PEDAGOGY

# A prime number is...

![alt text](/filestore/BlogImage/4ec79380-9ace-44dc-8fb7-7a2786ef44fc/39bda2bf-f49b-4d3a-a0c0-78e022627359TeacherDiaryblogimage2.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.
7.4 - This class are well-behaved and passionate about improving their maths skills. They are at their happiest when using LbQ and the tablets. They are a confident group of students who are unafraid of asking for help when they need it, whether that be from each other or from me. Their average current estimated grade for the end of year 11 is grade 4.
### 20th June 2019
Aim of the lesson: find out if students have a firm foundation and establish any gaps in knowledge using [Year 7 Baseline Question Set 1a](https://www.lbq.org/search/mathematics/assessment/assessment/b2310a00a-761f-4694-8c27-f196cf92f06f).
Length of session: 38 mins 33 secs
Number of students: 26
Number of answers: 801
Answers right first time: 77%
### Learning by Questions lesson overview
LbQ have created baseline Question Sets for year 7 based on the primary curriculum – as maths is cumulative, it is important to know that students have a firm foundation in the earlier years so that we know where the gaps are.
I decided to run the Question Set under normal classroom conditions, as I felt that this would be the most productive; they could discuss the mathematics with pupils around them and the matrix would produce a useful reference as to where the pupils are at.
### Teacher intervention
![alt text](/filestore/BlogImage/4ec79380-9ace-44dc-8fb7-7a2786ef44fc/3b318493-4e5d-420a-8f68-18b5065cdf6dLesson20.JPG "Matrix")
**Q4. Which 2 digits go in the place value grid?**
![alt text](/filestore/BlogImage/4ec79380-9ace-44dc-8fb7-7a2786ef44fc/f3519ea7-e689-43dd-bf2b-d4e9de489d50Question4.jpg "Question 4")
Some pupils simply did not know that 3/4 as a decimal was 0.75 - this was obviously alarming! I paused the session as this was something that I needed to make sure that everyone knew. Pupil 20 asked, "What does it mean by place value grid?" She thought that the 10 x 10 grid was the place value grid and this had confused her slightly. I asked them, “what is 3/4 as a decimal?”
One pupil replied, "0.75." I asked the pupils to discuss how the 10 x 10 grid illustrated the fact that 3/4 was equal to 0.75. I could tell from the conversations that they couldn't justify this using the 10 x 10 grid. I asked them how many squares were in the 10 x 10 grid. They said, “100.”
I asked them, “out of these 100 squares, how many are coloured in?” They started to count them one by one until eventually someone shouted, "75."
I said, “yes, 75 out of how many?” They said 75 out of 100. I wrote 75/100 as a fraction on the board. I said, “what is 75/100 as a decimal?”
They said, “0.75.”
I said, “yes, exactly - 75/100 is ¾, as you can see from the 10 x 10 grid and we know that this is 0.75.” I don't think that all pupils had 100% got this, but there were certainly pupils who had done.
**Q12. Which number between 12 and 16 is a prime number?**
Pupil 9 asked me about this initially and then several others, so I decided to pause the session. "What is the definition of a prime number?" I asked.
I received the usual, "a number that can be divided by one and itself." This is what primary school teachers incorrectly tell our kids.
I told them that the definition of a prime number is a "number with _exactly_ 2 factors - not more than 2 and not less than 2." We discussed the 2 factors of the number 3 (1 and 3) and the fact that it was prime. We did this again for the number 11 and the fact that it was prime. We discussed the 4 factors of 8 (1,2,4,8) and the fact that it was not prime. Then we talked about the number 1 - its only factor (1) and the fact that it was _not_ prime even though primary school teachers would have you believe with their own definition that it is!
**Q23 - What is the size of angle _a_ in degrees?**
![alt text](/filestore/BlogImage/4ec79380-9ace-44dc-8fb7-7a2786ef44fc/b53afd54-cb30-45fd-80c9-9cc9dbc0a622Question23.JPG "Question 23")
Pupil 14 asked me about this and I showed her how to split the pentagon into 3 triangles. "How many degrees are in one triangle?" I asked her.
"180," she replied.
"How many triangles are there?" I asked.
"3," she replied.
“So what do all of the interior angles add up to?” She paused, then correctly said, “540.”
"So how do you calculate one of them?"
"540 divided by 5," she said.
“There you go then!”
**Q24. John, Claire and Ged are comparing their pocket money. John has 15p more than Claire, Claire has 12p more than Ged, and they have a total of 99p. How much does Ged have? Include the unit p (pence) in your answer.**
Pupil 22 asked me for help with this question. I said, "In these questions, you always call the smallest amount/person x. Who is the smallest?”
"Ged", she replied.
“If Claire has 12 more than Ged, then Claire must be x + what?”
"x + 12," she answered.
I said, “so algebraically, what number is John?”
She paused, then said "x + 27". This was correct and we were making progress. I said, “so algebraically, what number are these people in total? She said, "x plus x + 12 plus x + 27.”
I said, “well done - and what number do all of these add up to?”
"99" she replied. I told her that that was all of the help I would give her and left her to finish the problem.
We had to finish the lesson slightly earlier than expected due to an incident that had occurred the previous day. I gave merits to the top 5 pupils and told them that we would complete this next lesson.