Preparing for the
Evolution workshop1. Assign the children to 8 mixed ability groups. There is a form below if you want to use it. The children will work in these groups on various activities during the day, and there will be fossil prizes for some of these activities. One child in each group should be nominated as the data recorder and writer – they will write down what the children find in their various activities and experiments. This should be the most able child, in terms of maths, science and writing. 2. Arrange the tables in 8 blocks of equal size, then put two of these together to make a long table (for the tree of life activity). 3. The tables should be cleared completely before I arrive, as I will need to set out some materials for the morning activities before we start. Also please clear a large space on the side of the classroom for the models we will use. 4. I will need your interactive whiteboard for my photos and films so please have it up and running. It is important that we can see films and photos clearly, so please ensure everything is working, and have blinds closed if necessary. If your projector does not give a clear image we may need to use another classroom if that is possible. I will also need to use your computer to show the photos and films. Please let me know if there are any technical problems. 5. Please provide the following materials: 8 pencils; lots of thick coloured markers/felt tips; 8 calculators 6. We will need to have a 15-minute break at 10.30. After break we will do the adaptation activities, when children in their 8 groups do 5 activities in rotation. Some of these are complicated; of course I will explain them and there will be instructions, but it would be extremely helpful to have extra adults to assist. Ideally we would have 1 adult per activity, i.e. 5, not including myself as I will need to monitor all the activities. If you are short of staff you might ask parents to come in – I am sure they will find it interesting! 7. In the afternoon we will carry out some inheritance and natural selection games, using 10-sided dice (to simulate the effects of chance in the survival of an animal). To help prepare children for this it might be helpful to do a lesson on probability, covering some basic concepts and perhaps using coins or dice. On the last few pages there is an extensive list of topics you might cover, and some suggested activities. 8. If you feel your children may have difficulty with probability, and with complex simulations using dice and cards, you can choose easier options for the afternoon. In the inheritance session we can look at twins, with a photo game, instead of looking at the inheritance of genes for red hair. In the natural selection session, we can look at the evolution of bacterial resistance to antibiotics, which involves no dice rolling. The ‘medium’ option is looking at the evolution of the peppered moth, with a simple roll of 10-sided dice to see how many moths survive. The ‘advanced’ option uses gene cards with two alleles for colour vision in monkeys. Children roll to see what genes each baby monkey gets from its parents, then they roll to see how many babies of each genotype survive. Roles in the groups are divided to make this easier. Details and photos on the website may help you choose your options (you can tell me your choice on the day). 9. If you like, you could also prepare the children for some of the concepts we will cover: classification of animals into vertebrates and invertebrates; classification of vertebrates into mammals, birds, reptiles, fish and amphibians; family trees – children could research and construct their own; family resemblances – children could bring in family photos to show resemblances; how do we take after our parents? Looks but also other traits such as personality, skills, tastes, or even weaknesses such as allergies and poor eyesight. Do we inherit all traits equally from each parent? Some children may look more like one parent, while having the personality/skills of the other. You could get children to research all this and we can discuss it in the workshop. 10. During lunch (or after school if you prefer) I will have fossils for sale, at low prices – 10, 20 or 50p, plus a few higher quality fossils for £1 or £2.
Probability is an important force in life so it is well worth spending
time reinforcing this concept with children. In the evolution lesson we use 10-sided dice so we can roll percentages. If you don’t have 10-sided dice ordinary 6-sided dice are fine.
1. How many outcomes are possible with a coin or die? – children count
the number of faces
2. What chance is there of each outcome? – discuss, and test by doing
lots of coin tosses/dice rolls, and adding them up for the whole class.
For say 50 tosses of a coin, each child is unlikely to get 25 heads and
25 tails, but the more they do, the closer the proportions reach ½. So
the children should be able to see that each outcome has the same
probability. Unless you have a bad coin/die, each outcome is equally
likely.
3. Following from 2, because each outcome is equally likely, does that
mean that you always get ½ as many heads and ½ as many tails? Or if you
roll a die 36 times will you get 6 of each number? – children can roll a
die 36 times (they can roll several dice at a time to save time)
and see for themselves that very
rarely will you get 6 of each number. Discuss why this is. A die roll is
random – so any combination is possible. And each roll is independent –
unaffected by what came before (because there is no such thing as
magic). By collating large numbers of rolls (add up how many of each number is rolled by the whole class) you can see how the more rolls you do, the closer you get to these ‘ideal’ proportions.
You can do the same for gender – how many boys and girls are there in
the class? It will probably not be ½ and ½. Work out the percentages.
Then look at the school as a whole – it will probably be closer to ½.
Now compare this to the population of the UK. For under 65s, the
fraction of females is 49.9%. We will look at this further in the
lesson. (In over 65s the ratio is not equal as women live longer than
men)
To test this understanding, ask children:
a. can you predict what I will roll on this die? (no)
b. If I have rolled the die 30 times and not rolled a 6, what is the
chance now of rolling a 6? (the same, 1/6).
The idea that outcomes of rolls, coin tosses, or other random number
generators like the lottery, are random and independent is very
important, yet one that many people struggle with. For example:
c. In the National Lottery, which has the best chance of winning – 1, 2,
3, 4, 5, 6, or 11, 13, 34, 36, 44, 47?
We intuitively feel that the sequence 1, 2, 3, 4, 5, 6 is less likely
because it seems less random. But each sequence has exactly the same
chance of winning as any other – about 1 in 14 million.
So, given that the numbers on a die roll are random, and independent
(any roll is not affected by any other), there is no way to predict any
roll, and there is no such thing as a ‘lucky number’. Unless you have a
time machine!
But what we can predict is how the numbers will tend to fall out when
you do a lot of rolls/coin tosses. So we can predict that the proportion
of numbers when you do hundreds of dice rolls will be close to 1/6 for
each number, just as the sex ratio in world population is very close to
½. Of course other factors can influence probabilities, such as women’s
longer life expectancy, or loaded dice, or how careful you are when
crossing the road.
4. How can we represent probabilities as numbers? The chance of rolling
a 6 on a 6-sided die can be written as:
1 in 6
a fraction, 1/6
a decimal, 0.166…
a percentage, 16.6%
When using 10-sided dice, the numbers can easily be converted to
percentages (which is why we will use them).
For example, the chance of rolling a 10 is 1/10 = 10%.
5. Dice can be used for more complex probabilities. For example, instead
of tossing a coin you can roll a 6-sided die to get two outcomes of ½
chance each.
Ask children how you could do this. A roll of 1, 2, or 3 might be one
outcome (like heads), and a 4, 5, or 6 are another (tails). So to work
out which team kicks off in a football game, instead of tossing a coin
you could roll a die – a roll of 1-3 means one team wins, 4-6 means the
other team wins.
Get children to say what the probability is of rolling a 1 or 2 (2 in 6,
i.e. 1/3), or a 1, 2, 3 or 4 (4 in 6, i.e. 2/3).
If 3 children each wanted a sweet, how would you roll a die to decide
who gets it?
Child A wins on a roll of 1 or 2, B on a roll of 3 or 4, C on a roll of
5 or 6. Each then has an equal chance – 1/3.
Are there any other ways of determining this? Yes - child A could be 1
and 3, B could be 2 and 4, C could be 3 and 6. But this is harder to
remember!
In the evolution lesson we use 10-sided dice to see if an animal
survives. For example, a moth has a 40% chance of being eaten by a bird
– how would you roll to decide this? (1, 2, 3 or 4 means it is eaten).
7. Compound probabilities are also very important and interesting. The
chance of predicting a roll on a die is 1/6. But what is the chance of
predicting two rolls in a row? Say we do two rolls and they are a 3
followed by a 5. What is the chance of predicting this?
All we do is multiply the number of outcomes each time – i.e. 6X6 = 36.
So there is a 1 in 36 chance. This is true for all 36 combinations of
numbers. Again you could do a lottery with children guessing the two
numbers. There a good chance one or more children will predict both
numbers. But when you do more rolls, the chance is very small. For 4
rolls the chance of guessing the sequence is 1 in 6X6X6X6 = 1 in 1296 or
0.07%.
This is how gambling works of course. A fruit machine will give you a
very small chance of winning a lot of money, but it may be difficult to
understand this – and so some people will lose a lot of money.
An interesting example is the National Lottery. The chance of predicting
the 6 numbers in the jackpot is about 1 in 14 million. Ask children what
their chance would be if they made 2
different guesses.
The chance is doubled, to 1 in 7 million. What if you made 100 guesses?
The chance is 100 times greater – i.e. 1 in 14 million/100 = 1 in
140,000. To have a 1 in 10 chance of winning, you would have to buy 1.4
million tickets.
You could test this with another lottery to predict 2 dice rolls – but
each child now gets 2 guesses, or 3, and so on. There should be more
winners.
8. You could look at how probability comes into real life. Children
could have a homework project, perhaps reading newspapers or just
keeping their eyes open. As well as games and gambling, there are
countless ways probability is part of life – as we saw with the ratio of
males to females. For example:
Weather: the Met Office gives
forecasts in probabilities (e.g. 30% chance of rain)
Health: your chance of lung cancer depends on gender (1 in 14 males, 1
in 18 females) and whether or not you smoke (one study showed that for
men, 0.2% of those who never smoked got lung cancer, while 24% of
smokers did). A lot of probability in life is unfortunately about
illness/accidents!
Observing nature: each day children could look in their gardens before
school to see birds. If they keep a record and you add up all the data,
you might get a probability that on any one day they will see a magpie,
or a pigeon, or whatever is appropriate. Or perhaps a cat or a dog on
the way to school.
Of course probability is an important factor in many games – children
could work out the chance of picking out a certain card from a shuffled
pack (1/52), or a suit (1/4), or a face card (4X4/52 = 16/52 = 31%).
You can therefore work out the chance of certain hands in a game like
Blackjack (21). What is the chance of getting 21? (This is complicated
so for more able children – they need to count all possible combinations
of 2 cards which make 21, and divide by the number of all possible
combinations of 2 cards.)
1. You have a bag with 50 white and 50 black marbles in.
What is the chance you will pick out a matching pair? – let’s say you
pick out a white – there are now 49 whites and 50 blacks left in the
bag. So your chance of picking another white is 49/99 = 49.5%, i.e just
under ½. This is of course the same if you pick out a black too, so
either way it’s 49.5%.
What is the chance you will pick out a non-matching pair? Then it will
be 50/99 = 50.5%.
This is like the sock drawer problem. To help learning, you could get
the children to transfer this understanding to a related problem. There
are 20 black and 20 white socks in a drawer. It’s dark (power cut?) so
you pull out 2 socks at random and put them on. What is the chance they
match? The answer is 9/19.
Or, how many do you need to take out to make sure you have a matching
pair? If you take out 3 then there have to be two matching (more a logic
problem than probability).
2. On 2 coin tosses, what is the chance you will get a head at some
point (on either toss)?
- this is an important question, because often we want a certain
outcome, and want to know how many times we need to repeat the roll/coin
toss/etc. to have a good chance of getting what we want.
To answer this, get children to work out all possible combinations of
outcomes: (H = head, T = tail)
H, H
H, T
T, H
T, T
So there are 4 combinations.
Now add up all those which include a head: we can see a head in the
first 3 above.
So the chance of getting a head in 2 coin tosses is 3/4 = 75%.
What about 3 coin tosses?
3. You can apply this to dice too. The chance of getting a 6 on either
of two rolls is worked out like this:
Chance of a 6 then a 6: (1 in 6) X (1 in 6) = 1 in 36
Chance of a 6 then 1-5: (1 in 6) X (5 in 6) = 5 in 36
Chance of a 1-5 then 6: (5 in 6) X (1 in 6) = 5 in 36
The total is 1 + 5 + 5 = 11 in 36, or 30.6%.
4. To apply this to real life, imagine the forecast for the weekend is
10% chance of rain on Saturday and 10% on Sunday. What is the chance it
will rain some time this weekend?
The chances are 1 in 10 for rain each day. You have to work out and add
up the combined chances of all possibilities.
Chance of rain on Sat
Chance of rain on Sat and
Chance of rain
Add these up: 1 + 9 + 9 = 19 in 100, i.e. 19%.
What if the chance were 30% on Saturday and 40% on Sunday? What is the
chance it will
Chance of rain on Sat
Chance of rain on Sat and
Chance of rain
Total = 12 +18 + 28 = 58%
So the chance of a completely fine weekend = 100-58 = 42% |