PEDAGOGY

# Groans of realisation

![alt text](/filestore/BlogImage/230b6507-6b2d-4289-ab82-78d553de3dc4/2639115f-063f-4c96-8bce-6221023f13dbTeacherDiaryblogphoto.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 8.3 - my class of year 8 pupils is a lively one. They sometimes find it hard to focus. They love to use Learning by Questions and when they use it correctly, there is a great class atmosphere and learning is effective. The average estimated class grade for the end of year 11 is grade 5.
### 8th May 2019
Aim of the lesson: to revise the calculations required to find the median using [Calculate the Mean, Median, Mode, Range and Outlier.](https://www.lbq.org/search/mathematics/statistics/averages-and-range/calculate-the-mean-median-mode-range-and-outlier)
Length of session: 27 mins 22 secs
Number of students: 27
Number of answers: 662
Answers right first time: 64%
### Learning by Questions lesson overview
I had just finished marking the year 8 end of year exam and I noticed that the majority of pupils in this class had got the question on finding the median incorrect. Instead, most pupils had calculated the mean.
I started the lesson with a quick example of finding the mean, median, mode and range of a
list of 4 numbers: 3, 4, 4, 7. This allowed us to quickly recap the 4 different calculations. Pupil 3 correctly pointed out that calculating the median for an odd number of values was "easier" than for an even number of values. We explored this to illustrate how they differ.
We talked about the range being a measure of consistency and I came up with a quick example using the number of goals scored by a football team.
Team A goals scored: 0, 5, 13
Range = 13
Team B goals scored: 3, 4, 4
Range = 1
### Teacher intervention
![alt text](/filestore/BlogImage/230b6507-6b2d-4289-ab82-78d553de3dc4/d04edb54-1f4f-481a-bb86-d924e961edc6Lesson16.JPG "Matrix")
One pupil asked, "what is an outlier?"
Another pupil called out, "the odd one out." I liked this answer - the others knew exactly what was meant by this.
**Q7. There are 10 players in a netball squad. The coach records the number of games each girl plays in the season. What is the median number of games played by each girl?**
**18, 18, 14, 15, 14, 17, 13, 15, 18, 17.**
I noticed that this question was turning orange at the top, so I looked at the question then paused the session. I asked, "what is the mistake that everyone is making here?"
Pupil 9 replied, "they haven't put the numbers in order."
This was met with several groans of realisation, "Oh, yeah!" said several pupils.
**Q11. Franky wants to know people’s favourite flavour of ice-cream. What is the mode flavour of ice-cream?**
![alt text](/filestore/BlogImage/230b6507-6b2d-4289-ab82-78d553de3dc4/81918318-0511-4c1f-b591-50d5eac5eb61Lesson16Q.11.JPG "Question 11")
I pointed out that the language could change for this question and it could be phrased as:
‘What is the modal flavour of ice cream?’ I asked the class, “how can you find the mode flavour?”
Pupil 10 said, "it's the one with the highest frequency." This was an impressive response and allowed the others to answer the question correctly.
**Q12. A shop has three bags of apples left at the end of the day. From these remaining bags, calculate the mean weight of an apple. Include the unit g (grams) in your answer.**
![alt text](/filestore/BlogImage/230b6507-6b2d-4289-ab82-78d553de3dc4/a5b3e699-8d0e-41ec-ad2c-fcfe1abb7585Lesson16Q.12.JPG "Question 12")
Pupil 26 had answered this question correctly first time - unlike 90% of the class. Hence, he was keen to share his explanation, "all you do sir, is add up all of the weights then divide this by the total number of apples." I agreed with him and gave him praise - you could tell he was very pleased with himself. Despite his efforts, some pupils were still dividing by 3 instead of 20.
I said, “if I was trying to calculate the mean shoe size of this class, would I divide by 30 (the number of pupils in the class) or would I divide by 4 because there are 4 rows of tables in the classroom.” They said 30. I said, “exactly, so why would you divide by 3 because there are 3 rows in the table?” The penny dropped.
This had been a great lesson with these pupils and I am confident that they are much more proficient with calculating averages than what they were when they sat their end of year exam.