PEDAGOGY

# We had problems

![alt text](/filestore/BlogImage/2fe17fb4-968d-4921-a7c0-ee77542d239e/8c2c91c1-8562-42b1-960b-1e6f931a622aTeacherDiaryblogphoto.jpg "Duncan diary")
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.
### 6th June 2019
Aim of the lesson: to introduce the topic of ratio using [Write and Simplify Ratios](https://www.lbq.org/search/mathematics/ratio-and-proportion/ratio/write-and-simplify-ratios).
Length of session: 24 mins 35 secs
Number of students: 25
Number of answers: 445
Answers right first time: 59%
### Learning by Questions lesson overview
I started the lesson by asking the class to put their hand up if they'd ever done anything to do with ratio before. Only three raised their hand, so I knew I was starting from the very beginning.
Yesterday, I scanned through the LbQ Question Sets on ratio and noticed that they were all labelled as being year 8, so I knew that these would all challenge the class. The Write and Simplify Ratios Question Set would be the perfect starting point after a 10 minute discussion at the board.
### Teacher intervention
![alt text](/filestore/BlogImage/2fe17fb4-968d-4921-a7c0-ee77542d239e/56f1ac5d-c5de-441b-b7f1-b7b4cad06042Lesson18.JPG "Matrix")
The pupils copied the following into their books:
![alt text](/filestore/BlogImage/2fe17fb4-968d-4921-a7c0-ee77542d239e/f149b814-129d-4db4-98ce-44500cce1fe0Lesson18starter.png "Starter")
We chatted about the different elements that make up a cake and the fact that you wouldn't put the same quantity of butter into a cake as you would with sugar. We talked about how the ratio shows you how many more times the amount of butter is compared to sugar.
Then we talked about the relationship between fractions and ratios. Next, we did three examples on the whiteboard about cancelling down ratios and highlighting the fact that you could divide by 100 then divide by three or alternatively you could simply divide by 300 - either way you get the same answer. Pupils understood this quickly and so we ran the LbQ Question Set.
Q2. What is the ratio of marbles to buttons? Give your answer in its simplest form. Use a colon (:) to separate the values.
![alt text](/filestore/BlogImage/2fe17fb4-968d-4921-a7c0-ee77542d239e/637f8b74-5fa5-4ae4-9e0c-e2636bb697b3Lesson18Question2.JPG "Question 2")
This question quickly turned yellow and amber, so I paused the session and chatted to the whole class. They knew that the ratio was 6:9 but most pupils were forgetting to simplify this ratio to 2:3.
Q7. A bus is carrying 48 passengers. 28 of the passengers are children. What is the ratio of children to adult passengers? Give your answer in its simplest form. Use a colon (:) to separate the values.
![alt text](/filestore/BlogImage/2fe17fb4-968d-4921-a7c0-ee77542d239e/9e43545c-3716-4c1f-8cd8-6425e760e429Lesson18Question7.JPG "Question 7")
Despite the helpful diagram, pupil 9 asked me for help with this question. I asked her, “how many passengers are there?”
She said “48.”
I asked her, “how many children are there?”
She said “28.”
I said, “what do you think I'm going to ask you next?”
She said, "how many adults are there?"
I said, “yes!”
She said “20. So it’s 28:20?”
I said, “no - you have to give your answer in its simplest form.” The penny dropped.
Q13. A kitten has a mass of 0.5 kilograms and its mother has a mass of 3 kilograms. What is the ratio of the kitten’s mass to the mass of its mother? Give your answer in its simplest form.
Pupil 9 asked about this question. I said to her, "how many grams are in a kg?
She said, “10.”
I said, “no,” and then asked the whole class.
They all shouted “1000.” I asked her to convert the two weights into grams and then take things from there. She was fine with this.
Q11. A jug contains 150 ml of cordial and 2 litres of water. What is the ratio of cordial to water in the jug? Give your answer in its simplest form.
Almost half of the class were struggling with this question, so I paused the session to speak with the whole class. "How many millilitres in a litre?" I asked.
“1000” they all said.
"So what do you have to do then?"
"Convert 2 litres into ml" said pupil 13.
"Well done," I replied. “So what is the ratio of cordial to water before it is simplified?” “150 : 2000,” they said. I unpaused the session and let them carry on.
Q14. One-third of a class are boys. What is the ratio of boys to girls in the class.
This question was causing a few issues - especially for Pupil 12. "What fraction are boys?" I asked.
“⅓,” she said.
“So what fraction are girls?” I replied.
“I don't know,” she said.
“How many thirds are in a whole?” I asked.
“two,” she said fairly confidently.
I asked her, “how many halves are in a whole one?”
She said, “two.”
I asked her again, “how many thirds are in a whole one?”
She said, “two again.” We had problems.
I asked her, “how many quarters were in a whole one?”
She thought about it, then said, “four.”
I said "convince me."
She said, “because if you cut a pizza into quarters there are 4 of them.”
I drew a pizza and cut it into thirds. I said, "here's a pizza. I’ve cut it into thirds. Are there two of them?”
She smiled and said, “there's three of them.”
I asked her, “how many eights are in a whole one?”
She said, “8.”
I asked her, “how many 88ths are in whole one?”
She said, “88.”
The penny had dropped.
I then paused the session, and we talked about the ratio of boys to girls being 1/3 : 2/3 and the fact that this was the same as 1:2.
The pupils had made a lot of progress. An hour ago, they knew very little about ratio and now that seemed quite competent at writing and simplifying ratios.