Quantum Physics – with a Coin

Find a coin.

Go on, rummage in a pocket, purse or wallet and find something a reasonable size like a UK 2p or 10p coin, about 1 inch or 2.45cm in diameter. This is all you need to explain quantum physics to someone.

Yes I did just say quantum physics. Surely that’s only for geniuses you cry! Quantum physics is a subject that intrigues and is hopelessly misunderstood in equal measure. This little demonstration will really impress your friends and explain all the basics of quantum physics in simple language. Let me show you how.

I’m assuming you can toss a coin. Throw it up and catch it then slap it down on the back of one hand. Did you get heads or tails?

Quantum Physical States and Probability

The only outcomes possible in a coin toss are heads or tails. You can balance a coin on its rim if you are careful and have a flat table, but that outcome never occurs in a coin toss, due to the slapping-it-flat-on-the-back-of-your-hand action.  There is no way to get heads and tails at the same time as they are on opposite sides of the coin. So I’m going to go ahead and say that the result of a coin toss is one of two possible states, either heads or tails.

Toss the coin a few times and you’ll find out that the number of heads and number of tails usually balance out. You should have an unbiased coin. This would mean the chance of getting a head each time you toss is the same as the chance of a tail, 50:50 chance of either state.

What if we suspected one side had been weighted and so the coin was biased? Tossing the coin hundreds of times would give us a very reliable way of finding if it had been tampered with. The numbers of heads and tails should balance out. If 40% of the time the coin’s state was found to be heads and 60% tails we know it is biased towards tails.

Tossing the coin allows us to find out information about what states are possible and what is the chance of ending up with any one of those states.

Now we’ve established that, what state is the coin in before you catch it?

You might say “no state” but that would mean there was no head-ness or tail-ness there at all, nothing. That’s not quite right as the coin is there. You can see it spinning in the air. How do you describe that?

 

Superposition in Quantum Physics

Quantum physics has a neat word for describing the mixture of head-ness and tail-ness that a spinning coin has before you catch it. The word is superposition. Superimposing is a technique used in photography or film where one image is put on top of another. The final image is a composite of the two. Superposition is a bit like that.

The spinning coin is not devoid of states, we can’t say it has no heads or tails to it. Instead it is a constantly changing superposition of the two states. This superposition tells us nothing about what state this unique toss will end in. That depends on all sorts of things like how fast it is spinning, how high we throw it, when we catch it etc. It won’t help us work out the outcome of an individual throw.

The superposition does contain information about any bias in the coin. As it spins, a heavier side to the coin will spend more time at the bottom of the spin and the lighter side would spend more time at the top. There is some information there we could extract about how the pattern of heads and tails would look after 100s of throws, if only we had a way of measuring it.

 

Taking A Quantum Measurement

You already know how to measure the state of the coin. You catch it and slap it down on your hand. Look at the coin and there is your measurement.

But this involves permanently altering the condition of the coin. You are forcing it into one of two possible states. When I measure my height I don’t force a mixture of all possible heights into 5 foot 10 inches. There is no probability of getting anything other than 5’10”. This measurement of the coin is different to normal measurements. The act of measuring the system we are interested in (the spinning coin), fundamentally alters the system we are interested in. Bummer.

There is no way around this I’m afraid. To get information about the possible probabilities of either heads or tails we toss the coin 100s of times. Then we interfere with the spinning superposition each and every time, forcing it into a single state. Only by repeating this measurement over and over do we get enough data to work out a pattern.

This is true of quantum objects like electrons. It is called The Measurement Problem. Only in quantum physics does the act of measuring the system permanently change the system. Or to put it another way, extracting information from the superposition destroys it. This is called collapsing the wave function.

What is a Wave Function?

Waves bob you up and down in the sea or make use of your hand to signal your departure or arrival. In both cases something is oscillating between two positions over and over. Up and down on the sea and side to side with your hand.

Lots of natural phenomena can be described using the language of waves. The variation in light intensity due to day and night, seasonal mean temperature changes, hormone levels in menstruating women, anything which has a repeated variation across a range of values is wave-like.

Physicists use the mathematical language of waves to describe quantum states. The spinning coin has a repeated variation in a range of values, it flips from heads to tails and back again as it spins. We can use wavy maths to describe this variation. The mathematics of waves is even more helpful as it allows us to add waves on top of each other and work out the resulting wavy shape. Like different tides or ripples interfering with each other at a point on the sea.

The spinning coin has a changing superposition of the heads and tails states. The chance of measuring either state depends on which way up the coin is pointing when you catch it. As the coin rotates it is found in a 100% heads state only once each rotation and only for a very short time, likewise for the tails state. The the rotation moves one side of the coin slightly higher and the amount of “heads” reduces slightly and the amount of “tails” increases. Or more correctly the probability of getting heads reduces slightly and the probability of getting tails increases slightly. So the chance of ending up with heads or tails is continuously changing as the coin rotates. If you plotted the probability shape on a graph it would rise and fall and rise and fall just like a wave.

The wave function is the name given to a mathematical wave shape which describes this varying chance of getting a particular state in a measurement.

Collapsing the wave function forces a single state on the coin, in this case either of the extreme positions, giving a head or tail.

 

Now the Quantum Physics Bit!

All this talk of coins is preparing us for the big moment to tie all this in with teeny tiny quantum particles.

There is an experiment which shows exactly what we have been talking about with coins, but with electrons. It’s called the double slit experiment. It is the classic way of introducing people to the weirdness of the quantum world. Electrons behave like a wave superposition of states until you force a measurement on them and then they behave like a lump with a fixed state.

Instead of throwing electrons up and down and catching them with some clever laser trap equivalent of a coin toss (or something!), the electrons are thrown at a screen. The screen can detect the hits from the electrons and emit a tiny light burst. So a pattern builds up showing where the hits occur.

When you shine a wavy source, like a torch, on a screen you get a bright spot in the middle and it gradually dims as the light spreads out at the edges. If you fire a lot of blobs at a screen there is a big build up of bobs in the middle and fewer out to the sides. It is hard to tell one result from the other.

So the physicists put something in the way of the screen. A big sheet with two narrow slits in it.

quantum double slit experiment

Diagram of the double slit experiment from Wiki-Commons

Now you can tell the difference between the pattern produced by wavy things and the pattern produced by blobs. Waves overlap and produce a new wavy pattern as shown in the picture above. The blobby particles are simply split into two streams of blobs by the slits and produce two splats on the screen. No superimposing happens for them.

Electrons are supposed to be blobs not waves. They are particles. When a beam of electrons is fired at the slits they start to build up a pattern on the screen. The pattern is a wavy interference pattern!

quantum double slit interference pattern

Each dot represents the impact of an electron on the screen. Many hits build up to produce an overall wave interference pattern, even though electrons are particles. This is evidence of the wave-particle duality of electrons. Experiment performed by Dr Akira Tonomura in 1989 at Hitachi. Creative Commons ShareAlike licence.

Here we are looking at information contained in the wave function of the electrons. Only when hitting the screen are they being forced into a state. Then their position state is fixed to a definite value. Just like the coins spinning in the air contained information about the probability of heads or tails, so the electrons shooting towards the screen contain information about the probability of where they will show up in the interference pattern.

We can collapse the wave function earlier on and force the electrons into a position state much sooner if we measure them. We can put a sensor on the double slits and record which slit the electrons go through. This destroys the supposition of location states and forces the electron to be in the left or right slit. Like catching a coin destroys the supposition of heads or tails and forces the coin to be one or the other. Then the electrons behave like blobs and build up in two patches on the screen. The waviness of the electrons has been lost.

This experiment was astounding. To actually see the theoretical wave nature of the electrons supposition and then be able to collapse the wave function and bring their blob nature back again has boggled many a mind over the years. Tiny particles can be waves or can be blobs depending on how they are interacting with their surroundings. Some interactions collapse the wavy behaviour and force the electrons into a fixed state. What we understand as measurements always collapse the wavefunction because our measurements require a value, a fixed state to give a result.

Conclusion

Tossing a coin will never look the same again! Each time you catch a coin you can think about how every photon of light hitting your eyeball has just collapsed its wavefunction, every click of the TV remote, every interaction of microwaves with food in your kitchen is a quantum measurement happening in front of you.

Now we need to talk about Schrodinger’s Cat…

schrodinger's cat experiment

A thought experiment proposed by Erwin Schrodinger. Picture from https://www.nobelprize.org/educational/physics/quantised_world/

Don’t Teach from Definitions! Just Don’t.

frustrated student

I settled down to watch a TV programme about schools, “Living with the Brainy Bunch”. It’s not something I would normally do having worked in schools for 13 years, a bit too much of a bus man’s holiday. The premise of this show was, however, intriguing. Two failing students were going to spend time living with a top grade student and their family to see if this would improve their prospects. How very Pygmalion. I was genuinely interested to see what the outcome would be.

But then in the middle of the documentary I found myself shouting at the TV screen. A teacher in the background of one scene committed the cardinal sin of physics teaching. The title of the lesson and aim were up on the board and the first thing they did was say “this is Ohm’s Law” and wrote it down, V=IR. Noooooooooooooo!

 

What is Wrong with Definitions?

There is a wealth, a plentitude, an embarrassment of research which clearly shows that rote physics teaching achieves poorer results in the short, medium and long term compared with active learning. This article published in Nature in 2015 summarises developing thought on the subject.

The rote style of teaching is adopted by people rushed for time, overly reliant on the exam specification or who don’t know what good physics teaching looks like. It makes for lessons which are instantly forgettable and do nothing to develop the students’ understanding. And understanding not parrot-fashion learning is crucial. The bread and butter basics of physics teaching should be understanding and thinking skills.

Charles Tracy and Peter Main from the Institute of Physics wrote an article called “Defining physics”[1] and have suggested a rather long winded but none the less instructive way of thinking about what physics actually is. Peter Main outlines his definition of physics as

a way of thinking, a reductionist view of the world where phenomena can be understood in terms of a relatively small number of physical laws and limited only by the complexity of a system or phenomenon. [2]

He argues that defining physics by its content misses out the crucial ways of thinking that studying physics should develop (when done correctly). Why develop these ways of thinking? Because you can’t DO physics in any effective way at all without developing these ways of thinking. Tracy and Main include critical thinking, deep understanding, logical and experimental consistency, use and development of models, awareness of simplifications, the excising of prejudice in thought patterns and ability to go beyond “common sense” in their list of physics skills. None of these are being taught or practised when teaching is done by copying a definition in words and symbols and then applying it to examples.

Teaching from definitions is teaching content only, and in the most dry and uninteresting way. You remove all thinking for the students and present a fait accompli. Effectively you are conveying this message “some other smart people came up with this, I’m not going to tell you how, just shut up and learn it OK?”. You do this and you are a disgrace to the profession.

Telling a student an answer, e.g. plug it in V=IR, and you enable them to solve a single set of simple problems. Explain to them how and why V=IR came about and they have an understanding that will enable them to solve many problems. Allow them to discover the relationship for themselves and work out how to use it and you’re a bloody genius. This is what we should all be doing in our classrooms.

 

Teaching from Definitions and the Impact on Girls

Teaching from definitions is stated by female students as one of the things which turns them off physics. This was an interesting outcome from the research “Girls in the Physics Classroom”[3].  From that publication note this particular quote:

Physics makes greater use of precise technical language and symbolic representation than the other science disciplines – probably than all other school subjects apart from mathematics. Most physics teachers are steeped in the use of, and sometimes the abuse of, this type of language. For example, it is not uncommon to hear “V = IR” used to denote Ohm’s law. For many pupils – boys and girls – this use of language and symbols is mystifying and it reinforces the impression that the subject does not connect with their world. Teachers who “talk equations” at an early stage in physics education risk alienating many students – girls in particular – from the subject.

The author goes on to say how pupils at KS4 begin to heavily link maths to physics but not because they are frequently using maths in analysing data or solving problems. No they get used to being presented with equations out of a useful context.

“It’s all about remembering equations. I can work out the resistance of a wire but I don’t know what it means.”

 

Girls especially found that this was a problem because they felt unable to “ask questions about a word or equation” and so felt that their understanding was stalled. Teachers who only introduced equations once the underlying concepts were well established were able to keep girls’ interest for longer.

It is important to understand that the reluctance of girls to engage with technical shorthand language is not a result of their reduced understanding. Indeed the author stresses that when questioned by the researchers the girls had an equal understanding to their male peers. Historically girls outperform boys in GCSE science including physics. In 2016-2017 169,455 girls achieved A*-C in maths and science GCSE compared to 163,256 boys [4].

The difficulty appears to be cultural. Boys are cultured to use technical language and be rewarded with peer status and the approval of older authority figures when they do. Think about how boys discuss football stats or the specifications of their mobile phones, cars, computers. They spend years developing a confidence with numerical shorthand and technical language in competitive communications with their peers. Girls are socialised to use more expressive and empathetic language. I can’t tell you how weirdly you are treated as a young woman if you try having a conversation about the amount of memory, processing speed and other specifications of a tablet, laptop or phone. Bafflement not at the content of the conversation but at my motivations, awkward silences and “what is wrong with you?” are all responses I have had when trying to talk geek to other girls.

When a teacher uses technical language and algebraic shorthand in a physics class they are unwittingly displaying a bias in favour of one gender. The use of a snappy V=IR shorthand feels instantly familiar to boys. Girls aren’t familiar with this way of speaking and seem uncomfortable with using it, holding back their replies. Then a boy shoves up his hand or calls out and gives a terse one word reply, the teacher accepts it and the lesson moves on. But you have lost the interest of the girls. Overtime this communication bias leads them to give up on answering questions in class. They feel less able to access the lesson and join in the teacher-pupil conversation.

The advice from the report was as follows:

Teachers, both male and female, in the most successful schools made more sparing use of technical language, used terminology in context and avoided algebraic shorthand. They used everyday language wherever possible and, where terminology was needed, it was carefully defined and pupils’ understanding was checked…

 

…The guiding principle was to establish ideas and concepts before the use of terminology or equations.

Once understanding is established the teachers introduced the terminology and rigorously policed its correct use. No sloppy reference to “electricity” when “current” is the word required.

It can’t be overstated how much the use of language effects students studying science. Too much technical jargon and it feels more like a foreign language lesson than something relevant to real life. As one girl in the report says:

“If physics is relevant then we ought to be able to talk about it using normal language. I used not to ask questions because I didn’t know how to put them – I didn’t have the right words. [Teacher X] doesn’t mind this and encourages us to have a go. If we use the wrong words [Teacher X] doesn’t correct us or make us feel embarrassed.”

We need to make our lessons as inclusive and easy to comprehend as possible. That doesn’t mean leaving out technical scientific terms. It does mean developing the understanding first through direct experience of the phenomena and its applications then slowly building in the correct language and algebraic shorthand once this is established.

 

The Importance of Discussion, Analogy and Relevance

Before students can develop a facility with technical language they need to have a handle on the topic. This means discussions about the uses and phenomena associated with the topic. How discussion is done in a classroom can vary. Little or no discussion takes place in rote lessons. The teacher asking a closed question “what is ….” and getting a terse response is not discussion.

To aid context and understanding students need time to explore what they know about a topic amongst themselves. Small group discussions work well when combined with the requirement to produce a group response or an answer on a small white board. Questions like “What is it about electricity that makes it so useful to us?”; “What happens when we turn a light switch off?”; “Why do we have to have a system of pylons and cables around the country?”; and “Why can’t we store electricity?” are so much more useful than “what is the definition of current?” [3].

This discussions and group responses can all occur using ordinary language. Then the teacher can lead the whole group in the development of these ideas. “Why can’t we store electricity?” is bound to lead to a discussion of the role of a battery in a circuit. From this charge separation, electric fields and the transfer of energy through the movement of charges in a wire can all be demonstrated and explained.

Mental images of what is going on are very useful, particularly in some topics. Electricity is notoriously lacking in direct visual input, and so requires a suitable analogy. All students benefit from this but teachers need to be careful they don’t use out of date or again biased examples. As one female student says “I’m not interested in how Beckham bends a ball or what the acceleration of a Ferrari is – why should I be?”. An even better approach is to see if students can devise their own analogies. All of this aids understanding and model building before any equation needs to be introduced.

I would leave equations until after the students have done an experiment or seen a demonstration where the relationship of interest is clearly shown. It is so much easier to infer and remember a result from data you have collected yourself. Set up a simple circuit with a resistor. Take some readings, plot a graph, draw a gradient. Then introduce Ohm’s Law.

Lastly, understanding is aided when physics is contextualised. It is a mistake to assume all students want modern, real world examples when asking for relevance. What is relevant can vary from person to person. It is enough to say that a topic is relevant because it helps explain X, Y or Z. Or maybe it connects with some wider moral or philosophical issues (origin of the Universe), some ethical argument (use of nuclear power), even a conspiracy theorist’s misunderstandings (climate change). They may well want to hear about applications of this topic in their daily lives but they also like to know about applications beyond their limited experiences. Sometimes it is relevant because it is the pathway to a desired career goal, relevant in a pragmatic way. If you wish to study architecture, physics can be relevant even if not everything is about the construction of buildings.

 

The Death of Definitions

I started out by saying teaching from definitions is a method used by rushed teachers, those reliant on the specification and those who don’t understand how best to teach.

What if you are rushed for time? The curriculum demands increase year on year and sometimes cramming triple science GCSE into a double science timetable requires corners to be cut. So cut the definitions. Teach circuits with circuits even if you have to demonstrate rather than do a class practical. Get students to take the readings with you, volunteers can write the data up on the class board. They can still work out the relationships you need individually and they will learn as they do.

People are often told “don’t teach to the specification” I think this doesn’t go far enough. Some people actually teach the specification. There is nothing wrong with using this document to guide your lessons but you don’t get students to work through 3-4 points from the spec each lesson. It is a check list to ensure you cover each point, not an instruction manual. Teaching from specification or textbooks indicates lack of confidence.

The best remedy to lack of confidence in physics teaching is to find out how to teach the subject from an expert. Buy a good book, enrole on a CPD course or get support from physics specialists in your school or online, for example TalkPhysics.

Or you could keep reading the articles on here, The Physics Teacher.

 

References

[1] Main, P. C. and Tracy, C. M. (2013) “Defining physics.” Physics World, 26(4), 17–18

[2] Main, P.C. “Thinking Like a Physicist: Design Criteria for a Physics Curriculum”  Schools Science Review March 2014, 95(352)

[3] “Girls in the Physics Classroom” 2006,

[4] https://www.gov.uk/government/statistics/revised-gcse-and-equivalent-results-in-england-2016-to-2017 viewed 14/7/2018

Teaching Radioactivity – A simple demonstration of alpha, beta and gamma

This is one of my all time favourite fun classroom activities. You would not normally equate teaching radioactivity to a roomful of bemused Year 10 students as fun but prepare to be amazed by this simple way to demonstrate the sizes, penetrating power and ionising properties of alpha, beta and gamma radiation.

 

Equipment Needed

One large exercise ball, 50-70cm in diameter pre-inflated

A pea shooter with peas/pellets or a potato gun with potato

A low power laser pointer, the sort used for presentations

This is best done in a large area like a sports hall or even outside weather permitting.

toy pea shooter with pellets

Safety Considerations

You may wish to give out goggles to protect eyes from the pea shooter.

The laser pointer/light beam should be directed towards peoples bodies about waist-chest high and not at faces. It would take 10 whole seconds of unblinking gaze at a typical classroom laser to damage your eyesight. There is a lot of hysteria around the use of low power laser pointers designed for presentations which is entirely unwarranted. The greatest risk of eye damage comes from the pea shooter.

 

How to do it

Choose, and I do mean choose as without fail the most disruptive student in the class will volunteer for this, three students to be the radiation.

The other students line up in 2-3 rows. If you have a class of 30 that would be 3 rows of 9 with the 3 students being radiation stood separately. To be really fancy you could even stagger the rows so students in the row behind are in the gaps of the row in front.

Now each radiation is going to irradiate this block of students who are modelling a material, e.g human skin.

The alpha (exercise ball) student should roll their particle towards the “material” and it will move fairly slowly and bounce off of the top layer of students. Let the alpha radiation have a few attempts to “ionise” the material. When “ionised” the student in the material should raise their hand. This allows everyone to see where the radiation is affecting the material.

Next the pea shooting/potato gun beta student irradiates the rows with their beta particles which are much smaller and faster, and can penetrate a bit further. Again students should raise their hand if hit by the peas and ionised. Let the student try 3-4 times to hit someone.

Finally the laser pointer student can shine their gamma rays through the material and onto the rear wall, penetrating a long way but ionising no where near as much. A straight beam from a laser pointer will skim one student at most.

It is important that the radiation is randomly directed and not aimed at the rows of students as real radiation doesn’t have a conscious intent to interact with matter. This is a limitation to the model which can be discussed at the end. I considered blindfolding the radiation students to increase the random nature of their interaction with the matter students but few teenagers are comfortable being blindfolded in front of the rest of their classmates and generally become too self conscious.

Learning Points

Alpha radiation = exercise ball – large, slow, very ionising, not penetrating

Beta radiation = peas from shooter – smaller, faster and moderately ionising and penetrating

Gamma radiation = laser beam – very fast (speed of light), very penetrating, not very ionising

The sizes and speeds of alpha, beta and gamma radiation are readily apparent from this demonstration. Alpha particles are around 8000 times heavier than an electron and consist of two protons and two neutrons bound by nuclear forces. Gamma is part of the electromagnetic spectrum and is represented as a light beam to show this.

The penetration of the radiation is modelled by the number of layers of students that can be touched by the radiation. The large exercise ball as an alpha particle will bounce around the front row but no deeper. The peas can shoot in further but only go a certain distance as they have a limited speed as a projectile. The laser/light beam will reach the opposite wall.

Ionising power is represented by the number of students being touched by each radiation hit. The slower larger exercise ball will hit at least 2 students each roll. Each hit can be seen as knocking out an electron and ionising the atom. The pea shooter will hit maybe one student each time. The laser pointer randomly aimed may hit one or two people in total.

At the end of the demonstration activity each student should complete a chart summarising the relative mass, speeds, penetrating and ionising effect of the three types of radiation. It helps to summarise the properties of each type as you go along. This can be done socratically by prompting the students with questions – how far did this “radiation” penetrate? How many atoms could it ionise? Why do you think that was? etc.

Limitations to the Model

As with all classroom models this demonstration has various limitations and it is instructive for the students to consider how this model isn’t like real atoms interacting with radiation.

The main points are that real atoms have much more empty space in them and many more electrons.

The alpha particle is deflected by repulsion of like charges not by physically hitting a large, solid atom as this model suggests.

The shell model of electrons taught to 14-16 year olds isn’t well modelled by this demonstration as we have nothing to represent the orbiting electrons. No indication is made as to the nature of the bonding between the atoms in this “material” either.

Conclusion

Students have always responded very well to this activity. It works well for less able students who find book-learning challenging as they vividly remember what happens in the demonstration and you can refer back to how “Jo was hit with the exercise ball, do you remember?” and they always do.

More able students enjoy getting out of the classroom and doing something a bit silly and are able to find the flaws in the model and extrapolate the scenario more easily than less able students who may need to be led to the learning outcomes in smaller more structured steps.

Try it out and let me know what you think.

Hubble’s Law – Using Historical Data 1

When teaching physics I think there is a lot of reliance upon writing down a law, Hubble’s Law for example, on the blackboard at the start of a lesson. Then without much or indeed any explanation as to how this result came about, students are left to to work out some example problems or do a couple of experiments using this result.  They are expected to accept without question the “Law of Physics” we have given them. This doesn’t encourage critical thinking and this approach is one of the reasons so many students are turned off physics as a subject.

Chalk and talk teaching is unhelpful and frankly boring. A better way to teach is to supply information and allow the students to discover the results for themselves. Not only is this more interesting, but by doing the work themselves the students learn more effectively and this method mimics the actual scientific process of discovery and deduction. Now I appreciate we don’t have access to large telescopes and apparatus, I’m not suggesting we reproduce the entire experiment! We can make use of historical data to enable students to reproduce important results for themselves. I’m going to write a few posts which show how the data from various famous experiments can be used when teaching physics.

Teaching Hubble’s Law

 

Hubble’s Law describes the expansion of spacetime

Hubble’s Law is an example of a topic which can be taught this way. Usually it is taught by stating the relationship between distance and recessional velocity (Hubble’s Law V=Hr) and this equation is used to deduce the age of the universe etc. Some discussion is made of the interpretation of the recessional velocity – students are expected to understand that spacetime itself is expanding between the observer on Earth and the distant galaxy not that all galaxies are flying away from us.

So turn the lesson around and start with the data. Hubble’s original research paper is short and the data produces a nice line graph. Students can be given the data and be tasked with reproducing his graph of results. They can then construct their own interpretation of what the linear relationship implies. It is good practice to get students to label their graphs with a sentence or two describing the data for example: “a graph to show the relationship between recessional velocity of galaxies and the distance to those galaxies”. Teasing out precisely what relationship; linear, inversely proportional or whatever, can follow.  Students can find a value for the Hubble constant from the gradient of their line of best fit. Comparing this to present day values shows the considerable advances in our measurements of redshifts and distances.

A little bit of algebraic manipulation draws out the units for the Hubble constant as being per unit of time. Time from what? is the key question to ask. What is the start time and what is the end time to find the difference in times that go with the difference in distance to give us a velocity? Change in distance/change in time = velocity. Every time I have taught this one student at least realises that 1/Ho is the time since the galaxies started to move apart and is therefor an estimate for the age of the Universe. You don’t have to tell them, they can work it out! This starts all sorts of discussion about how appropriate this estimate of the age of the Universe is. It is a great way to introduce the earlier, hotter, radiation dominated phase of the Universe where the rate of expansion was slightly different and then further back to Inflation and the Hot Big Bang Theory.

Active learning, the idea that students are working out the relationships not being passive recipients of them as Laws of Physics, has been shown time and time again to produce better learning outcomes. Students understand the topics better and recall more of the information correctly when assessed.

Here is a worksheet which allows more able GCSE 14-16 year olds or AS/A2 16-18 year olds to plot Hubble’s data. A scientific calculator is required and this activity wouldn’t be suitable for students who struggle with large numbers or data processing.

I have also attached Hubble’s paper “A Relation Between Distance and Radial Velocity Among Extra Galactic Nebulae” from 1929.

Equipment needed: graph paper, rulers, pencils and scientific calculators or log tables.

A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY AMONG EXTRA-GALACTIC NEBULAE by Edwin Hubble

Hubble’s Law worksheet

Phases of the Moon for Young Children

Recently I went in to my daughter’s primary school and spent the afternoon running an activity for the 60 children aged 6-7 in her year group. They had been studying the Solar System and I’m happy to offer my services as an expert of all things astrophysics. I ended up delivering a lesson which introduced the key science skills of observation, spotting patterns and making a prediction as part of the topic of the phases of the moon.

Misconceptions and Remedies

There are many common misconceptions regarding the Moon which children arrive with at secondary school. It never ceases to surprise me how many 11 year olds don’t think the Moon is ever visible by day, despite the fact that they have all seen it! This is easily fixed with a few reminders of times they have seen the Moon outside, often it is actually in the sky during the lesson, or photos can be shown with the moon in daylight.

They have no grasp of the relative sizes, distances or position of the Moon with respect to the Earth. I have often spent a lesson with tennis balls and plasticine blobs getting the students to make scale models with the Moon 30 times the Earth’s diameter away. I always discuss how the photos we commonly see of the Earth-Moon as a pair are doctored to bring the Moon much closer – this really does need explaining to students.

Typical Earth-Moon image:

Actual Earth Moon separation:

Students without fail believe the Moon orbits the Earth’s equator. In fact the Earth is tilted by 23 degrees to the ecliptic and the Moon is a further 5 degrees above that. Reminding students of the Earth’s own tilt is often enough to get them to realise the Moon must alternate its position above and below the equator. They also benefit from discussion about the locations where solar eclipses occur to further realise the Moon can’t stay over the midline of the Earth. This nicely introduces the idea of the ecliptic plane of the Solar System and the various orbital tilts that planets have. The idea of planetary alignment and paranormal events is quite common in science fiction and fantasy shows on TV, conjunctions are never perfectly aligned however and you can explain why.

So there are some significant gaps in the children’s understanding of our Earthly relationship to our nearest neighbour in space. In an attempt to get the children thinking about what they could see of our Moon with their own eyes, I planned a Phases of the Moon lesson.

Lesson Plan – Outline

AIM: to introduce the names for the phases of the Moon and to recognise the shapes associated with the names. To observe the shape of Moon over the course of a week and predict what it would look like the following week. More able students will be able to offer an explanation in terms of the shadow face/illuminated face of the moon and our position with respect to those two hemispheres.

TIMING: 45 minutes

5 minutes: Elicitation and questions

20 minutes: Copy and name the moon phases, practise naming the phases

10 minutes: Observe the “moon” in pairs

10 minutes: Discuss conclusions and explain observation task

LOCATION: A room large enough for 30 children to sit and with space to walk around the illuminated ball (see below). Curtains or blinds will be needed to darken the room.

APPARATUS: One large inflatable gym ball, roughly 60cm in diameter, with a stool to sit it on; a bright torch positioned to shine straight onto the ball from the side; some A4 pictures of the Moon printed from NASA’s website and therefor publicly useable (all NASA pictures are usable for educational purposes). A worksheet and pencil each.

ORGANISATION/BEHAVIOUR MANAGEMENT: The children need to sit and write on their sheets for part of the lesson. They sat on the floor or a bench in 3 rows. Ideally I would give them clip boards to use next time. When pairs of children are observing the ball the remainder of the class needs to be kept busy. During this time one teacher practised the shapes and names with them again which worked well.

Lesson Plan – Activity Details

ACTIVITIES:

  1. Elicitation and questions: Firstly students are seated facing the front and asked what they know about the Moon. Do they know what it is made from? How can we see it? Does it always look the same? Why do you think that? How do people on Earth find out about the Moon?
  2. Introduce vocabulary: Following this the students are given a pencil and worksheet, the teacher holds up a picture of the Moon and asks for the name for its shape (full moon, gibbous moon, half moon, crescent moon, new moon). Some students will know some of the names. They copy the word down and sketch a picture of the moon in that phase. Repeat until all 5 are done.
  3. Memorise shapes: The students put down their pencils and worksheets and try to make the moon phase shapes with their arms or bodies (depending on how much space you have). The teacher leads by saying a phase and the children have to find a way to make themselves resemble the shape.
  4. Observe the shadow face/illuminated face: in pairs, the students come and look for the dividing line between the bright face and the shadow face of the gym ball “moon”. They look from the front, side and behind and link the shape of the bright surface that they can see to the shape of the Moon at different times of the month.
  5. Observation experiment: The rear side of the worksheet has a chart where the children can write the day or the week, whether they could see the moon (due to cloud cover), was it visible at day or night and what shape it had. They go away and complete this during the week – realistically in children aged 6-7 most will do 3 or 4 observations out of a possible 7.
  6. Make a prediction: The final task on the worksheet is to make a prediction about what shape the Moon will have in a few days time. The students are using the pattern they have seen in their observations and linking it to the order of the phases introduced in the class activity.

 

FOLLOW UP: It was left to the class teacher to follow up this activity throughout the week with reminders and a discussion on their results the following week. The vocabulary of the phases of the moon can be easily incorporated into their continued work on the Solar System topic; in written work describing a trip to the moon, in art work, as part of maths learning about shape (sphere, hemisphere, crescent etc) and fractions (whole, half, quarter).

Evaluation

So how do I think it went? I have never taught science to such a young group of children before and on the whole they were interested and well behaved.

The worksheet seems to be pitched at the right level, most students could read it and understood what to do however some students needed to be shown where to draw the picture and where to write the word. Some students took a little longer to write than others and there was discussion about how best to show shadow and a New Moon which was interesting, eventually they solved these issues for themselves.

The A4 pictures of the moon phases were large enough to be seen be everyone as I sat in front of the group.

They enjoyed standing up and making moon shapes with their arms over their heads, a big circle for a full moon, D shape for half moon, banana shape for a crescent and so on. If I had thought this through a bit more I could have taken them to the centre of the hall (we were in the main school hall) and made a bit more of this.

Some children really wanted to touch the ball and trace the line between the shadow and bright side, so if I repeated the lesson I would take some plasticine or a coil of rope for the ball to sit in so it didn’t wobble around so much on the stool.

The one thing I felt needed improving was the time when I showed the illuminated big ball to the pairs of students. Those waiting in their seats were not occupied enough. Partly this was due to were I had had to position the ball, the sun was very bright through the windows that afternoon and the corner of the hall was the only suitable dark enough spot even with the curtains pulled. That meant far fewer students than I had anticipated could walk around the ball at a time, I had planned for 8-10 students to walk and view both sides, front and back at the same time. One class teacher stepped in and led the group in practicing the shapes and tested them on the words while their classmates took turns to look at the ball. The other teacher didn’t and the students eventually became restless.

I would prepare a word search or pairing/matching game for this period of the lesson if I did it again to reinforce the vocabulary while they waited.

With one group we had a good discussion about how scientists find things out which led nicely onto the homework observation task. We ran out of time with the other group which meant the task was explained with less context. This bothered me but the students didn’t seem to mind. The students very much enjoyed asking questions about how scientists work, one asked me if scientists have rows with each other about who is right, which of course they do very politely via academic publications.

Additional Resources

moonphasepictures – Word document of A4 lack and white Moon phase photos

Phases of the Moon – students’ worksheet

Teaching Ideas for Sound and Waves

Here is a selection of ideas for teaching a sound waves topic to KS3 or the equivalent of 11-14 year olds. Sound and waves in general is a topic with great experimental potential. Simple activities can be used as starters to begin lessons and elicit students knowledge or as ways to demonstrate ideas. General trends such as rising pitch or volume can be shown easily. A microphone, oscilloscope or simple sound analysing software can be used to collect numerical data if needed.

The key ideas to demonstrate and emphasise are that sound is a vibration and that these vibrations need a medium to move through.

Simple Demonstrations and Activities

To show how sound travels differently through solids, liquids and gases – ask the students to work in pairs, one is to bang on the table top with their knuckles and the other to listen to the volume of the sound. The repeat with the second student listening with their ear firmly on the desk. Discuss their observations of the difference in volume. Discuss hearing sounds underwater in a pool or bath tub.

Tuning forks to demonstrate vibration – bang a tuning fork on a rubber bung and hold to the ear (to hear the sound) and then to your lip (to feel the vibration)

Large speaker connected to signal generator to show vibration – turn the speaker so the cone faces upwards, place small bits or paper or tiny polystyrene balls on top, play a note through the speaker and observe the vibrations. Ask students to predict what a higher or lower pitched note will do to the paper pieces. You can ask them to sketch what sound waves they think would represent each pitch and volume. This is a nice way of introducing amplitude and frequency as displayed in graphs.

Reeds out of plastic straws – follow the instructions here make and play reed instrument to produce a simple plastic straw reed. Need straws and scissors. Can shorten the straw by cutting pieces off to make a higher pitched note.

Rulers and change in pitch – twanging a ruler on the edge of a desk and quickly shortening the length hanging over the edge by pulling it in demonstrates nicely how more rapid vibrations produce a higher pitch.

Ripple tanks – all sorts of things can be shown with a ripple tank but at this level the demonstrations should reinforce the main topic, show how a more rapidly rotating motor on the dipper produces shorter, more tightly packed waves. Relate time and frequency, wavelength and distance to show wave velocity = distance/time = wavelength/time = wavelength x frequency. Students can measure the wavelength if a spotlight is shone down into of the tank and paper placed underneath. They can count the number of waves hitting the side in 30 seconds and find an approximate frequency.

The medium which is vibrating doesn’t move – ripple tanks can demonstrate this as the waves don’t push all the water out of the tank. It is important to compare and contrast the physical mechanism of tides and waves at sea as students are familiar with the tides bring water higher up the shore. This is of course due to an external force of gravity from the Moon and not a result of wave motion. This is a common source of misunderstanding in waves topics. Bobbing a cork up and down in the ripple tank shows this as the cork doesn’t move to the side. This principle can then be generalised to all waves including sound waves.

Standing waves in a tube – if you are feeling adventurous you can connect a clear, plastic tube (length >1m) to a microphone and cover the other end with plastic. Sprinkle some light particles (polystyrene balls, oatmeal, tissue paper etc) inside the tube and use a signal generator to produce a sound wave. Altering the frequency will cause the material inside to shift along to the nodes of the vibrations in the tube giving a rough measure of the wavelength.

Interpreting waveforms – supply students with a printout or display on the board various sound wave patterns and ask them if they can predict what sort of sounds they represent. Here is an example of the kinds of waveforms that can be used;

Examples of waveforms – what sounds would they produce?

Thought Experiments

Why do double glazed windows deaden noise? You may have to explain how they are constructed (two panes with a vacuum between).

Why can no one hear you scream in space?

What will limit how high a note a human can sing? Why do women sing higher then men?

Why did people used to listen with their ear on railway tracks?

Is it hard to breathe near a loud speaker at a concert? Does thunder produce strong winds? What does this say about the motion of air as sound travels through it?