Our teacher diary follows one maths teacher's journey using Learning by Questions. 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.
### ![alt text](/filestore/BlogImage/f8ec82cb-3c55-4469-ac7b-bfa70edd8a55/58a17718-a6a3-4bb9-948a-c5ede219badfDuncanPicEdit.png "Duncan")
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.
## 11th January 2019
Aim of the lesson: conclude the topic of fractions by using [Fractions Topic Review](http://www.lbq.org/Questions/UserQuestionSetPreview/Find-Gradients-of-Straight-Lines/).
Length of session: 33:24
Number of students: 27
Number of answers: 691
Answers right first time: 74%
## Learning by Questions lesson overview
We have had several lessons on Fractions and I thought this would be the ideal way to conclude the topic, as it mixes up all the various calculations and question styles.
## Teacher intervention
![alt text](/filestore/BlogImage/9945c822-5a85-44a8-894d-252ccdb0bd9c/b4f6ba89-5ddd-4855-b9a0-a1523372a868Lesson311012019.jpg "Matrix")
### Q5. Calculate 4 ÷ 2/5
Pupils were entering 20/2 instead of simply 10. A useful lesson in simplification for them.
### Q11. David uses 3/8 of a kilogram of flour to make a cake. If he halves the recipe how much flour will he need? Give your answer as a fraction and include the units kg (kilograms) in your answer.
Several pupils entered 6/8 which was very interesting. I pondered why they thought that 6/8 was half of 3/8. I thought they were automatically doing 3/8 divided by 1/2 instead of multiplying by 1/2.
I paused the lesson. Pupil A said that he "did 1.5/8" then "double it to get rid of the decimal numerator" which I thought was good use of literacy.
Pupil B asked, "is it not easier to do 3/8 x 1/2 = 3/16?”
Pupil A then said, "to halve a fraction, you can just double the denominator."
This was an excellent whole class discussion.
### Q14. Julie completes an 5/6 mile run in three minutes. How far does Julie run in one minute? Give your answer in miles and don't include the units in your answer.
Pupil C asked for help. I asked her, if you know how far you can go in 3 mins, how do you calculate the distance in one minute? She replied, "Is it 5/6 divided by 3? I smiled and said yes.
### Q13. The price of a coat is reduced in a sale by 2/5. If the sale price of the coat is £24, what was the original price of the coat? Include the £ sign in your answer.
This question provided the best discussion of the lesson. This was a well written question and helped them out with the higher tier paper.
I asked them, how many fifths in the original price?
Pupil D said, "5."
I said, yes, if you reduce 5/5 by 2/5, what do you have?
Pupil E said, “3/5.”
I said, yes. You have 3/5 of the original price and this is equal to how many pounds?
Pupil F said, "24"
Then, very interestingly, pupil F said, "Ah, so you do 24 divided by 5 then times by 3.”
I paused, then realised what she was doing. She had of course thought that the question said, "what is 3/5 of 24," but it actually said 3/5 of the original price = £24 which is completely different.
I highlighted this to the class and showed them the conceptual difference.
Pupil G then said, "you divide the 3/5 by 3 to get one fifth. So 1/5 = £8.”
Then pupil H said, “so the original price was £40 because 8 x 5 = 40.”
A great conversation and another great lesson with 9 set 1 and Learning By Questions.
*Pupil names have been omitted.