PEDAGOGY

# To break this down...

![alt text](/filestore/BlogImage/3d7ae3a4-e4cc-4f46-ab1b-58e65a79675d/de062f25-7527-41a5-adb6-938259b0d03027fe0a35-f6ea-4d5d-b82e-86e1342be3e7TeacherDiaryblogimage2.jpg "Duncan blog")
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 7.3 - This is a class of 26 middle to lower ability pupils who are well behaved and have responded well to using LbQ so far. Their average current estimated grade for the end of year 11 is grade 4 and I teach them for six hours per fortnight.
## 9th January 2020
**Learning Objective:** to answer reasoning questions on LbQ
Length of session: 16 minutes 29 seconds
Number of students: 27
Number of answers: 248
Answers right first time: 58%
Correct after feedback: 33%
**Introduction to lesson:**
Pupils copied the following into their blue books:
![alt text](/filestore/BlogImage/3d7ae3a4-e4cc-4f46-ab1b-58e65a79675d/24ab85ea-f975-4dcd-b755-850892915196DuncanblogJan28picture1.png "Image 1")
We discussed the significance of reasoning questions and the role that LbQ plays in developing their ability to answer these questions at GCSE. Our example was :
Sonny says he can simplify 16/48 by dividing by 2 each time. Ben says he can do it in one step. Is Ben correct? Explain.
I asked the class to discuss this question and to use the back of their books to work it out. They were very quiet, which meant that they were struggling. I thought this would be a fairly straightforward question for them to investigate as we had covered simplifying fractions several lessons ago but nobody could offer the answer of “dividing by 16.” On reflection, the examples that we covered were dividing by integers from 2 to 12 and they had never experienced cancelling fractions by dividing by 16 – hence the silence.
To break this down, I asked them to complete the question like Sonny did (see slide below).
![alt text](/filestore/BlogImage/3d7ae3a4-e4cc-4f46-ab1b-58e65a79675d/4708efc8-be57-4eba-b9f5-d426d1c6803fDuncanblogJan28picture2.png "Image 2")
We then talked about this being 4 steps and again, I asked them could these 4 steps be done in ONE single step. They were still quiet, but pupil 7 said “you could divide by 8!”
We talked about dividing by 8 and that this would cancel 16/48 to 2/6. I asked the class, what is 16/48 cancelled down by 4 steps, like Sonny did? They said 1/3. So, I asked them, how do you get from 16/48 to 1/3 in ONE single step. The penny dropped. Pupil 11 said “dividing by 16.” I then asked them in the back of their books to answer, using full sentences, the initial question.
I then explained them that this was what I was expecting them to type in when answering LbQ’s blue reasoning questions.
**Was the LbQ question set adapted and why?**
Yes, because I was wanting the pupils to practise reasoning, I decided to omit level 1 and the second half of level 2. This provided them with 5 questions from level 2 as a nice introduction to the LbQ task followed by the 5 reasoning questions from level 3.
![alt text](/filestore/BlogImage/3d7ae3a4-e4cc-4f46-ab1b-58e65a79675d/ae57cf67-ad44-4867-969e-398090655eafDuncanmatrix.JPG "Matrix")
**3 key interventions during the LbQ activity:**
**Intervention 1**
**How many parts of the grid do you need to shade to make a fraction equivalent to 6/8?**
Pupil 5 asked me for help with this question. We discussed, in the context of the question, what was meant by shading 6/8 of the grid. With a little encouragement, she arrived at the fact that this meant shading 6 out of every 8 squares. I used the paint tools to split the grid into shapes of 8 squares (see slide below). I asked her how many of these 8 should I shade in? 6, she replied. She understood this but was completely stuck on the last shape which was 4 squares that were left over at the end. I didn’t want to do too much for her so I left her to ponder about how many of those final 4 should be shaded in. She got there eventually.
![alt text](/filestore/BlogImage/3d7ae3a4-e4cc-4f46-ab1b-58e65a79675d/335392d5-c422-4b0b-8ece-d4e56b7d2819DuncanblogJan28picture3.png "Image 3")
**Intervention 2**
Pupil 26 then asked me to go through question 5 again. He couldn’t grasp shading in six out of eight when there were “only 4 squares!” I asked him to cancel down 6/8. He said ¾. Then the penny dropped!
**Intervention 3**
Question 7 was a challenging reasoning question. However, too many pupils were entering quick and short responses such as:
![alt text](/filestore/BlogImage/3d7ae3a4-e4cc-4f46-ab1b-58e65a79675d/7c354376-cbed-464d-8f8c-35eca6e1c1ddDuncanblogJan28picture4.png "Image 4")
…and hadn’t listened to what I said during the example.
Unfortunately, the 5 level 2 questions had taken more time than expected and the pupils didn’t get as much opportunity with reasoning as I would like. Therefore, the next lesson, we will just focus on reasoning questions and will omit level 1 and 2.
LbQ has allowed me to introduce reasoning questions to these year 7 pupils which I would not normally have done at such an early stage using traditional teaching methods – purely due to a lack of suitable resources. However, work still needs to be done and in future lessons I need to ensure that they have the maturity as well as the understanding to answer these questions effectively. This could be achieved by adapting a question so that only the reasoning questions (level 3) are given – this is a work in progress.