## FREE Olympic GCSE Maths lesson – archery and circles

Actually it’s a Paralympic Maths lesson: teach area and circumference of circles in the context of Paralympic Archery.

Like what you see? More lessons like this are freely available on **ActiveTeach** – no login required.

## Rugby World Cup Maths: FREE Activity to download

The **Rugby World Cup** is upon us. There’s a lot more mathematics to rugby than you might think, and we’ve created a bespoke *Beast Index* to prove it.

Keep your class on their toes with these **AO1** and **AO3 problem-solving questions** on averages & range, and using formulae:

## Fibonacci Sequences – the Golden Rule about the Golden Ratio, which we just found out…

We just found out something new….

It turns out that** if you take the first ten terms of**** any Fibonacci sequence, the sum of those 10 terms is equal to the 7th term multiplied by 11.** Got it?

OK, let’s unpack that. Here’s the most basic Fibonacci sequence:

1,1,2,3,5,8,13,21,34,55

If you plug these into your head/calculator, you will find that the sum of these 10 terms is **143**.

Much quicker: take the 7th term (in this case 13), multiply that by 11 and you get, as if by magic… **143**.

And it works for any Fibonacci sequence. Let’s imagine one with bigger numbers starting with (to pick a number completely at random) 42:

42, 42, 84, 126, 210, 336, 546, 882, 1428, 2310

So we add all the terms up on a calculator and get **6,006**.

Now, much quicker, jot down the 7th term (here: 546), multiply it by 11 and, hey presto: 546×11=**6,006**

It’s a trick you can cheerfully teach to your maths students – get them to take it home and impress their parents. Something along the lines: “hey, dad/mum, I bet I can add up a Fibonacci sequence faster in my head than you can using a calculator”.

Our thanks to the **Republic of Maths** blog that brought this to our attention, via **this video link**.

**One final note:** the covers on our (as in: Longman’s) **AQA GCSE Maths Student Books **this year were inspired by spirals. A spiral galaxy on our **Foundation sets book**, a spiral staircase on our **Higher sets book**, and a **chameleon’s tail **on our **Middle sets book **(someone must’ve been wondering what this image was?) –

## Sherlock Holmes GCSE Maths Challenge – episode 4 solution

Many congratulations to the **Episode 4** winners of our **Sherlock Holmes maths competition:**

**Jonathon Cox at The Littlehampton Academy**

for successfully working out where Holmes and Watson must go next.

**And the answer is:**

**OXFORD CIRCUS.**

We’ll be sending the winners a **FREE Class set of Longman’s unique AQA A-A* and G-F Practice Books (15 copies of each) ****and a tin of Cadbury’s Heroes.**

Coming up next… a spot of Christmas shopping in Episode 5 on Wednesday.

Here is the **winning solution to episode 4:**

The solution to how far away Moriarty is from the tunnel.

The path of the firework is y=300+44x-x^2. This is a quadratic so using the quadratic formula to find x when y=0

x= (-b +/- square root (b^2 – 4ac))/(2a)

where a=-1, b=44 and c=300

x = (-44 +/- square root (44^2 – 4X-1X300))/(2X-1)

x = (-44 +/- square root (1936 + 1200))/(-2)

x = (-44 +/- square root (3136))/(-2)

x = (-44 +/- 56)/(-2)

Either x = (-44 – 56)/(-2) = -100/-2 = +50 (where the tunnel is)

or x = (-44 + 56)/(-2) = 12/-2 = -6 (where Moriarty must have fired the firework from)

So 50 – -6 = 56 metres away from the tunnel

Moriarty is 56 metres awayThe Code.

Using the Coordinates of the Tate Modern (34, 14) and the code FG DG.

Using a shifted substitution D=1, E=2, F=3 etc

The Coordinates generated from substitution of CK EE gives (08, 22) which give the coordinates for Oxford Circus

Moriarty’s Target is Oxford Circus

## EPISODE 4: Sherlock Holmes Maths Competition – FREE AO3 Maths challenge for 5th November

**SHERLOCK HOLMES AND THE MYSTERY OF THE DEVIL’S EYE**

**Episode 4 – “G U N P O W D E R , T R E A S O N A N D P L O T”**

**The story so far… **Called to investigate the disappearance from Harrods of the world’s largest ruby, the **Devil’s Eye, **Holmes and Watson follow a trail from there to the London Eye. Further clues at the London Eye lead them into a Halloween, midnight chase through the tunnels under the Thames. Ably assisted by **two Maths teachers from Gloucestershire College**, they solve the probability clues and arrive at… **B O R O U G H M A R K E T!**

Emerging from the tunnels, Holmes and Watson finally catch a glimpse of the thief in **EPISODE 4**:

And here’s the accompanying **worksheet**:

**WHAT TO DO: **

**DOWNLOAD THE PDFs, SOLVE THE CLUES, AND SUBMIT YOUR ANSWERS TO: ****SherlockH_221B@yahoo.co.uk**** **

**BY MONDAY 15th NOVEMBER.**

The winning entry will be drawn at random from all correct answers, and will receive a **FREE Class set of Longman’s unique AQA A-A* and G-F Practice Books (15 copies of each) ****and a tin of Cadbury’s Heroes.**

**If you’re NEW to this competition…**

View **this page of our blog** to keep up to date with all the action. The competition is free to enter, and you can join in any Round/Episode. All the page references in the Episode point to maths support in our** AQA GCSE Middle sets Student Book**. All new and existing subscribers are entitled to receive a single free copy of this book – **request your copy by leaving a comment on this post.**

**GOT ANY QUESTIONS?** Just leave a comment on this post and we’ll get straight back to you.

## Quick reminder…

Don’t forget our **Halloween Maths Challenge **remains open until this Sunday, 31st October.

**Episode 3** of our **Sherlock Holmes Maths competition**: solve the mathematical clues and let us know where Holmes should go next to track down the thief of the world’s largest ruby!

Since many schools are on half-term this week, we actively encourage teachers to have a go on their own behalf – no need to enter on behalf of their class. All details of the competition can be found **here**.

This episode’s winner will receive: a **FREE Sherlock Holmes DVD (the 2009 Guy Ritchie movie) and a tin of Cadbury’s heroes.**

## Sherlock Holmes Episode 1 solution…

Our thanks to everyone who’s taken part in **Episode 1** of our Sherlock Holmes competition: **The Mystery of the Devil’s Eye!**

In **Episode 1**, Holmes and Watson are called to Harrods by a frantic Inspector Lestrade: the world’s largest Ruby, the Devil’s Eye, has been stolen and he doesn’t know where to go next. There are just a few cryptic clues that only a master of deduction, *and mathematics,* could solve…

**AND THE ANSWER IS…**

**THE LONDON EYE! **

Our congratulations to this week’s winners: **CLASS 10 Set 3 from Sutton Grammar School in Surrey.**

Here’s their answer:

If you work out the volume of the ruby; (area of rectangle + area of trapezium) x length

((10 x 3.5) + (7 x 2.5)) x 11 = 577.5 cubic cm.

The Mass is density x volume; so 4 x 577.5 = 2310 g

If we split the answer 2310 in to 2 parts we got the co-ordinate (23, 10)

This is THE LONDON EYE

{and the thief keeps talking about eyes at the start of the note}

[We also worked out the thief got through Door B; if you draw the lasers as lines on the graph, all the doors are blocked except B]

We’ll be sending the winners a **Sherlock Holmes DVD** and a **tin of Cadbury’s Heroes** in the post!

DON’T MISS OUT ON WHAT HAPPENS WHEN HOLMES AND WATSON ARRIVE AT THE LONDON EYE IN EPSIODE 2:

**NEXT WEDNESDAY, 6TH OCTOBER**

And remember, you can join this competition at any time. There will be six Episodes in total, with a prize to the winner of each one. You can keep up-to-date with all details of the competition on **this page of our blog**.

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