## Mr McVey’s Mysterious Maths – Cricket World Cup Edition

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

## Conditional Knowledge in Mathematics

Analysis of proficient mathematicians’ problem-solving shows that their thinking is highly organised. It draws on a well-connected knowledge base of facts, methods and strategies that have been used to solve problems with a similar deep structure before. Successful problem-solving is therefore not just an activity but an outcome of successful learning of the facts and methods and their useful combinations as strategies. Conversely, if a problem-solver does not have conditional knowledge, they are more likely to be distracted by the surface features of problems. This has implications for how problem-solving as an activity is implemented in classrooms where teachers expect students to learn how to problem-solve by problem-solving.

Teachers could use a curricular approach that better engineers success in problem-solving by teaching:

• the useful combinations of facts and methods
• how to recognise the problem types
• the deep structures that these strategies pair to

Students need to be fluent with the relevant facts and methods before being expected to learn how to apply them to problem-solving conditions.

Teaching for Mastery has been at the heart of our lessons and in the forefront of our mind when teaching mathematics and planning our five-year curriculum for coherence. We have worked hard as a department, ensuring that key facts are mastered and effective representations expose the structure of the mathematics to enable conceptual understanding. We ensure fluency by carefully planning a wide range of questions and tasks in our lessons where students need to draw on prior knowledge. Our next target is to improve conditional knowledge by embedding variation tasks into our lessons to enable pupils to make connections and improve their reasoning skills. We are also embedding mathematical thinking strategies to enable pupils to improve their problem-solving skills.

Mrs Bennett

Mathematics Department

## Lancashire University School of Mathematics

Lancaster University School of Mathematics (LUSOM) Online and on Campus Revision Sessions

As part of our continuing links with LUSoM, there are a number of taster sessions and lectures, both online and on the campus that are available for pupils in KS3 and KS4.

LUSoM Revise

This is a 13-week revision programme designed for Year 11 pupils aiming for grades 7 – 9 at GCSE. Starting in September, and meeting each week online, these sessions will go through various key topics to secure a top grade at GCSE and support the transition to A-level Mathematics.

These sessions received fantastic feedback last year with 96% of pupils agreeing they found the lectures very useful and 86% confirming they sessions were at the correct difficulty level.

Each session will cover a different topic, and hence students should aim to attend all 10 sessions.

To register for this, please visit https://go.cardinalnewman.ac.uk/form/reviselectures23?event_id=123

LUSoM Extend

This programme is designed for high-ability KS3/KS4 students who have a passion and interest for mathematics and want to go beyond their normal lessons. The sessions will cover material which is not on the GCSE syllabus and will show students some of the incredible uses that mathematics can have once it’s taken at a higher level.

Meeting once every half term on campus for 1.5 hours, students will tackle mathematics in completely new contexts to develop their problem-solving techniques and their breadth of mathematical knowledge.

Last year, 100% of students agreed that these sessions helped in developing mathematical thinking, increased the depth of understanding and improved presentation skills.

To register for this, please visit https://go.cardinalnewman.ac.uk/form/lusomextend2023?event_id=124

Miss Hasan

The Mathematics Department

## Getting the most out of Method Maths – GCSE Exam Practice for Years 10 and 11

At the start of a new academic year, I would like to take the opportunity to remind all Year 10 and 11 students of the importance that Method Maths can have in revision and the practice of mathematics.

Method Maths is a website that the school subscribes to and it has played an effective role in assisting pupils to prepare for their examinations and practice mathematical skills throughout the two years of the GCSE maths course.

Method Maths provides access to past GCSE papers of both the Foundation and Higher tiers and provides guided support when needed to assist students to understand and complete past exam questions. The website also marks your answers as you go so that you can check your progress. It also indicates what grade of work that you are currently achieving, as well as showing what needs to be done to improve your grade.

The Method Maths website is also used in school as part of our intervention strategies and has been shown to make a positive impact on results.

All students have been allocated a Method Maths account and their classroom teacher has or will provide these details. Room 11 is available after school on Wednesdays for Method Maths practice supported by members of the mathematics department.

Mr S Cheal

The Mathematics Department

## Sparx Maths

This year in the Mathematics department, we are continuing to use Sparx Maths which provides personalised homework for each student. It creates a weekly set of questions tailored to the level of understanding and learning pace of each student. The questions are designed to be achievable, whilst offering the stretch that learners need to make progress. Questions from previous topics will also be included in the homework so that students can keep practising the skills they have learned.

We appreciate that you will of course want to support your child with their home learning but please try not to help them with a question until they’ve had a go first. It is really important that students complete their homework independently, and that questions are marked as correct. In the Maths department, we provide a lot of support in school to enable every student the opportunity to achieve 100% on their homework. There are drop-in sessions most lunch times, including a Sparx Maths club on a Monday in room 11. This way, Sparx can make sure you child continues to set homework that is at the correct level for them.

Over the summer, Sparx Maths has had some up-dates. There is a new look when you login, which is better on the eyes when it comes to reading and answering the questions. There has also been an up-date when it comes to the bookwork checks. This previously picked random codes but they have now adopted the use of 1A, 1B, 1C etc going onto 2A, 2B etc. This allows the student to easily find the code for the requested bookwork check rather than sifting through all their work.

Achievements

The top 3 pupils with the highest XP currently for each year group are:

## The Essence of Teaching for Mastery

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

## Year 9 Trigonometry

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

## Sparx Maths

After our first year of using Sparx Maths,  there has been some tremendous achievements across school. We have answered over 2.1 million questions correctly in 26,626 hours across 800 students. The impact of changing to Sparx Maths has been that engagement has improved threefold!

Currently the top 3 Maths classes are:

The top 3 students in each year are:

Well done to the above students in their continued pursuit for excellence in Mathematics.

Mr Cafferkey

Maths Department

## Stemettes

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

Mr S Cheal

## Introducting Miss Phillips

Hello! My name is Mrs Phillips and I have joined the team at PGHS as a maths teacher. Prior to this I have been a maths teacher at another Preston school for 15 years. What I love most about my job is how rewarding it is to help students achieve what they are capable of and being able to give them the guidance and support to do this.

In my spare time I am involved in the Scout association as a cub leader in Ormskirk. I have an 8-year-old boy and we love camping, Lego and board games.

I am a keen runner, I completed the London marathon last year and more recently completed my first 45-mile ultra-marathon.

I am really excited to be teaching here at PGHS and look forward to getting to know you in the coming weeks.

Mrs Phillips

Maths Department