Sharpen your neurons with the maths test just taken by 300,000 UK school pupils
Today youll be attempting questions from a maths test that 300,000 Britons aged 11 to 13 took just over a week ago. (Thats years 7 and 8 in England and equivalent years in Scotland and Northern Ireland).
The United Kingdom Mathematics Trusts annual Junior Challenge aims to get students excited about maths with 25 appetising and intriguing problems to be solved in an hour. Ive chosen my favourite ten below, and Im giving you no more than 25 minutes to solve them. Did you hear that at the back? You might find the first ones easy, but Im expecting ten out of ten.
Ill be back at 5pm BST today with full explanations of the answers and Ill also compare your marks with the marks of the pupils who sat the test. If you are reading this on mobile, click +Follow Alex Bellos above and youll get a notification when the update appears.
Please make a note of your answers. When you press submit the screen will reveal the correct answers, but not mark individual submissions.
On some devices the image for Q4 is stretching. The image should show that the top angle of triangle C, the bottom left angle of triangle D, and the bottom angle of triangle E are right angles.
Thanks to the United Kingdom Mathematics Trust for letting me reprint these problems. Schools wanting to participate in their national challenges can find out how to do so here.
Earth is home to gobs of species, from tiny to gargantuan, and ordinary to downright weird. Take this whimsical octopus spotted by NOAA Ship Okeanos Explorer’s remotely operated vehicle near Shallop in the Atlantic O (Image courtesy of NOAA Okeanos Explorer Program, 2013 Northeast U.S. Canyons Expedition)
Calculating how many species exist on Earth is a tough challenge. Researchers aren’t even sure how many land animals are out there, much less the numbers for plants, fungi or the most uncountable group of all: microbes.
Now, researchers have attempted to use the laws of math to make an estimate that includes both micro and macro life. The researchers estimated that there may be as many as 1 trillion species out there.
The research is based on scaling laws, which predict a proportional change linking two variables. For example, scaling laws apply to the change in metabolic rates as body size changes, and to the number of species found by geographical area.
Indiana University researchers Kenneth Locey and Jay Lennon analyzed data sources that sampled 20,376 sites for bacteria, archaea and microscopic fungi, and 14,862 sites for trees, birds and mammals. Using the total abundance of individuals, the researchers were able to work out the scaling rules that linked the number of individual organisms to the number of total species.
The method led to an estimate of between 100,000,000,000 (that’s 100 billion) and 1,000,000,000,000 (that’s a trillion) species of microbes on Earth.
“Until now, we haven’t known whether aspects of biodiversity scale with something as simple as the abundance of organisms,” Locey said in a statement. “As it turns out, the relationships are not only simple but [also] powerful, resulting in the estimate of upwards of 1 trillion species.”
It has been estimated that there are 100 trillion individual bacterial cells in a single human body, and a nonillion (10^30) individual bacterial and archaeal cells on Earth, the researchers wrote Monday (May 2) in the journal Proceedings of the National Academy of Sciences. If these individuals represent a trillion or so species, that means very little is known about Earth’s microscopic denizens, Lennon said in the statement. The genomes of only 100,000 microbial species have been sequenced, and only about 10,000 species have been grown in a lab, he said.
“Our results show that this leaves 100,000 times more microorganisms awaiting discovery and 100 million to be fully explored,” Lennon said.
Pinning down exact numbers of microbial species is tricky, however. Previous estimates have pegged the number at between 10 million and a billion, according to a 2004 review paper in the journal Microbiology and Molecular Biology Reviews. A 2011 paper in the journal PLOS Biology put the total number of species at 8.7 million, but that study’s methodology calculated the existence of only 10,000 bacterial species, a contradiction of the 2004 review that put the minimum known bacterial species above 35,000.
And it’s not just bacteria that are the problem. Even estimates of nonmicrobial species vary wildly. Researchers reported in 2014 in the journal Trends in Ecology & Evolution that estimates of the number of species on the planet have “failed to converge over more than six decades of research.” The estimates range from 0.5 million to 10 million and are often logically inconsistent, the authors of that 2014 study wrote: “For example, estimates of species richness for coral reefs have exceeded estimates for all marine species, and estimates for all marine species have exceeded global estimates for all realms combined.”
Here are the questions, answers and explanations. I have also included the percentage of children who got it right and the percentage of Guardian readers who did. In one question children did better than Guardian readers (although this was the one with the image that stretched) and in two others the scores were equal. Well done all round, anyway.
I hope you enjoyed the mental work out – Ill be back with another puzzle in two weeks.
1. What is the value of 1/25 + 0.25? Answer: 0.29
1/25 = 4/100 = 0.04.
So 1/25 + 0.25 = 0.04 + 0.25 = 0.29
Children: 52 per cent correct (3 per cent did not answer).
Guardian readers: 81 per cent correct.
2. Gill is now 28 years old and is a teacher of Mathematics at a school which has 600 pupils. There are 30 more girls than boys at the school.
How many girls are at Gills school? Answer: 315.
Let there be g girls in Gills school. Then there are (g 30) boys at the school.
So g + g 30 = 600 . Therefore 2g = 630 , that is g = 315.
Children: 52 per cent (2 per cent did not answer).
Guardian readers: 81 per cent.
3. One of the three symbols +, , x is inserted somewhere between the digits of 2016 to give a new number. For example, 20 16 gives 4.
How many of the following four numbers can be obtained in this way?
36, 195, 207, 320
All four numbers may be obtained: 20 + 16 = 36; 201 6 = 195; 201 + 6 = 207; 20 x 16 = 320.
Children: 39 per cent (3 per cent did not answer).
Guardian readers: 62 per cent.
4. A square is folded exactly in half and then in half again. Which of the following could not be the resulting shape? Answer: D
With ministers committing nearly 80m to the European Space Agency’s (Esa) human spaceflight programme – an essential contribution to secure Tim’s place in orbit – the question can be answered in different ways.
You can assess the research he has carried out in orbit or the profile he has given to the UK’s space industry or the inspiration he’s provided to a new generation.
Let’s start with the last of those because the man himself has always wanted to enthuse children about science and engineering to help encourage a British technological renaissance.
Several years ago, just after he had started training in Houston, we met at a restaurant near the Nasa centre and Tim’s face lit up when he described ideas for engaging schools in space-related experiments.
So how did he do?
Well, the numbers are pretty staggering. By the latest estimate from the UK Space Agency’s education specialists, at least one million pupils in British schools have been involved in his projects so far.
And, because a detailed analysis has yet to be done, the total may in reality be far higher.
Some 30 projects ranging from fitness challenges to computer coding to amateur radio hook-ups made up what ranks as the largest public engagement exercise for any Esa astronaut.
Take the Rocket Science scheme: about 8,600 packets of seeds from rocket plants were sent to thousands of schools and other academic institutions reaching more than 600,000 children.
Half the packets contained seeds that had spent six months in space, the other half held seeds that had stayed on the ground – and in classrooms across the country pupils are cultivating the plants to see if there’s a difference.
Libby Jackson of the UK Space Agency says the exercise allows teachers to explain some key principles in research such as blind trials and randomisation, and to emphasise the importance of sustainability in food production.
“Add space as the context and it makes it all the more exciting,” she says. “The enthusiasm has been fantastic.”
Then there were live link-ups in which Tim, floating in front of an ISS camera, could speak directly to children themselves.
The Cosmic Classroom saw lucky kids gathered for an event in Liverpool but a further 400,000 watched a webcast, and all of them had a chance of posing questions.
At the same time, special exhibitions called Destination Space were staged at 20 science centres around the country and some 350,000 have attended so far to learn about Tim’s mission.
Will any of this make a difference to the number of children choosing to study the STEM subjects – science, technology, engineering and mathematics?
The first test will come in September when schools see who confirms for those classes but it will take many years to get a genuinely reliable answer, particularly for a sense of how many then go on into STEM careers.
In the first research of its kind, a team from University of York will attempt to investigate this over the coming years – looking at whether there really will be a “Tim Peake effect” like the “Apollo effect” in which the Moon landings fired up a whole generation.
Libby Jackson says the anecdotal evidence of a positive response is already clear, and she adds: “I haven’t met a teacher or parent who hasn’t said it’s all great – I think the numbers engaged in Tim’s mission will be staggeringly high.”
And that engagement will not end with his return. While 650 primary schools used Peake-related materials in their teaching this year, the total next year will be 750 – and excitement will surely build as Tim tours the country on his return.
Space station science
So what about Tim’s involvement in the science on the space station?
By their very nature, the 250 experiments under way tend to be long-running so no single astronaut will ever have a pivotal role in them during their time on board, let alone be able to claim a ‘eureka’ discovery.
But Tim has done his bit in a wide range of projects, some relevant to people on Earth, others aimed at future space missions, including allowing his own body to be used in a range of medical experiments. A good question would be to ask how many blood samples he’s taken.
He took part in an airway study in which his exhalations were monitored for nitric oxide which may be an indicator of internal inflammation – relevant to asthma sufferers on Earth and to future astronauts visiting the dusty environments of the Moon or Mars.
He worked on an investigation of metal alloys in which samples are heated to 2000C and levitated – a technique, impossible back here, which avoids any risk of contamination from the container holding the experiment.
He helped to study the endothelial cells that line blood vessels and degrade with ageing. These appear to grow differently in microgravity, so samples have been cultivated in a growth medium and will be analysed back on the ground.
By remote control, he steered a robotic rover in a simulated Martian terrain in Stevenage to test how future astronauts could guide robots and work in tandem with them.
Prof Mike Cruise, who heads Esa’s human spaceflight science advisory committee, told me that while “you can’t unpick the role of any individual person”, Tim had “exceeded expectations” and that his “personal authority” had helped to reach people who would not normally be interested in science.
Finally, what has Tim Peake’s mission done to highlight Britain’s space industry, worth at least 10bn, but often operating without much public or political attention?
According to Lord Willetts, a former science minister, Tim has been “a brilliant ambassador” and he says “his flight has achieved more than we dared hope”.
It was David Willetts, at a crucial Esa meeting in 2012, who skilfully negotiated a relatively minor role for Britain in the agency’s human spaceflight programme which helped secure Tim’s mission.
“It’s hard to measure, but I believe Tim has given Britain some real confidence that we are a serious player in space. People didn’t recognise that we design satellites and instruments for Mars and beyond, that a Mars rover is being built in Britain.”
The hope will be that further big industrial orders will follow, boosting the scale and ambition of the space projects undertaken here.
For decades, successive governments had shown no interest in sending people into space – the first Brit to make it, Helen Sharman, flew with the Russians after winning a competition.
David Willetts is among those hoping that Tim’s flight will not be the last. Like many, he’s become an enthusiast, seeing the fervour whipped up among children and the value of having a glamorous standard-bearer for a potentially vast industry.
And the excitement is infectious. A few weeks ago, walking along a corridor in the House of Lords, his mobile rang. It was a Houston number. Tim Peake, hurtling 250 miles above the planet, was calling for a chat.
A British astronaut was ringing a peer in Parliament – without any formal Cabinet decision or public discussion, we have suddenly become a spacefaring nation.
The question is whether other missions will follow. And that depends on the strength of the Tim Peake effect, and whether it’s enough to convince ministers to keep paying.
Apple CEO Tim Cook doesn’t mince words when it comes to children’s education.
“We believe coding should be a required language in all schools,” Cook said at Apple’s WWDC on Monday.
To that end, the company is launching Swift Playgrounds, a new app for the iPad that teaches kids to code in a simple, colorful way. Through Swift, the programming language Apple launched two years ago, kids can learn the fundamentals of coding, commanding playable characters to executing tasks.
Challenges get more advanced as the games progress, and Swift Playgrounds provides a preview of the content with graphics and a description of the steps you take as you progress through each challenge. The app will be available on iOS 10 in the fall.
The learn-to-code movement is sweeping across the U.S., largely due to the expected influx of jobs needed in computer science and other sciences, technology, and mathematics (STEM) fields in the coming years. There will be a huge need for technical jobs but a lack of talent to fill them.
According to the Bureau of Labor Statistics, 71 percent of available jobs in STEM industries are in computing, but just eight percent of STEM graduates have degrees in computer science; computing jobs are expected to grow at twice the rate of jobs in other areas.
Stepping up to fill the gap between the education systems and the workforce are companies, nonprofits, and government-sponsored educational programs that aim to bring computer science and coding courses to classrooms. Apple’s efforts include providing Swift Playgrounds for free on all iPads, a device that is popular with teachers and educators.
Perhaps the most widely recognized effort is that of Code.org, a nonprofit working to bring coding education to all levels of K-12 study. Backed by some of the biggest names in tech, including Google, Apple, Microsoft, and Facebook, the organization rallies classrooms across the country to learn to code through both paper and digital activities.
President Barack Obama participated in the organization’s Hour of Code in 2014, becoming the first sitting president to learn to code.
The learn-to-code movement is not without detractors. Coding jobs are just one part of the technology industry, and while it’s helpful to understand the building blocks of the apps and services we use every day, cultivating digital literacy is perhaps more important than being able to write and execute algorithms or build an app.
Of course, addressing the dearth of digital literacy or coding programs in the classroom by stopgapping the lack of programs with apps built by technology giants could have a ripple effect throughout educational institutions.
For Apple, the solution is obvious: Give kids and schools a free app to teach them Swift, and they will, in turn, build apps for Apple’s platform. It’s a win-win situation for all those involved.
At Monday’s WWDC keynote, the youngest audience member was 9 years old. And in introducing Swift Playgrounds, Cook said that he hopes “this gift to kids and schools around the world” helps to make coding a daily part of education programs so other youngsters can be introduced early to a world of apps and software.
Being a parent can be one of the most rewarding experience of somebody’s life. But as they get older, children have the ability to make even the calmest parents completely exhausted with their hardheadedness! Andthislittle baby might be the most stubborn girl you’ve ever seen in your whole life!
Dad happens to be a math teacher, so it would make sense that he would want to teach his little girl how to properly count to 5. But for whatever reason, this little girl doesn’t seem to believe much in the number 4. When Dad asks her to count to 5 she happily replies, “One, two, three, five!”
So while this girl might not end up being the best in the world at mathematics, something tells us that her self-confidence will lead her down a road of success. She’ll probably become a boss one day, and even if she’s wrong, she’ll make everyone follows her lead! Or maybe this lesson will make her one of the world’s leading mathematicians. We’ll see in a few years’ time.
Eventually, the girl’s giggling mother comes up with a pretty smart solution to this problem. “Count to four.” The girl’s response leaves Dadfinallyvindicated. It really doesn’t get much cuter than this.
This Hubble extreme deep field image shows many galaxies outside the Milky Way. (NASA; ESA; G. Illingworth, D. Magee, and P. Oesch, University of California, Santa Cruz; R. Bouwens, Leiden University; and the HUDF09 Team)
We all know that the universe is expanding, right? Well, if you weren’t aware, now you are. We live in an expanding universe: Every galaxy is flying away from every other galaxy. This naturally leads to a common question: If the universe is expanding, what’s it expanding into? More universe? Nothing? Something resembling a vague fog? Where’s the edge of our cosmic soap bubble?
Well, our universe does have an edge that is, if by “our universe,” you mean the observable universe. The speed of light is just that a speed and the universe has only been around for so long (about 13.77 billion years), which means only so much of the universe has been revealed to us via the light that has traveled those vast cosmic distances. And what’s outside our observable limit? That one’s easy: It’s just more stuff, like galaxies and black holes and new, fantastic varieties of cheese. It’s forever unreachable by us, sure but it’s still over there. [Our Expanding Universe: Age, History & Other Facts]
From our perspective, it looks like we’re at the center of everything, and every single galaxy is flying away from us. So that, naturally, leads to the “There’s got to be an edge” line of reasoning. But let’s say you hopped over to Andromeda, our nearest galactic neighbor. From that new vantage point, it still looks like you’re at the center of the universe and everything is flying away from you. Now let’s go really crazy and pretend we can teleport you to the most distant observable galaxy, on the far edge of our observational reach. Guess what? Yup, from your position, it looks like you’re at the center of the universe, and every galaxy including the distant Milky Way is racing away from you.
That’s what we mean when we say “The universe is expanding.” Every galaxy is receding from every other galaxy (with a few minor exceptions from local mergers, but thats the subject of another article).
But there’s got to be a limit, right? It’s not like the universe is infinite, right? Right?
Well, probably not. While it is very, very, very large, the universe is not likely infinitely big.
But it still doesn’t need an edge.
Think again about hopping from galaxy to galaxy. From the Milky Way, the universe looks like an enormous soap bubble growing in size, with us at the center. But from another galaxy, this universal bubble looks different, because there’s a different galaxy at the “center” of the bubble.. What we might be tempted to call an “inside” or an “edge” of our universe is meaningless from the new perspective. And that’s true for every single galaxy.
I’ll say it again: “Expanding universe” just means every galaxy is moving farther apart from every other galaxy. That’s it! No edge. No bubble. Nothing to expand into. The math is simple: The universe gets bigger with time. And that’s it.
Let’s take a step back. Everyone knows those common analogies used to describe an expanding universe: Galaxies are like ants crawling around on a beach ball. We’re all raisins in a loaf of bread. And oh! the beach ball is inflating! Yes! The loaf of bread is rising in the oven! Space is expanding, and the galaxies are carried along with it! See? Easy!
Those analogies certainly get across an important point: The galaxies aren’t flying or shooting or waltzing away from each other. It’s the space underneath them that’s doing all the work of expanding; the galaxies are just along for the cosmic carpet ride.
But those analogies also carry a fatal flaw. We can all easily imagine an inflating beach ball or a rising loaf of bread, and we immediately think of them as expanding into something: empty air. The beach ball has a skin. The loaf has a delicious, crunchy crust. They have edges, and they’re moving into something.
Our minds have played a trick on us, and it’s cheating us from being fully awestruck at what’s going on.
When we use the ants-on-a-beach-ball analogy, the first thing people say is, “Why ants?” I don’t know; deal with it. And the second thing people say is, “Oh, the center of the universe is right there, in the middle of the ball.” At that point, I have to jump in with the limitations of the analogy:Our entire universe is the surface of the beach ball. And the surface of the ball has no center. Just as the surface of the Earth has no center. We could’ve made the poles anywhere we pleased.
In the beach ball model, our entire universe is a two-dimensional surface, full of idiot ants trying to crawl toward each other but failing because some jerk keeps inflating it. OK, fine, whatever. That model universe is two-dimensional, but in our mind’s eye, we immediately think of it expanding into a third dimension a dimension that the ants can’t access, because they can’t jump. But that extra dimension provides a “place” for the surface of the ball to expand into.
But our real universe is three-dimensional. While string theory suggests there might be extra dimensions, they’re all supertiny, so those don’t count. So is there a fourth extra dimension that provides the “stuff” for our universe to expand into?
Maybe, maybe not. Here’s the thing: The mathematics could support a fourth dimension for our 3D universe to expand into. And we would definitely have an “edge” in this extra dimension, the same way you can point to the “edge” of a 2D beach ball surface.
But it doesn’t have to.
We don’t need a fourth dimension to wrap around our universe. We have a complete and consistent mathematical description of the expansion of the universe using only the normal, workaday three dimensions that we know and love. So that means we can have an expanding universe without needing an edge or a thing for it to expand into.
I’ll admit I have trouble wrapping my head around this concept. But that’s the beauty of using mathematics to understand the universe: We can create and manipulate concepts that our brains simply couldn’t handle on their own!
(CNN)Stella Uzochukwu, a former electronics engineer, is doing something profound. She is teaching girls how to code in defiance of Boko Haram, whose brutal crusade against western-style education — among other things — has robbed children of education in northern Nigeria.
School girls in the Odyssey Educational Foundation‘s after school STEM program are being encouraged to pursue careers in science and technology, and have built a robot to tackle the country’s waste problem.
For this year’s competition, students had to build and program robots that could pick up and drop off pieces of garbage on a play area. Unused plastic bags have also been turned into play marbles by the girls.
“There was a particular incident last year where we wanted to engage kids in coding during the school holidays”, explains Uzochukwu, “but none of the kids were allowed to come into school because of these attacks”.
“Their parents wanted to keep them at home so we had to cancel it”, she adds, “it was very sad because we wanted to teach them how to write apps”.
The mentality amongst parents in Nigeria is “they’d rather die with their children at home than send them to school to die on their own”.
Despite these challenges, Uzochukwu has persevered. Last year, the charity moved into a dedicated center so kids would not have to come into their school after hours, alleviating security concerns.
Although the school is co-ed, it has focused its efforts on teaching girls science and tech, deliberately arranging a ratio of three girls to one boy in its clubs: “Most of the boys are already doing maths and science and they love it, but we wanted to encourage it amongst girls as well.”
When traveling to India to complete a masters degree in telecoms management, Uzochukwu discovered school clubs in India gave extra STEM tuition to children.
She also noticed that in her masters class of ’42 there were just three women, including herself. Upon returning to Nigeria, she set up the charity.
Her seven strong staff go into communities and encourage parents to send their girls to school. Mothers are taught to make soap, creams and other ointments to supplement their income in order to pay for school fees.
The goal is to ensure kids can learn how to repair computers, laptops, and phones, “so when they get out of school they will not be roaming the streets”.
“Learning programming, coding and mathematics is what I think marks the difference between underdeveloped and developed nations.”
Below are two sets of six dots in a hexagon. The number beside each dot describes the number of lines coming from that dot. On the left each dot only has a single line coming from it. On the right each dot has two lines.
In their article, the Vote Leave politicians said they would seek to spend some of the cash saved by quitting the EU on cutting VAT from household gas and electricity bills, a tax imposed by the then Conservative government in 1993.
Energy and environment
This issue covers energy availability and environmental protections.
What the leave and remain sides are saying about energy & environment in the #EUref campaign
The EU is in the process of developing an integrated energy market
There are several EU-wide policies to tackle climate change including the Emissions Trading Scheme
It also legislates on issues such as water quality and air pollution
EU environmental regulation can be an unnecessary burden on business and push up energy prices
Other European countries would still want to sell their electricity to the UK after Brexit
Most of the UK’s gas imports come from Norway Britain is not dependent on Russia
Leaving the EU would see energy bills rise by 500m
Britains energy security is stronger as part of the EU because it negotiates as a large bloc
The UK has cleaner water and air, and lower greenhouse gas emissions, thanks to EU action
EU referendum issues guide: Explore the argumentshttp://www.bbc.co.uk/news/uk-politics-eu-referendum-36027205Explore all the issuesChoose an issue:What both sides are sayingAll issuesMain viewsShare this pageEU referendum issues guideWhat the leave and remain sides are saying in the #EUref campaign
“The least wealthy are hit particularly hard,” they wrote.
“The poorest households spend three times more of their income on household energy bills than the richest households spend. As long as we are in the EU, we are not allowed to cut this tax.
“When we Vote Leave, we will be able to scrap this unfair and damaging tax.
“It isn’t right that unelected bureaucrats in Brussels impose taxes on the poorest and elected British politicians can do nothing.”
VAT on domestic fuel bills was cut to 5% under the Labour government – the lowest rate allowed under EU rules.
‘Hits poorest hardest’
In 2014, the average bill for a customer of a big six energy firm was 1,190.
Mr Gove told the BBC it had been a “mistake” of the previous Major government to introduce the tax, adding: “The Conservative government at the time did so because of the economic damage that the exchange rate mechanism of the European Union had caused.
“I think it is now time to acknowledge that that was an error.”
The justice secretary said it would be up to the prime minister and the chancellor to axe VAT, but said he backed such a move because it was “an unfair tax that hits the poorest people hardest”.
Mr Osborne tweeted his attack on Vote Leave’s claim, saying leaving the EU would lead to a smaller economy, “a hole in public finances” and higher taxes including VAT.
Energy Secretary Amber Rudd said it was “unequivocally” not the case that bills would fall if the UK left the EU, and that membership actually helped keep household costs down.
Remain campaigners said Leave-backing Conservatives Liam Fox, John Whittingdale and Iain Duncan Smith had previously voted against moves to reduce VAT on domestic fuel.
Britain Stronger in Europe also released a report which they said detailed Leave’s “unaffordable” spending commitments.
They said more than 20 commitments, totalling 110bn, had been made – eclipsing the potential saving from leaving the EU.
Vote Leave’s Chris Grayling dismissed the figures as “a complete fallacy” and “absurd mathematics”, saying his side had been merely illustrating what could be done if the UK’s contributions to Brussels were clawed back.
With just over three weeks to go before polling day, two opinion polls for The Guardian gave the Leave side a narrow lead.
Meanwhile, Business Secretary Sajid Javid warned of the impact of leaving the EU on small and medium-sized enterprises.
He cited Department for Business, Innovation and Skills analysis, estimating that 8% export to the EU and a further 15% are in the supply chains of other businesses that export to the EU.
But Vote Leave’s John Longworth said the government’s figures were “extremely questionable”, that businesses were held back by EU “red tape” and that Mr Javid had “changed his mind” over the EU.