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A day or not a day? The time it takes for the earth to revolve once on its axis. Which is 24 hours… What is a day?

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A day or not a day? Actually, it’s not.

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The earth moves round the sun… Everyone knows that! A day or not a day?

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…and when you face the sun, it’s daytime… …when you don’t, it’s dark! A day or not a day?

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Let’s assume you’re right, that it takes 24 hours for the Earth to make one full turn on its axis… A day or not a day?

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Now imagine yourself at midday, looking out at the sun…

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A day or not a day? One full turn later, it’s midday again. Where are you?

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A day or not a day? Still facing the sun…

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A day or not a day? Several full turn later, it’s midday again. Where are you?

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A day or not a day? Still facing the sun?

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A day or not a day? Five months and lots of full turns later, midday again… where are you?

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A day or not a day? Now we’re really in trouble! Facing away from the sun so definitely dark at midday.

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A day or not a day? A day is 24 hours, but that’s not how long it takes for the earth to revolve on its axis So what are you saying? A day isn’t 24 hours?

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A day or not a day? So how long does it take?

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A day or not a day? How would you work it out? What do you know?

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Stonehenge No-one actually knows for certain what Stonehenge – or other Henges - were built for, but they have properties which suggest that they had religious purposes – and some people still use them as places of worship. Many have special alignments with the sun on certain days of the year. At Stonehenge the sun aligns with the Heel stone on June 21 st – the Summer Solstice.

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Constructing a Henge Many Henges are not actually circular but seem to have 3 centres. Look at the shape of Avebury hengeAvebury henge One theory is that a single centre would mean that centre point would ‘have too much power’. …but unless someone is very, very old, they don’t really know for sure!

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Constructing a Henge How can we construct a shape which is ‘round’ but not circular and has 3 centres? Look at the diagram on the next slide. Can you work out which centres and lengths have been used to construct the shape?

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Constructing a Henge

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Firstly construct the Henge using the pencil and paper method. How does the shape change when you place the 3 centres differently? You might then try constructing it outside or by using Dynamic Geometry Software (DGS) Using DGS will enable you to more easily explore how the shape changes.

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Teacher notes: A day or not a day? In this activity students will use basic arithmetic, but with a complex problem. They will need to convert measures and work with time. It is suitable for all students who like a challenge! Show slides 1 to 15 Slide 16 How can we work out how long it takes the Earth to revolve once on its axis. Ask students to discuss this problem in pairs. They need to arrive at the following: –It takes 365 ¼ days for the Earth to orbit the sun –Every 24hours the Earth has to turn a little bit extra to remain facing the sun at midday. There are then 2 ways to calculate the time it takes for the Earth to turn once:

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Teacher notes: A day or not a day? 1.During the year, the Earth actually completes one extra turn. –Minutes in a year = 365.25 x 24 x 60 = 525 960 –Turns in a year = 366.25 –Minutes per turn = 525 960 ÷ 366.25 = 1436.068 = 23 hours 56 mins 4 seconds 2.Thinking about how far the earth has to turn in each 24 hours, it’s a full turn plus 1/365.25 of a turn which is 1.00274 turns. –Seconds in a day are: 24x 60 x 60 = 86400 –Second per turn are: 86400÷ 1.00274 = 86164 –This is 23 hours 56 minutes and 4 seconds Students might be able to work out what they need to do for the calculation, but may need support in carrying it out. Working with a partner will help. Ask students to feedback their solutions to the problem

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Teacher notes: Constructing a Henge This activity gives students the chance to experiment with geometry using pencil and paper methods. It is suitable for students of all abilities. It is also possible to create an outdoor version, which could be photographed from above. Students can then explore ‘roundness’ (see Monthly Maths April 2013) and check to see how round the shapes they’ve created are.Monthly Maths April 2013 Using Dynamic Geometry Software will make it easier it explore how the shape changes as the centres are moved.

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Teacher notes: Constructing a Henge Show the students slide 19 Show students the diagram on slide 21. Ask them to discuss in pairs how the coloured shape might have been constructed from points A, B, C and D. Copies of the slide could be printed out for students to explore and test out their ideas. If they have some ideas then let them use paper, pencil, compass and ruler to have a go at constructing one for themselves. If they are struggling to work out how it has been created then hand out the instruction sheets, allowing them to read and make sense of the instructions for themselves.

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