According to the Montessori plan, the fourth Great Lesson ought to be the Story of Writing, but I bought an abacus for my Great Lesson on Maths and abacuses are about to come up in our Penrose Maths Lessons so I decided to switch the Great Lessons around so that I could produce the abacus and have it available for the relevant Penrose lesson.
As we are moving further from the Montessori roots, perhaps it’s not surprising that I didn’t even notice until after giving this Great Lesson that I haven’t even read the Montessori version. This one is all me.
I took most of my inspiration from The What on Earth Wallbook of Science and Engineering and a great Maths History Timeline that I found through a home education Facebook page.
For what it’s worth, here’s my talk, we laid the Wallbook out to give the boys something to look at between demos:
About 3000BC, Babylonian mathematicians devised a counting system based on the number 60. This has had a lasting impact on mathematics. Can you think of any examples where 60 is an important number?
[Boys came up with degrees in a circle being six sixties and there being sixty seconds in a minute and sixty minutes in an hour.]
[I showed them how to use a protractor to measure some angles.]
Around 1000BC, merchants in China and the Middle East developed abacuses to speed up calculations. Some people still use them today. Being able to perform calculations quickly has driven technology and mathematics has inspired all sorts of experiments and discoveries.
Pythagoras was a Greek mathematician, he lived from 569 till 475BC (can you remember what BC stands for? Higher numbers are longer ago than lower numbers.) Pythagoras is probably most famous for discovering a rule about right-angled triangles. The square of the hypotenuse (that’s the side opposite the right-angle) is equal to the sum of the squares of the other two sides.
[I used an illustration in The Math Book to explain this idea to the boys, but you could easily draw your own picture. See below.]
You know about times tables. Some numbers are answers to lots of times tables and others aren’t answers to any times table sums.
[We have a wooden toy called a Times Table Abacus I used this to help the boys find which numbers came up a lot and which ones didn’t come up at all.]
Numbers that can’t be fairly shared into any number of groups are called Prime Numbers. A man called Eratosthenes (276-194BC) made something called a ‘sieve’ to find prime numbers.
The ‘sieve’ is a series of steps.
1) Let ‘p’ equal 2.
2) On your number chart [I used a 100 number square], cross off all the multiples of p.
3) Find the smallest uncrossed number that is bigger than p. This is a prime number.
4) Let this new prime number equal p.
5) Repeat steps 2-4 until you reach the end of your chart.
[We used these steps to find all the prime numbers under a hundred.]
Diophantas is often called the Father of Algebra – though, as with most big titles, some people demur. Algebra is, at it’s simplest, replacing numbers with letters. You’ve actually done algebra before.
[I used our whiteboard – as a side note, whiteboards are great and everyone should have one, all puzzles are more inviting when drawn on s whiteboard and it saves going through endless sheets of A3 paper – to write this puzzle:
2 + ? = 5
The boys solved this. Then I replaced the ? with x.
I drew a couple more very simple equations and asked the boys to solve them.]
Algebra can be used with more than one unknown and to solve very complex problems.
Around 200AD, Mayan people developed a number system with a symbol for zero. [I showed the boys a fun page about zero from Maths – a book you can count on]
As you know, the Romans used Roman Numerals, which don’t have a symbol for zero. Around 1203 a book by Fibonacci popularised Arabic Numerals in Europe. [I showed an illustration of various number systems from Train Your Brain to be a Maths Genius.]
Arabic Numerals are the ones that we use now.
In 1654, Pascal published a book about probability. This is all about predicting how likely it is that certain things will happen.
[I used the whiteboard to draw a probability tree for flipping a coin three times.]
In 1822, Charles Babbage and Ada Lovelace designed and built a mechanical computer. It was designed to help work out sums and they called it ‘The Difference Engine’.
In 1880, Greenwich Mean Time was established. Before this, different parts of England had their own timezones.
In the same year, John Venn developed Venn Diagrams. [We drew a simple Venn Diagram of our family together.]
Hewlett Packard made the first scientific calculator in 1972.
In 1975, Benoit Mandelbrot developed Fractal Geometry using (then very new) computers to generate self-replicating patterns. [I used another picture from The Math Book.]
Maths and technology have always gone together, our desire to improve one feeds the development of the other. Who knows where Maths will go next?
As we learn more about the world, we are able to answer questions that used to be unanswerable.
In 1995, Andrew Wiles was able to prove Fermat’s Last Theorem, which people had tried to do for more than three hundred years. Who knows what great discovery will be next?
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