Year 9 Maths

At the moment in Year 9, we are studying Pythagoras’ Theorem. Born in 570 BC, Pythagoras was a Greek philosopher who made important developments in mathematics, astronomy and the theory of music.

We have been looking at how the theorem works, as well as solving problems using the theorem. We learnt that if we label the length of the sides of a right-angled triangle a, b and c as shown, then the area of the largest square is c × c or c2 and the areas of the smaller squares are a2 and b2. We can then write Pythagoras’ Theorem as a2 + b2 = c2, allowing us to work out the length of missing sides in right angled triangles.

Firstly, we looked at how to calculate the hypotenuse, which is the longest side of a right-angled triangle and recently, we have been looking at how to justify if a triangle is right angled or not and solving problems involving using the theorem.

I have really enjoyed learning about Pythagoras’ Theorem and Miss Hasan has made it really easy to understand. I think it’s amazing that the theorem works for all right-angled triangles!

By Amy M, Year 9

Number calculations in Mathematics

Number Calculations in Mathematics

In years 7 and 8, the students have recently been brushing up on their number calculations skills. Having checked in with addition, subtraction, multiplication and division, we have also been looking at the Order of Operations (you might have heard of this as BODMAS or BIDMAS), as well as knowing the different buttons available on a calculator. Below are some examples of lessons where students were successful.

BIDMAS Codebreaker

Use the correct order of operations to calculate the answers then convert the answers to letters using the table provided. Unscramble the letters to find two mathematical words.  Year 7 will be looking at this in the final two weeks up to Christmas.

Fluency in Mathematics

One of the three aims of the KS3 National Curriculum for Mathematics aims is to ensure that all students:

·         become fluent in the fundamentals of mathematics, through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. This is also one of the 5 big ideas of mastery.

Fluency rests on a well-built mathematical foundation with three parts:

1.    An understanding of the meaning of the operations and their relationships to each other, for example, the inverse relationship between multiplication and division;

2.    The knowledge of a large repertoire of number relationships, including the addition and multiplication facts, as well as other relationships (for example, how 4 x 5 helps us to work out 4 x 50 with understanding);

3.    A thorough understanding of the base ten number system, how numbers are structured in this system and how the place value system of numbers behaves in different operations, for example 24 + 10 = 34 and 24 x 10 = 240.

England Are Fabulous

Fluency relies on three main ideas:

Efficiency

Accuracy

Flexibility

So what does it look like in our classrooms?

I asked my year 7 class to do this calculation on their mini-whiteboards:

7002 – 1999

Every student went straight to the column method for subtraction and the results were varied.

As you can see, the correct answer is 5003, but is this the most efficient way?

We know that £10 – £5 gives us the same answer if we do £11 – £6.

For the calculation above, a more efficient method would have been:

7003 – 2000 = 5003 or maybe using the number line to ‘add on’.  

Many students are faced with calculation problems involving money such as:

£10 – £1.93. In my experience, many students would do 10.00 – 1.93 as a column subtraction and get ‘stuck’ with borrowing, however, if they did 9.99 – 1.92, there would be no borrowing in their calculation. Alternatively, they could use the ‘add on’ method.

These are just a few examples. The mathematics department are now building into their KS3 curriculum ‘calculating smartly’ lessons.

Can you do these calculations ‘smartly’?

Mrs S Bennett (Teaching for Mastery Lead for Abacus NW Maths Hub)

Sparx Maths Competition

The Maths department are currently running a Sparx Maths XP Boost competition this half term that will finish on the 12th December. All students need to gain XP on Sparx maths during this time by completing the mini games and XP Boost tasks each week.

Every Maths class are competing against each other, along with students competing for the XP Crown.

Currently the top 3 Maths classes are:

Keep up the fantastic work! Everything is still to play for as there are still many more weeks to go until the competition closes. Good luck!

Mr Cafferkey

Maths Department

Mr McVey’s Mysterious Maths – Words & Letters Edition

For this challenge, I’ve set you a couple of word or letter-based problems.

As ever, any student who can provide me with the correct solutions either by email or in person, will earn themselves a fantastic Head’s Breakfast!

Good luck!

Problem 1 – Wordy Sequence

When we write numbers as words, we can count the letters in those words, and get more numbers!

For example, 700 can be written as SEVEN HUNDRED, which is twelve letters long.

Bearing this in mind, can you figure out what this sequence represents and work out what comes next?

1, 4, 3, 11, 15, 13, 17, 24, ?

Problem 2 – Letters and Numbers

In the tenth century, the Persian mathematician Al-Karaji showed how we could use letters to represent numbers, paving the way for what we now call algebra.

In the equation A – B = 1, the value of A could be 4 and the value of B could be 3, because 4 – 3 = 1. This wouldn’t work the other way round though because 3 – 4 does not equal 1!

In each of the questions below, match the numbers you have been given to the capital letters to make the sums correct.

Mr McVey

Maths Department

The Football World Cup in Numbers

As the Football World Cup 2022 has just begun in Qatar with a thumping 6-2 win to England, I thought it would be fun if I investigated some of the important numbers that make up this and previous World Cups. I hope you enjoy the list that I was able to put together.

$229 billion: The estimated cost Qatar is spending to host the World Cup. It includes building seven new soccer stadiums, a metro link connecting the stadiums, an airport, hospitals, hotels and shopping malls. By comparison, Russia spent $11.6 billion to host the 2018 World Cup.

$17 billion: The estimated revenue increase Qatar will get for hosting the World Cup. FIFA is expected to generate $7 billion in revenue.

3 million: The number of World Cup tickets sold. The top 10 ticket buyers by country are: Qatar, United States, Saudi Arabia, England, Mexico, United Arab Emirates, Argentina, France, Brazil and Germany.

2.8 million: The population of Qatar, making it the least populated country to host the World Cup.

1.2 million: Qatar estimates 1.2 million visitors during the World Cup tournament. They expect 1,300 daily flights throughout the World Cup. The Ministry of Health announced a negative COVID test is no longer needed to enter the country.

4,468: The size of Qatar in square miles. Qatar is the smallest country ever to host the World Cup.

209: The number of countries that are FIFA members.

84: The average high temperature (in Fahrenheit) in Qatar in November. In December, the average high temperature cools down to 75 degrees Fahrenheit. When the World Cup final typically is in July, the average temperature is 106 degrees Fahrenheit.

32: The number of countries competing in the 2022 World Cup. There are 64 total matches. In 2026, when the United States, Mexico and Canada are hosts, the tournament will expand to 48 countries – its largest field ever with 80 total matches.

26: The number of players on each roster, up from 23 in previous World Cups. The extra demands of squeezing in a World Cup in the middle of the club season is one of the reasons cited.

25: The average age of the USA team; the youngest of all 32 World Cup squads.

17: The record number of players from Bayern Munich that are playing in the World Cup. They will be competing on eight different teams. Manchester United had 16 players in 2018 as did the South Korean Seoul Army Club in 1954.

16: The number of World Cup goals that Giroslav Klose of Germany has scored. This is more than any player. Klose played in the 2002, 2006, 2010 and 2014 tournaments.

13: The number of European nations competing in the World Cup more than any other continent. They are Germany, Denmark, Belgium, France, Croatia, Spain, Serbia, England, Switzerland, Netherlands, Poland, Portugal, Wales.

8: Only eight countries have won the World Cup: Brazil, Germany, Italy, Argentina, France, Uruguay, Spain and England. Mexico has qualified for 16 World Cups without ever winning the tournament.

5: The number of World Cup titles won by Brazil, more than any other nation. Brazil is also the only country to have participated in every World Cup. Brazil has also qualified in more semi-finals matches (11) than any other nation. Germany and Italy have won four titles each.

3: The number of World Cup titles won by Pelé more than any other player. Named the greatest soccer player of the 20th century, Pelé was a member of Brazil’s World Cup championship teams of 1958, 1962 and 1970. 20 players have won two World Cup titles.

If you have any other interesting numbers regarding the World Cup, please feel free to pass them on.

Mr S Cheal

Mathematics Department

Year 7 Mathematics

As part of their learning journey in Mathematics, students in Year 7 have recently been taught how to add and subtract directed numbers using double sided counters. These manipulatives have been really helpful in making this topic visual and interactive, so the students understand how, and more importantly, why we arrive to a particular answer. Students were given a snapshot of this topic during our Year 6 Sampling Day that was held towards the end of the last academic year. It was great to see how so many students still remembered that lesson!

Students were first introduced to the concept of a ‘zero pair’, which is a pair of numbers that when added, equal zero. For example, we have that 1+ (-1) = 0.

Students then completed different calculations involving negative numbers using the counters. They first practised adding directed numbers, then subtracted directed numbers and then a mixture. It was fantastic to see how hard all students worked during this series of lessons.

Miss Hasan

Maths Department

Literature and Languages Festival

Our Literature and Languages Festival took place from 10th October to the 21st October. A variety of activities, competitions and events took place and it was a huge success. Please click the link below to view the newsletter articles about the festival.

Mr McVey’s Mysterious Maths – European Languages Edition

Everybody loves a good Sudoku, the fun Japanese number puzzle!

As you probably already know, the aim is to complete the large 9 x 9 square, ensuring that each row, column, and smaller 3 x 3 square is filled out with the numbers 1-9, without repeating any numbers within the row, column or square. Simple, right?

The two puzzles below come with a twist though. To celebrate the European Day of Languages which was on 26th September, I’m challenging you to complete the puzzles in French and German!

Any student (or parent) who can provide me with both correctly completed puzzles either on paper or by email (take a picture of your completed entry), will receive a fantastic prize!

Bon chance! (Or should that be viel Gluck?!)

Mr McVey

Email: r.mcvey@penworthamgirls.lancs.sch.uk

  • Arts Council England - Artsmark Gold
  • Lancashire Socio-economic Equality Badge
  • SMART
  • UNICEF
  • School Mental Health Award
  • Ofsted - Outstanding Provider
  • Arts Council England - Artsmark Gold
  • Lancashire Socio-economic Equality Badge
  • SMART
  • UNICEF
  • School Mental Health Award
  • Ofsted - Outstanding Provider