## Mr McVey’s Mysterious Maths – Olympic Edition

With the 2024 Olympic Games beginning on 26th July in Paris, I’ve decided to set a medal themed challenge to keep you busy over the summer.

Solutions can be emailed to me at r.mcvey@penworthamgirls.lancs.sch.uk

Given the following clues, can you work out the number of gold, silver and bronze medals that France, Italy and Japan won?

• Japan has 1 more gold medal, but 3 fewer silver medals, than Italy.
• France has the most bronze medals (18), but fewest gold medals (7).
• Each country has at least 6 medals of each type.
• Italy has 27 medals in total.
• Italy has 2 more bronze medals than gold medals.
• The three countries have 38 bronze medals in total.
• France has twice as many silver medals as Italy has gold medals.

Good luck!

## Sparx Maths

This year, there has been some tremendous achievements across school on Sparx Maths. We have answered over 1.7 million questions correctly in 16,689 hours across 800 students. Well done everyone!

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

Mathematics Department

## United Kingdom Mathematics Trust

Junior and Intermediate Mathematical Challenges 2024 – A year in review

As we all draw to the end of another successful year at Penwortham Girls’ High School, I would like to review the extraordinary results achieved by the students in Years 7, 8, 9 and 10 in the United Kingdom Mathematics Trust Challenge this year. I thought, given our results this year, it would be worth going back over previous years and comparing the current cohort. Having now been completing the UKMT Mathematical Challenges for close to fifteen years at PGHS, I am pleased to report that this has, by far, been our most successful set of results ever.

As ever, over 4000 schools across the UK take part in this event and the standard of participation is high.  Only the best achieving students can receive an award and to do so is recognition of the effort and ability of our students.

All credit is due to the students themselves who set about their respective challenges with enthusiasm and a desire to achieve an award. Whilst all who participated are worthy of praise, there were a number of students whose results are worthy of special mention.

The following Year 9 and 10 students achieved awards in the Intermediate Challenge:

Gold awards were achieved by the following:

(Year 10) Saskia H (also best in school) and Neve H.

(Year 9) Poppy M.

Silver awards were achieved by the following:

(Year 10) Megan L, Sophie S, Cheuk C, Lucy H, Chloe W, Ann-Marie J, Harriet C and Holly W.

(Year 9) Naomi S, Fatima S, Lily S and Isabella S.

Bronze awards were achieved by the following:

(Year 10) Niamh L, Mariella M, Rosie Y, Vidhya P, Grace C, Emily J, Anmol A, Elizabeth C, Nusaibah B, Grace B, Eden F, Ruby W, Ruby R, Imogen F, Abigail K, Deanna K, Rebecca L, Jasmine Y and Emily B.

(Year 9) Natalia N, Tanisha S, Saniya S, Uswa H, Hana S, Daisy L, Maisie B, Olivia H, Evelyn W, Daisy H, Mollie H and Jessica O.

The following Year 7 and 8 students achieved awards in the Junior Challenge:

Cherlotte Y (Year 8) – Best in School, Best in Year 8 and Gold award

Lucy R (Year 8) – Gold award

Hannah R (Year 7) – Best in Year 7 and Silver award

Silver awards were achieved by the following:

(Year 7) Karma A, Heidi A, Gauri-Radha C, Amelia N, Violet C, Bella P, Veronica K and Hollie I.

(Year 8) Georgia B, Eva P, Lily H, Ruby M, Klara B, Ava T, Safaa D, Emily T, Laila B, Charlotte T, Isabella F, Maryam H, Julia M, Sophia W and Jenya Z.

Bronze awards were achieved by the following:

(Year 7) Isabelle C, Julia K, Ellie B, Grace D, Aryana S, Alicia E, Ellouise-May W, Alisia J, Gabriella R, Tess W, Lucy B, Abbie B and Amelia F.

(Year 8) Haalah N, Beatrix W, Jasmine H, Erin H, Emily M, Caitie S, Abigail W, Freya G, Beaux W, Sahasra V, Martha S, Yasmin S, Amala K, Jessica B, Safiyyah R, Lilah C, Anya M, Micah T and Isabelle M.

On a final note, I would again like to congratulate all of the students who took part in the Mathematical Challenges.  Your results have set a very high bar for all others to follow.

We are very much looking forward to seeing what you are capable of next year.

Mr S Cheal

Mathematics Department

## IDL Numeracy

Some of our year 7 and year 8 students have started using IDL Numeracy as an intervention platform during their maths lessons. IDL Numeracy is a maths software resource that helps improve attainment in mathematics. A lot of the students are familiar with the platform as they already access IDL Literacy. The lessons on IDL Numeracy ensure inclusivity by reducing the stress those with dyscalculia would ordinarily feel when faced with mathematical problems.  There are a variety of different lessons on the platform, all engaging and effective. Each question is solved by moving items around the screen or clicking on the right items. The students have enjoyed working independently at their own pace on the IDL Numeracy.

Mrs Phillips, Mathematics Department

## Mr McVey’s Mysterious Maths – July 2024 Edition

With the recent bout of nice, sunny weather (at the time of writing anyway!), it’s been nice to get out in the garden, catch some rays and maybe have a barbeque. Even better, if you have a greenhouse, you may have harvested a bumper crop of sweet and juicy strawberries.

This edition’s puzzle is based around a gardener who hasn’t quite thought through their strategy for picking strawberries efficiently. Can you work out the answer? Send me your solutions either by email r.mcvey@penworthamgirls.lancs.sch.uk or give them to me in person to win a coveted Head’s Breakfast.

Good luck!

Problem:

A gardener planted a row of 100 strawberry plants in his garden, setting them exactly 1 metre apart. Each plant produced just one strawberry.

When picking time came, the gardener placed a basket 1 metre from the end of the row, and then proceeded to pick and carry each strawberry to the basket one by one.

Starting and ending at the basket, how far had the gardener walked when he finished picking all 100 strawberries?

## Well done, Year 11

With the exam season over for another academic year, the Maths Department just wanted to say a big well done to all of Year 11 for their approach to their GCSEs. Demonstrating extreme resilience and dedication over three exam papers, they also maintained a calm and positive outlook throughout what was an intense and stressful time.

In addition, Mrs Hasan would like to say well done to the Further Maths students for their enthusiasm and commitment to the sessions which were held once a week after school in preparation for their two exams. Their dedication to their independent learning outside of these sessions was exemplary.

We hope all your hard work pays off and look forward to seeing you all on results day. We wish you all the best in the next stage of your careers.

The Mathematics Department

## United Kingdom Mathematics Trust – Junior Mathematical Challenge 2024

On Thursday 25th April, it was time for our Year 7 and 8 pupils to take on the yearly challenge of the UKMT Junior Mathematics Challenge 2024.

This national event takes the form of a multiple-choice quiz based on using mathematical skills learnt in lessons to solve problems.

Over 4000 schools across the UK take part in this event and the standard of participation is high, only the best achieving students can receive an award, and to do so is recognition of the effort and ability of our students.

After good showings from previous year groups in their respective challenges last year, expectations were very high and I am proud to announce that this year the results were our best ever with our highest ever number of pupils receiving awards.

This year’s prize winners are as follows:

Cherlotte Y (Year 8) – Best in School, Best in Year 8 and Gold award

Lucy R (Year 8) – Gold award

Hannah R (Year 7) – Best in Year 7 and Silver award

Silver awards were achieved by the following:

(Year 7) Karma A, Heidi A, Gauri-Radha C, Amelia N, Violet C, Bella P, Veronica K and Hollie I.

(Year 8) Georgia B, Eva P, Lily H, Ruby M, Klara B, Ava T, Safaa D, Emily T, Laila B, Charlotte T, Isabella F, Maryam H, Julia M, Sophia W and Jenya Z.

Bronze awards were achieved by the following:

(Year 7) Isabelle C, Julia K, Ellie B, Grace D, Aryana S, Alicia E, Ellouise-May W, Alisia J, Gabriella R, Tess W, Lucy B, Abbie B and Amelia F.

(Year 8) Haalah N, Beatrix W, Jasmine H, Erin H, Emily M, Caitie S, Abigail W, Freya G, Beaux W, Sahasra V, Martha S, Yasmin S, Amala K, Jessica B, Safiyyah R, Lilah C, Anya M, Micah T and Isabelle M.

Congratulations to everybody involved and a big thank you to Mr Cafferkey for organising this year’s challenge.

The department is already looking forward to seeing what each year group can do in their respective challenges next year.

Mr S Cheal

The Mathematics Department

## Mr McVey’s Mysterious Maths – Euro 2024 Edition

With the European Football Championships due to begin in Germany on 14th June, this challenge involves solving three related problems. As usual, a correct set of solutions either emailed to me (r.mcvey@penworthamgirls.lancs.sch.uk) or handed to me in person will be rewarded with a Head’s Breakfast and a special prize.

Good luck!

1.       The driving distance between Munich and Hamburg is approximately 790 km. How many miles is this? (You can use the conversion that 1 mile ≈1.6 km).

2.       Amy and Olivia have tickets to watch the first match in Munich. Their tickets cost €95 each, plus a handling fee of €5 per transaction. Given the exchange rate of £1 = €1.17, calculate how much their tickets cost in total, giving your answer in pounds.

3.       The BVB Stadion in Dortmund is famous for its ‘Yellow Wall’ – the largest freestanding grandstand in Europe. The remainder of the stadium can seat 12 000 more spectators than this grandstand, and the ratio of seats in the grandstand to the remainder of seats is 25:37.

1. Calculate the seating capacity of the ‘Yellow Wall’.
2. Calculate the total seating capacity of the stadium.

## Enhancing Mathematical Problem-Solving Skills: Implementing RULER Tasks

As a Mathematics department, we are dedicated to equipping our students with the essential problem-solving and reasoning skills necessary for success in Mathematics, both in their academic journey and beyond. In line with the requirements of GCSE examinations and the broader objectives of fostering critical thinking, we have implemented several strategies aimed at nurturing these vital skills in our Key Stage 3 (KS3) and Key Stage 4 (KS4) students.

When students reach Year 11 and sit their GCSE examinations, they are expected to not only demonstrate proficiency in mathematical facts, concepts and techniques but also to apply their knowledge to solve both familiar and unfamiliar problems across a range of contexts. To ensure our students are well-prepared for this challenge, we have integrated problem-solving and reasoning tasks into every unit of work throughout the curriculum.

One of the approaches we are actively embedding is the use of ‘RULER’ tasks. RULER is an acronym that stands for Read, Underline, Layout, Evaluate and Review. These tasks are specifically designed to guide students through a systematic process of problem-solving, encouraging them to approach mathematical problems in a structured and methodical manner.

Each week, all students are engaged in a RULER task focusing on ‘Money Problems’. We have chosen this particular area of mathematics as it not only reinforces essential mathematical skills but also provides practical relevance to real-life situations. Through these tasks, students are challenged to apply their mathematical knowledge and reasoning abilities to solve problems related to budgeting, financial planning, and everyday transactions.

Here is an example of a RULER task:

Underline: Identify key information and underline relevant details

Layout: Organise the information and plan your approach.

Evaluate: Apply mathematical concepts and reasoning to solve the problem.

Review: Double-check your calculations and assess whether your solution is logical and practical. Reflect on the problem-solving process and identify any areas for improvement.

By engaging in RULER tasks, our students not only enhance their mathematical problem-solving skills but also develop valuable habits of mind, such as perseverance, attention to detail, and critical thinking. These skills are not only essential for academic success but also for navigating the complexities of the world beyond the classroom.

We are confident that by fostering a culture of mathematical curiosity and resilience, our students will be well-equipped to tackle the challenges they encounter in their academic studies and future endeavours.

Mrs Bennett
Mathematics Department

## Mr McVey’s Mysterious Maths – Easter 2024 Edition

Happy Easter!

To keep you occupied during the holiday, why not try the following puzzles? A full set of correct solutions either emailed to me (r.mcvey@penworthamgirls.lancs.sch.uk) or handed to me in person, will earn a Head’s Breakfast along with a little Easter treat!

Enjoy and good luck!

Problem 1

In one year, 78 862 314 Easter eggs were sold in the UK.

1. Round this number to the nearest one million.
2. Round this number to the nearest ten thousand.
3. If an extra 2 million eggs had been sold, what would this number be if it was rounded to the nearest one million.

Problem 2

A survey asked 56 253 people which type of chocolate egg they preferred. 32 132 people preferred milk chocolate and 16 482 people preferred dark chocolate. The rest preferred white chocolate. How many preferred white chocolate?

Problem 3

Mrs Sweeney is making Easter biscuits. Here is her recipe:

80g flour

40g butter

15g lemon zest

25 ml water

She has 120g of butter. How much of the other ingredients will she need for her recipe?