If like me, you’ve been following the Cricket World Cup in India over the past few weeks, you’ll no doubt have enjoyed the big hitting of the batters, the skill of the bowlers and the athleticism of the fielders. Despite England’s disappointing performance, the tournament came to a climax last weekend in Ahmedabad where 100 000 spectators saw Australia beat the home team India to lift their sixth World Cup.

Not only is cricket a thrilling sport, it also involves lots of exciting maths! My challenge to you is to work out the answers to the following cricket related questions. Answers can be emailed or brought to me in person and there will be prizes for full and correct solutions. Good luck!

1)    In cricket, an over is where 6 balls are bowled by the bowler. In the World Cup final, India batted for exactly 50 overs. How many balls are there in 50 overs?

2)    Australia only needed 43 overs to reach the winning target. How many balls did they face?

*For the next 2 questions, the average used is the mean.

3)    Mohammed Shami of India was the leading wicket taker in the tournament. He took 24 wickets for 264 runs, an average of 11 runs for each wicket taken. The second highest wicket taker was Adam Zampa of Australia who conceded 506 runs at an average of 22 runs for each wicket taken. How many wickets did he take?

4)    India captain, Virat Kohli, is a hero in his home country and one of the greatest batters ever to have played the game. In the 2023 world cup (up until the final) he averaged 71.1 runs in 10 innings. After the final (his 11th innings) his average was . How many runs did he score in the final?

*Disclaimer: Some of the batting and bowling figures have been changed slightly to allow integer answers!

Mr McVey

Mathematics Department

Penwortham Girls’ High Mathematics Department work extremely hard ensuring that all students are taught through a mastery style approach. This is achieved in many ways but mainly from the department working collaboratively to ensure that they have a coherent curriculum and ‘mastery’ lessons. So, what does mastery look like for our students?

In the classroom

• Students are taught through whole-class interactive teaching, enabling all to master the concepts necessary for the next part of the curriculum sequence.
  
  
• In a typical lesson, the teacher leads back and forth interaction, including questioning, short tasks, explanation, demonstration, and discussion, enabling students to think, reason and apply their knowledge to solve problems.
  
  
• Use of precise mathematical language enables all students to communicate their reasoning and thinking effectively.
  
  
• If a student fails to grasp a concept or procedure, this is identified quickly, and gaps in understanding are addressed systematically to prevent them falling behind.
  
  
• Significant time is spent developing deep understanding of the key ideas that are needed to underpin future learning.
  
  
• Key number facts are learnt to automaticity, and other key mathematical facts are learned deeply and practised regularly, to avoid cognitive overload in working memory and enable pupils to focus on new learning.

Penwortham Girls’ High School is part of a collaborative network of schools, all on their mastery journey, led by Secondary Maths Mastery Specialists from Abacus NW Maths Hub. Mr McVey is a Mastery Advocate for Penwortham Girls’ High School and Mrs Bennett is a Secondary Maths Mastery Specialists and an Assistant Maths Hub lead.

One of the activities that the Maths Hub likes to encourage, is for advocates from other schools in the collaborative network to observe live mastery lessons.

Mr Henshaw (Secondary Maths Mastery Specialist and Assistant Maths Hub Lead) delivered a live mastery lesson to a Year 10 mathematics class at our school.  

Teaching direct proportion using the directly proportional symbol ‘α’ is generally taught through a process.  In this lesson, the teacher demonstrated how this topic could be taught through understanding and thinking mathematically. Students had some prior knowledge from their Physics lessons.

Students had the opportunity to work in pairs to generate pairs of numbers that were directly proportional to each other.

They then worked collaboratively to identify whether the ratio tables were in proportion or not!

Students then were introduced to the ‘GCSE’ styles of questions.

The lesson ended with understanding of what direct proportion on a graph looked like.

Year 10 did us proud with exemplar behaviour and excellent interaction with the teacher and their peers. Not many students can cope with being watched by another teacher, let alone 15 teachers from different schools!

Mrs Bennett, Secondary Mathematics Teaching For Mastery Lead  

Recently 9F have been learning about trigonometry, specifically how to use it to calculate the lengths of sides of right-angled triangles. Mrs Bennett and Mr McVey have been trialling a new approach to teaching this topic, aiming to give the students a deeper understanding of the somewhat mysterious ‘sine’, ‘cosine’ and ‘tangent’ ratios.

Mrs Bennett introduced the concept, explaining how ancient mathematicians used the unit circle and stars in the night sky to develop the fundamentals of what we know today as trigonometry. The students also saw how lengthy tables of trigonometric values had to be used before the advent of the calculator. They certainly viewed their Casio ClassWiz in a new light after this!

From here, the students learned how to correctly label the sides of a right-angled triangle using the words opposite and hypotenuse. They then used the sine ratio to accurately calculate the length of these sides. In subsequent lessons, the cosine and tangent ratios have been explored with the adjacent side being brought into play. For the remainder of this unit of work, we will be looking at how to calculate the size of angles in the triangles and also at how this interesting branch of maths is used in real life.

Well done to all the students in 9F who approached their learning with great enthusiasm!

Mr McVey

Maths Department

As part of the Mathematics department’s recent collaboration with the Lancaster University School of Mathematics (Lusom), we were visited by Ms McConville, who presented a session to a group of Year 9 pupils. The focus of the lesson was “artificial intelligence” which has become something of a hot topic in the news. The session was produced by the “Stemette” programme, which is a pioneering social enterprise that encourages young women aged 15 to 25 to pursue careers in Science, Technology, Engineering and Mathematics.

During the lesson, the students received an introduction into the mind-boggling possibilities and potential risks of this fast-developing field. They were given some insight into how it has already changed the world we live in, as well as what A.I might be used for in the future. There was an interview with Marta, a German biochemist who decided to leave the lab work and help to develop A.I in this country instead.

The students also had plenty of opportunities to try out some current examples of A.I – some of these you may even have come across already yourselves. I have provided links to some of the A.I programmes that were looked at. Please feel free to investigate these for yourselves.

Since the session, the students have had further opportunities to look at the some of the A.I programmes and a special shout out to Grace B who has completed all the tasks on the Virtual Tools Game.

The students involved and myself, would like to thank Lusom and the Stemettes for their continued efforts in developing Stem subjects in schools. Further thanks to Lusom for their outreach programme and the links we have developed with them to promote further study of Mathematics.

The Akinator

https://en.akinator.com/

The Virtual Tools Game

https://sites.google.com/view/virtualtoolsgame?pli=1

Mr S Cheal

Assistant Head of Mathematics