1 = 5.87.   Some pupils still thought that 10^0 was zero and not 1. **Q22. Steven says that 14 x 1018 is written in standard form. Is he correct? Explain your answer.** We paused the session and talked about the importance of reasoning questions on the higher tier GCSE paper, and how the LbQ software is unique in that it allows pupils to gain practice in these style of questions. **Q23. Tallia says that 3 x 104 is larger than 6.7 x 103 . Is she correct?** Pupil C had a good answer for Q23, and so I enlarged this answer and shared it with the class. We talked about how this pupil had detailed the ordinary number equivalents and then used these numbers to answer the question. ![alt text](/filestore/BlogImage/80e3ddfa-3276-47e9-87cb-2211583bcffe/1c0cabda-be68-4cba-8970-196629393dbbLesson14Q23response.JPG "Question 23 response") **Q24. Maria says that 38 x 103 = 3.8 x 10** This question brought about many excellent responses - it is good to see that this year 9 class will have had 3 years practice, thanks to LbQ, when they sit their exam in June 2021. The reasoning questions should not phase them. ![alt text](/filestore/BlogImage/80e3ddfa-3276-47e9-87cb-2211583bcffe/42117a34-a6e9-4ed9-bdab-e358a5ea605cLesson14Q24response.JPG "Question 24 response") **Q26. Sort the numbers by size, from smallest to largest.** **8 x 104** **32,000** **1.4 x 105** **0.03 x 106** We talked about doing our number conversions in several smaller steps, instead of 1 large step. For example: 0.03 x 10^6   = 3 x 10^4 = 30000 Some pupils found this strategy much simpler At the end of the lesson, Pupil F said, "I like doing LbQ lessons sir, they are more interesting." I took this as a compliment rather than an insult!